fraction assignment for class 7

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Unit 5: Fractions

Equivalent fractions.

• Visualizing equivalent fractions (Opens a modal)
• Equivalent fractions (Opens a modal)
• Equivalent fractions (fraction models) Get 3 of 4 questions to level up!
• Equivalent fractions Get 5 of 7 questions to level up!

Comparing fractions

• Ordering fractions (Opens a modal)
• Comparing improper fractions and mixed numbers (Opens a modal)
• Compare fractions on the number line Get 3 of 4 questions to level up!
• Compare fractions and mixed numbers Get 3 of 4 questions to level up!

Adding and subtracting

• Visually adding fractions: 5/6+1/4 (Opens a modal)
• Adding fractions word problem: paint (Opens a modal)
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Fractions Worksheets Grade 7

Fractions worksheets 7th grade can be used to give students a better understanding of how to solve questions involving fractions numbers. These grade 7 math worksheets incorporate problems based on the application of arithmetic operators on fractions, word problems, and other questions associated with the concept of fractions.

Benefits of 7th Grade Fractions Worksheets

Fractions can sometimes be a confusing topic for young minds. To ensure that students have crystal clear concepts, they can solve the problems available in the fractions worksheets 7th grade. The well-curated questions are organized in an increasing level of difficulty and give students the flexibility to work at their own pace.

Printable PDFs for Grade 7 Fractions Worksheets

The 7th grade fractions worksheets is interactive, easy to use, and has several visual simulations that help students in assimilating the topic in a more effective manner. This worksheet is also available in PDF format that is free to download

• Math 7th Grade Fractions Worksheet
• 7th Grade Fractions Math Worksheet
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• Grade 7 Math Fractions Worksheet

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Class vii math, class 7 fractions, introduction to fractions, types of fractions, decimal fraction, vulgar fraction, proper fraction, improper fraction, mixed fraction, like fraction, unlike fractions, equivalent fractions, irreducible fraction, comparison of more than two fractions, addition of like fractions, addition of unlike fractions, properties of fraction addition, subtraction of like fraction, subtraction of unlike fraction, multiplication of fraction, reciprocal of fraction, division of fractions.

Fractions Test

Fractions Worksheet

Answer Sheet

The numbers having a ⁄ b are known as fractions. Here 'a' is known as numerator and 'b' is known as denominator.

• Decimal fraction
• Vulgar fraction
• Proper fraction
• Improper fraction
• Mixed fraction
• Like fractions

Fraction whose denominator is either 10, 100, 1000, etc. ... are known as decimal fraction. Few decimal fractions are shown below. 7 ⁄ 10 , 9 ⁄ 100 , 11 ⁄ 100

A fraction whose denominator is a whole number other than 10, 100, 1000 etc. is known as vulgar fraction. 2 ⁄ 7 , 5 ⁄ 9 , 7 ⁄ 13 , 9 ⁄ 20 , etc... all are vulgar fractions.

Fraction whose numerator is less than the denominator is known as proper fraction. Few examples are given below. 2 ⁄ 5 , 3 ⁄ 4 , 5 ⁄ 9 , 9 ⁄ 17 , etc...

Fraction whose numerator is more than or equal to its denominator is known as improper fraction. Few examples are given below. 5 ⁄ 3 , 9 ⁄ 5 , 10 ⁄ 7 , 25 ⁄ 23 . Etc...

A number which can be expressed as the sum of a natural number and a proper fraction is known as a mixed fraction. Few examples are given below. 1 2 ⁄ 3 , 2 3 ⁄ 5 , 3 5 ⁄ 7 , etc...

Fraction having same denominator, but different numerators are known as like fractions. Let's see some example. 5 ⁄ 12 , 7 ⁄ 12 , 11 ⁄ 12 are like fractions.

Fractions having different denominators are known as unlike fractions. Let's see some example. 2 ⁄ 5 , 5 ⁄ 7 , 9 ⁄ 11 , etc...

If a given fraction's numerator and denominator is multiplied or divided by same nonzero number then the resultant fraction will be known as equivalent fraction. Let's see some examples. 2 ⁄ 3 , 4 ⁄ 6 , 8 ⁄ 12 , 16 ⁄ 24 , etc... are all equivalent fractions.

A fraction is said to be irreducible form, if HCF of it's numerator and denominator is 1. If HCF of numerator and denominator is other than 1 then the fraction is known as reducible.

Example 1. Convert 45 ⁄ 63 into irreducible form. Solution. First we must find the HCF of 45 and 63. HCF of 45 and 63 is 9. Let's divide the numerator and denominator by 9. 45 ⁄ 63 = (45÷9) ⁄ (63÷9) = 5 ⁄ 7 Hence, 45 ⁄ 63 irreducible form is 5 ⁄ 7 .

Step 1. Find the LCM of the denominators of the given fraction. Step 2. Convert all the given fractions into like fractions in such a way that all the fraction's denominator should be LCM. Step 3. Compare any two of these like fractions, one having larger numerator is larger among the two fractions.

Example 1. Arrange the below given fractions in ascending order. 7 ⁄ 10 , 13 ⁄ 15 , 3 ⁄ 5 Solution. The given fractions are 7 ⁄ 10 , 13 ⁄ 15 , 3 ⁄ 5 . LCM of 5, 10, and 15 = 60 Now, let us change each of the given fractions into an equivalent fraction having 60 as their denominator. 7 ⁄ 10 = (7x6) ⁄ (10x6) = 42 ⁄ 60 13 ⁄ 15 = (13x4) ⁄ (15x4) = 52 ⁄ 60 3 ⁄ 5 = (3x12) ⁄ (5x12) = 36 ⁄ 60 So, 36 ⁄ 60 42 ⁄ 60 52 ⁄ 60 Hence, the given fractions in ascending order are 3 ⁄ 5 , 7 ⁄ 10 , 13 ⁄ 15 .

For adding two like fractions, the numerators are added and the denominator remains the same. Let's see some examples.

Example 1. Add 2 ⁄ 7 and 3 ⁄ 7 . Solution. 2 ⁄ 7 + 3 ⁄ 7 = (2+3) ⁄ 7 = 5 ⁄ 7

Example 2. Add 4 ⁄ 15 and 7 ⁄ 15 . Solution. 4 ⁄ 15 + 7 ⁄ 15 = (4+7) ⁄ 15 = 11 ⁄ 15

For addition of two unlike fractions, first change them to like fractions and then add them as like fractions. Let's see some examples.

Example 1. Add 3 ⁄ 5 and 7 ⁄ 15 . Solution. 3 ⁄ 5 + 7 ⁄ 15 LCM of 5 and 15 is 15. Now, convert 3 ⁄ 5 and 7 ⁄ 15 into like fractions. 3 ⁄ 5 = (3x3) ⁄ (5x3) = 9 ⁄ 15 9 ⁄ 15 and 7 ⁄ 15 are like fractions. Now add 9 ⁄ 15 and 7 ⁄ 15 . 9 ⁄ 15 + 7 ⁄ 15 = (9+7) ⁄ 15 = 16 ⁄ 15

Commutative

Associative.

Subtraction of like fractions can be performed in a manner similar to that of addition. Let's see some example.

Example 1. Subtract 11 ⁄ 15 from 13 ⁄ 15 . Solution. 13 ⁄ 15 − 11 ⁄ 15 = (13−11) ⁄ 15 = 2 ⁄ 15

Example 2. Subtract 15 ⁄ 37 from 22 ⁄ 37 . Solution. 22 ⁄ 37 − 15 ⁄ 37 = (22−15) ⁄ 37 = 7 ⁄ 37

Subtraction of unlike fractions can be performed in a manner similar to that of subtraction. Let's see some example.

Example 1. Subtract 7 ⁄ 20 from 13 ⁄ 15 . Solution. 13 ⁄ 15 − 7 ⁄ 20 LCM of 15 and 20 = 60 Convert both the fraction to equivalent fraction having denominator 60. 13 ⁄ 15 = (13x4) ⁄ (15x4) = 52 ⁄ 60 7 ⁄ 20 = (7x3) ⁄ (20x3) = 21 ⁄ 60 Now, subtract both the equivalent fractions. 52 ⁄ 60 − 21 ⁄ 60 = (52−21) ⁄ 60 = 31 ⁄ 60

Example 2. What should be added to 12 2 ⁄ 3 to get 15 5 ⁄ 6 ? Solution. 15 5 ⁄ 6 − 12 2 ⁄ 3 = 95 ⁄ 6 − 38 ⁄ 3 LCM of 6 and 3 = 6 Now, convert 95 ⁄ 6 and 38 ⁄ 3 into equivalent fraction having denominator 6. 38 ⁄ 3 = (38x2) ⁄ (3x2) = 76 ⁄ 6 95 ⁄ 6 − 76 ⁄ 6 = (95−76) ⁄ 6 = 19 ⁄ 6

Product of two fractions is equal to product of their numerators and product of their denominators. Let's see some examples.

Example 1. Multiply 5 ⁄ 7 and 3 ⁄ 4 . Solution. 5 ⁄ 7 x 3 ⁄ 4 = (5x3) ⁄ (7x4) = 15 ⁄ 28

Example 2. Multiply 10 2 ⁄ 3 and 2 1 ⁄ 5 . Solution. First, we must convert both the mixed fractions to improper fractions. 10 2 ⁄ 3 = 32 ⁄ 3 2 1 ⁄ 5 = 11 ⁄ 5 Now, multiply both the improper fractions. 32 ⁄ 3 x 11 ⁄ 5 = (32x11) ⁄ (3x5) = 352 ⁄ 15 = 23 7 ⁄ 15 Hence the answer is 23 7 ⁄ 15 .

Example 3. 2 ⁄ 5 of 20. Solution. 2 ⁄ 5 x 20 = (2x20) ⁄ 5 = 40 ⁄ 5 = 8

Example 4. John can walk 2 3 ⁄ 5 km per hour. How much distance will he cover in 2 1 ⁄ 3 hours? Solution. Distance covered by John in one hour = 2 3 ⁄ 5 = 13 ⁄ 5 Distance covered by John in 2 1 ⁄ 3 hours = 13 ⁄ 5 x 7 ⁄ 3 = 91 ⁄ 15 = 6 1 ⁄ 15 So, John will cover 6 1 ⁄ 15 km in 2 1 ⁄ 3 hours.

Two fractions are said to be reciprocal of each other, if their product is 1. In other words, if a ⁄ b is a fraction, then b ⁄ a is it's reciprocal. Let's see some examples.

Example 2. Find the reciprocal of 2 3 ⁄ 5 . Solution. 2 3 ⁄ 5 = 13 ⁄ 5 Reciprocal of 13 ⁄ 5 is 5 ⁄ 13 .

To divide a fraction by another fraction, the first fraction is multiplied by the reciprocal of the second fraction. a ⁄ b ÷ c ⁄ d = a ⁄ b x d ⁄ c

Example 1. Divide 5 ⁄ 9 by 15. Solution. 5 ⁄ 9 ÷ 15 = 5 ⁄ 9 x 1 ⁄ 15 = 1 ⁄ 27

Example 2. Divide 5 3 ⁄ 5 by 3 1 ⁄ 10 . Solution. 5 3 ⁄ 5 ÷ 3 1 ⁄ 10 28 ⁄ 5 ÷ 31 ⁄ 10 = 28 ⁄ 5 x 10 ⁄ 31 = 56 ⁄ 31

Example 3. Divide 35 by 5 ⁄ 4 . Solution. 35 ÷ 5 ⁄ 4 = 35 x 4 ⁄ 5 = 7 x 4 = 28

Example 4. Cost of 2 3 ⁄ 5 kg orange is Rs. 260. What is the cost of 1 kg orange? Solution. Cost of 13 ⁄ 5 kg orange = Rs. 260 Cost of 1 kg orange = 260 ÷ 13 ⁄ 5 = 260 x 5 ⁄ 13 = 100 Hence, cost of 1 kg orange is Rs. 100.

Class-7 Fractions Test

Fractions Test - 1

Fractions Test - 2

Class-7 Fractions Worksheet

Fractions Worksheet - 1

Fractions Worksheet - 2

Fractions Worksheet - 3

Fractions Worksheet - 4

Fractions-Answer Download the pdf

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Chapter 2 Class 7 Fractions and Decimals

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Updated from 2023-24 NCERT Book.

Get solutions of all questions of Chapter 2 Class 7 Fractions & Decimals free at teachoo. All NCERT exercise questions and examples have been solved with detailed explanation of each solution. Concepts have also been explained in the concept wise.

In this chapter, we will study

• What is a fraction
• What is proper , improper and mixed fraction
• What are equivalent fractions
• Comparing fractions
• Adding and Subtracting Fractions
• Then, we will learn how to Multiply Fractions and Mixed Fractions
• And how to divide Fractions
• And do some statement questions on multiplication and division of fractions
• What are Decimal Numbers
• Place value of Decimals
• Comparing Decimal Numbers
• Converting g → kg, mm → cm, mm → m, mm → km, cm → m, cm → km
• Addition and Subtraction of Decimal Numbers
• We will learn how to Multiply Decimal Numbers
• and How to divide Decimals
• And do some statement questions

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• NCERT Solutions for Class 7 Maths Chapter 2 - Fractions And Decimals
• NCERT Solutions

NCERT Class 7 Maths Chapter 2: Complete Resource for Fractions and Decimals

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals PDF is available on Vedantu for free download. Our highly experienced teachers have prepared these NCERT Solutions according to the latest version of the Class 7 NCERT Maths textbook. These Class 7 NCERT Solutions for Fractions and Decimals help students brush up on all the important concepts of this chapter, example sums, and practice questions. 

The usage of simple language in these solutions helps students be able to learn and practice the sums effectively. If a student has certain doubts, our well-made NCERT Solutions for Maths Class 7 Chapter 2 Fractions and Decimals will help to resolve them. You can download NCERT Class 7 Science from Vedantu to score more marks in your examination.  

Chapter 2 of Class 7 Maths is all about fractions and decimals. We all know what is a fraction and what is a decimal. But, we may wonder what is the use of learning these? Well, we use fractions and decimals in our daily life knowingly or unknowingly. Whether it's about money calculation or measuring baking ingredients or splitting a bill at any restaurant we are using fractions and decimals.

The NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals include exercises on proper, improper, and mixed fractions, as well as their addition and subtraction. Furthermore, some of the key topics covered in this chapter include fraction comparison, equivalent fractions, fraction representation on the number line, and fraction order.

Access NCERT Solutions for Class 7 Maths Chapter 2 – Fractions and Decimals

Exercise - 2.1

(i). $\text{2-}\frac{\text{3}}{\text{5}}$

Ans: The solution is given as,

$2-\frac{3}{5}=\frac{10-3}{5}=\frac{7}{5}=1\frac{2}{5}$

(ii). $\text{4+}\frac{\text{7}}{\text{8}}$

$4+\frac{7}{8}=\frac{32+7}{8}=\frac{39}{8}=4\frac{7}{8}$

(iii). $\frac{\text{3}}{\text{5}}\text{+}\frac{\text{2}}{\text{7}}$ 

$\frac{3}{5}+\frac{2}{7}=\frac{21+10}{35}=\frac{31}{35}$

(iv). $\frac{\text{9}}{\text{11}}\text{-}\frac{\text{4}}{\text{15}}$ 

$\frac{9}{11}-\frac{4}{15}=\frac{135-44}{165}=\frac{91}{165}$

(v) $\frac{\text{7}}{\text{10}}\text{+}\frac{\text{2}}{\text{5}}\text{+}\frac{\text{3}}{\text{2}}$ 

$\frac{7}{10}+\frac{2}{5}+\frac{3}{2}=\frac{7+4+15}{10}=\frac{26}{10}=\frac{13}{5}=2\frac{3}{5}$ 

(vi) $\text{2}\frac{\text{2}}{\text{3}}\text{+3}\frac{\text{1}}{\text{2}}$

Ans: The solution is given as,       $2\frac{2}{3}+3\frac{1}{2}=\frac{8}{3}+\frac{7}{2}=\frac{16+21}{6}=\frac{37}{6}=6\frac{1}{6}$

(vii)  $\text{8}\frac{\text{1}}{\text{2}}\text{-3}\frac{\text{5}}{\text{8}}$ 

Ans: The solution is given as,     $8\frac{1}{2}-3\frac{5}{8}=\frac{17}{2}-\frac{29}{8}=\frac{68-29}{8}=\frac{39}{8}=4\frac{7}{8}$

2. Arrange the following in descending order: 

(i) $\frac{\text{2}}{\text{9}}\text{,}\frac{\text{2}}{\text{3}}\text{,}\frac{\text{8}}{\text{21}}$

Ans: Converting into the fractions with same denominator,

$\frac{2}{9},\frac{2}{3},\frac{8}{21}\,\,\,\,\,\Rightarrow \,\,\,\,\frac{14}{63},\frac{42}{63},\frac{24}{63}$    

Arranging the terms in descending order,         $\frac{42}{63}>\frac{24}{63}>\frac{14}{63}$                           

Converting the fraction into simplest form,

$\frac{2}{3}>\frac{8}{21}>\frac{2}{9}$ 

(ii) $\frac{\text{1}}{\text{5}}\text{,}\frac{\text{3}}{\text{7}}\text{,}\frac{\text{7}}{\text{10}}$ 

Ans: Converting into the fractions with same denominator, $\frac{1}{5},\frac{3}{7},\frac{7}{10}\,\,\,\,\,\Rightarrow \,\,\,\,\frac{14}{70},\frac{30}{70},\frac{49}{70}$              

Arranging the term in descending order,

$\Rightarrow \,\,\frac{49}{70}>\,\frac{30}{70}>\,\frac{14}{70}$        

$\frac{7}{10}>\frac{3}{7}>\frac{1}{5}$ 

3. In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?

$\left( \text{Along the first row}\frac{\text{4}}{\text{11}}\text{+}\frac{\text{9}}{\text{11}}\text{+}\frac{\text{2}}{\text{11}}\text{+=}\frac{\text{15}}{\text{11}} \right)$

Ans: If the sum of fractions in each row, in each column and along the diagonals is same then it is a magic square.

Calculating the sum of,

first row $=\frac{4}{11}+\frac{9}{11}+\frac{2}{11}=\frac{15}{11}$                

second row \[=\frac{3}{11}+\frac{5}{11}+\frac{7}{11}=\frac{3+5+7}{11}=\frac{15}{11}\] 

third row $=\frac{8}{11}+\frac{1}{11}+\frac{6}{11}=\frac{8+1+6}{11}=\frac{15}{11}$ 

first column $=\frac{4}{11}+\frac{3}{11}+\frac{8}{11}=\frac{4+3+8}{11}=\frac{15}{11}$ 

second column $=\frac{9}{11}+\frac{5}{11}+\frac{1}{11}=\frac{9+5+1}{11}=\frac{15}{11}$ 

third column $=\frac{2}{11}+\frac{7}{11}+\frac{6}{11}=\frac{2+7+6}{11}=\frac{15}{11}$ 

first diagonal along top left to bottom right $=\frac{4}{11}+\frac{5}{11}+\frac{6}{11}=\frac{4+5+6}{11}=\frac{15}{11}$ 

second diagonal along top right to bottom left $=\frac{2}{11}+\frac{5}{11}+\frac{8}{11}=\frac{2+5+8}{11}=\frac{15}{11}$ 

Observe that the sum of fractions in each row, in each column and along the    diagonals is same, 

Hence, it’s a magic square.

4. A rectangular sheet of paper is $\text{12}\frac{\text{1}}{\text{2}}$ cm long and $\text{10}\frac{\text{2}}{\text{3}}$ cm wide. Find its Perimeter?

Ans: Given: A rectangular sheet of paper has

 \[\text{Length =12}\frac{1}{2}\] cm

 \[\text{Breadth =10}\frac{2}{3}\] cm

 \[\text{Perimeter of rectangle = 2 (length + breadth)}\] 

 $=2\left( 12\frac{1}{2}+10\frac{2}{3} \right)=2\left( \frac{25}{2}+\frac{32}{3} \right)$ 

   $=2\left( \frac{25\times 3+32\times 2}{6} \right)=2\left( \frac{75+64}{6} \right)$ 

   $=2\times \frac{139}{6}=\frac{139}{3}=46\frac{1}{3}$ cm

   Hence, the perimeter of the rectangular sheet is $46\frac{1}{3}$ cm.

5. Find the perimeter of 

(i) $\text{ }\!\!\Delta\!\!\text{ ABE}$,

(Image will be uploaded soon)

Ans: Given: In $\text{ }\!\!\Delta\!\!\text{ ABE,}\,\text{AB=}\frac{\text{5}}{\text{2}}\text{cm,}\,\text{BE=2}\frac{\text{3}}{\text{4}}\text{cm,}\,\text{AE=3}\frac{\text{3}}{\text{5}}\text{cm}$ 

The perimeter of triangle is equal to the sum of all the sides of the triangle. According to the given figure,

$\text{ }\!\!\Delta\!\!\text{ ABE=AB+BE+AE}$ $=\frac{5}{2}+2\frac{3}{4}+3\frac{3}{5}=\frac{5}{2}+\frac{11}{4}+\frac{18}{5}$ 

$=\frac{50+55+72}{20}=\frac{177}{20}=8\frac{17}{20}$ cm

Hence, the perimeter of $\text{ }\!\!\Delta\!\!\text{ ABE}$ is $8\frac{17}{20}$ cm.

(ii) The rectangle $\text{BCDE}$ in this figure. Whose perimeter is greater?

Ans: Given: In rectangle $\text{BCDE,}$ $\text{BE=2}\frac{\text{3}}{\text{4}}\text{cm,}\,\text{ED=}\frac{\text{7}}{\text{6}}\text{cm}$

The perimeter of the rectangle is given by,

\[\text{Perimeter of rectangle = 2 (length + breadth)}\] 

 $=2\left( 2\frac{3}{4}+\frac{7}{6} \right)=2\left( \frac{11}{4}+\frac{7}{6} \right)$ 

$=2\left( \frac{33+14}{12} \right)=\frac{47}{6}=7\frac{5}{6}\text{cm}$ 

Hence, the perimeter of rectangle $\text{BCDE}$ is $7\frac{5}{6}$ cm.

Compare the perimeter of triangle with the perimeter of rectangle,

$\text{8}\frac{\text{17}}{\text{20}}\text{cm }>\text{ 7}\frac{\text{5}}{\text{6}}\text{cm}$ 

Hence, the perimeter of triangle \[\text{ABE}\] is greater as compared to the perimeter of rectangle $\text{BCDE}$

6. Salil wants to put a picture in a frame. The picture is $\text{7}\frac{\text{3}}{\text{5}}$ cm wide. To fit in the frame the picture cannot be more than $\text{7}\frac{\text{3}}{\text{10}}$ cm wide. How much should the picture be trimmed?

Ans: Given: The width of the picture$=7\frac{3}{5}$ cm and 

The width of picture frame$=7\frac{3}{10}$ cm

The picture should be   

trimmed$=7\frac{3}{5}-7\frac{3}{10}=\frac{38}{5}-\frac{73}{10}$ $=\frac{76-73}{10}=\frac{3}{10}$ cm

Hence, the original picture should be trimmed by $\frac{3}{10}$ cm.

7. Ritu ate $\frac{\text{3}}{\text{5}}$ part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?

Ans: Given: The part of an apple eaten by Ritu $=\frac{3}{5}$ 

The part of an apple eaten by Somu $=1-\frac{3}{5}=\frac{5-3}{5}=\frac{2}{5}$ 

Compare the parts of apple eaten by Ritu and Somu,

 $\frac{3}{5}>\frac{2}{5}$ 

Observe that Ritu’s part is larger than Somu’s part.

Also, the larger share is more by $\frac{3}{5}-\frac{2}{5}=\frac{1}{5}$ part as compared to the smaller part.

Hence, Ritu’s part is $\frac{1}{5}$ more as compared to Somu’s part.

8. Michael finished colouring a picture in $\frac{\text{7}}{\text{12}}$ hour. Vaibhav finished colouring the same picture in $\frac{\text{3}}{\text{4}}$ hour. Who worked longer? By what fraction was it longer?

Ans: Given: Time taken by Michael for coloring the picture $=\frac{7}{12}$ hour and

Time taken by Vaibhav for coloring the picture $=\frac{3}{4}$ hour

Convert both fractions in the fractions such that their denominator is same,

$\frac{7}{12}$ and 

$\frac{3\times 3}{4\times 3}=\frac{9}{12}$ 

Observe that, 

$\frac{7}{12}<\frac{9}{12}\Rightarrow \frac{7}{12}<\frac{3}{4}$ 

Hence, Vaibhav worked for a longer time.

Calculate the time for which Vaibhav worked longer,

$\frac{3}{4}-\frac{7}{12}=\frac{9-7}{12}=\frac{2}{12}=\frac{1}{6}$ hour 

Therefore, Vaibhav took $\frac{1}{6}$ hour more than Michael.

Exercise - 2.2

1. Which of the drawings $(a)\,to\,(d)$ show:

(i). $\text{2 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{5}}$

(a)  (Image will be uploaded soon)              

Ans: corresponds to $\text{(d)}$  

Because,  $2\times \frac{1}{5}=\frac{1}{5}+\frac{1}{5}$                                                                

(ii). $\text{2 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{2}}$

(b) (Image will be uploaded soon)

Ans: corresponds to $\text{(b)}$

Because, $2\times \frac{1}{2}=\frac{1}{2}+\frac{1}{2}$

(iii). $\text{3 }\!\!\times\!\!\text{ }\frac{\text{2}}{\text{3}}$

(c)    (Image will be uploaded soon)     

Ans:   corresponds to $\text{(a)}$   

Because, $3\times \frac{2}{3}=\frac{2}{3}+\frac{2}{3}+\frac{2}{3}$ 

(iv). $\text{3 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{4}}$

(d) (Image will be uploaded soon)

Ans: Corresponds to $\text{(c)}$

Because, $3\times \frac{1}{4}=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$ 

2. Some pictures $\left( \text{a} \right)\,\text{to}\,\left( \text{c} \right)$ are given below. Tell which of them show: 

(i). $\text{3 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{5}}\text{=}\frac{\text{3}}{\text{5}}$

(a) (Image will be uploaded soon) 

Ans: Corresponds to $\text{(c)}$                    

Because, $3\times \frac{1}{5}=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}$  

(ii). $\text{2 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{3}}\text{=}\frac{\text{2}}{\text{3}}$ 

(b) (Image will be uploaded soon)                                                

Ans: Corresponds to $\text{(a)}$                   

Because, $2\times \frac{1}{3}=\frac{1}{3}+\frac{1}{3}$ 

(iii). $\text{3 }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{4}}\text{=2}\frac{\text{1}}{\text{4}}$

(c) (Image will be uploaded soon)                                                             

Ans: Corresponds to $\text{(b)}$                  

Because, $3\times \frac{3}{4}=\frac{3}{4}+\frac{3}{4}+\frac{3}{4}$      

3. Multiply and reduce to lowest form and convert into a mixed fraction:

(i). $\text{7 }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{5}}$        

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,   

$7\times \frac{3}{5}=\frac{7\times 3}{5}=\frac{21}{5}=4\frac{1}{5}$

(ii). $\text{4 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{3}}$ 

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,

$4\times \frac{1}{3}=\frac{4\times 1}{3}=\frac{4}{3}=1\frac{1}{3}$ 

(iii). $\text{2 }\!\!\times\!\!\text{ }\frac{\text{6}}{\text{7}}$    

$2\times \frac{6}{7}=\frac{2\times 6}{7}=\frac{12}{7}=1\frac{5}{7}$       

(iv). $\text{5 }\!\!\times\!\!\text{ }\frac{\text{2}}{\text{9}}$ 

$5\times \frac{2}{9}=\frac{5\times 2}{9}=\frac{10}{9}=1\frac{1}{9}$

(v). $\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ 4}$     

$\frac{2}{3}\times 4=\frac{2\times 4}{3}=\frac{8}{3}=2\frac{2}{3}$   

(vi)  $\frac{\text{5}}{\text{2}}\text{ }\!\!\times\!\!\text{ 6}$    

$\frac{5}{2}\times 6=5\times 3=15$

(vii)   $\text{11 }\!\!\times\!\!\text{ }\frac{\text{4}}{\text{7}}$    

$11\times \frac{4}{7}=\frac{11\times 4}{7}=\frac{44}{7}=6\frac{2}{7}$ 

(viii)  $\text{20 }\!\!\times\!\!\text{ }\frac{\text{4}}{\text{5}}$ 

$20\times \frac{4}{5}=4\times 4=16$

(ix)  $\text{13 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{3}}$      

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,    

$13\times \frac{1}{3}=\frac{13\times 1}{3}=\frac{13}{3}=4\frac{1}{3}$ 

(x)  $\text{15 }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{5}}$ 

Ans: Multiplying and reducing to lowest form and converting into a mixed fraction,   

$15\times \frac{3}{5}=3\times 3=9$                

4. Shade: 

(i). $\frac{\text{1}}{\text{2}}$ of the circles in box 

(ii). (Image will be uploaded soon)                

Ans: Half of the circles in the box are,

$\frac{\text{1}}{\text{2}}\,\text{of}\,\text{12}\,\text{circles=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ 12=6}\,\text{circles}$

(iii). $\frac{\text{2}}{\text{3}}$ of the triangles in box 

Ans: Two-third of the triangles in the box are, $\frac{\text{2}}{\text{3}}\,\text{of}\,\text{9}\,\text{triangles=}\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ 9=2 }\!\!\times\!\!\text{ 3=6}\,\text{triangles}$ 

(iv). $\frac{\text{3}}{\text{5}}$ of the squares inbox

(v). (c)   (Image will be uploaded soon)                          

Ans: Three-fifth of the squares in the box are,

$\frac{\text{3}}{\text{5}}\,\text{of}\,\text{15}\,\text{squares=}\frac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ 15=3 }\!\!\times\!\!\text{ 3=9}\,\text{squares}$

(a).$\frac{\text{1}}{\text{2}}\,\text{of}\,\text{(i)}\,\text{24}\,\text{(ii)}\,\text{46}$

(i) Calculating the value,

$\frac{\text{1}}{\text{2}}\,\text{of}\,\text{24=12}$

(ii) Calculating the value,

$\frac{\text{1}}{\text{2}}\,\text{of}\,\text{46=23}$ 

(b). $\frac{\text{2}}{\text{3}}\,\text{of}\,\text{(i)}\,\text{18}\,\text{(ii)}\,\text{27}$ 

(i) Calculating the value, $\frac{\text{2}}{\text{3}}\,\text{of}\,\text{18=}\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ 18=2 }\!\!\times\!\!\text{ 6=12}$

(ii) Calculating the value, $\frac{\text{2}}{\text{3}}\,\text{of}\,\text{27=}\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ 27=2 }\!\!\times\!\!\text{ 9=18}$ 

(c)  $\frac{\text{3}}{\text{4}}\,\text{of}\,\text{(i)}\,\text{16}\,\text{(ii)}\,\text{36}$          

$\frac{\text{3}}{\text{4}}\,\text{of}\,\text{16=}\frac{\text{3}}{\text{4}}\text{ }\!\!\times\!\!\text{ 16=3 }\!\!\times\!\!\text{ 4=12}$

$\frac{\text{3}}{\text{4}}\,\text{of}\,36\text{=}\frac{\text{3}}{\text{4}}\text{ }\!\!\times\!\!\text{ 36=3 }\!\!\times\!\!\text{ 9=27}$  

(d)  $\frac{\text{4}}{\text{5}}\,\text{of}\,\text{(i)}\,\text{20}\,\text{(ii)}\,\text{35}$ 

$\frac{\text{4}}{\text{5}}\,\text{of}\,20\text{=}\frac{\text{4}}{\text{5}}\text{ }\!\!\times\!\!\text{ 20=4 }\!\!\times\!\!\text{ 4=16}$

$\frac{\text{4}}{\text{5}}\,\text{of}\,35\text{=}\frac{\text{4}}{\text{5}}\text{ }\!\!\times\!\!\text{ 35=4 }\!\!\times\!\!\text{ 7=28}$ 

6.   Multiply and express as a mixed fraction:

(a)  $\text{3 }\!\!\times\!\!\text{ 5}\frac{\text{1}}{\text{5}}$       

Ans: Multiplying and expressing the term as mixed fraction,

$3\times 5\frac{1}{5}=3\times \frac{26}{5}=\frac{3\times 26}{5}=\frac{78}{5}=15\frac{3}{5}$

(b) $\text{5 }\!\!\times\!\!\text{ 6}\frac{\text{3}}{\text{4}}$          

$5\times 6\frac{3}{4}=5\times \frac{27}{4}=\frac{5\times 27}{4}=\frac{135}{4}=33\frac{3}{4}$ 

(c) $\text{7 }\!\!\times\!\!\text{ 2}\frac{\text{1}}{\text{4}}$

$7\times 2\frac{1}{4}=7\times \frac{9}{4}=\frac{7\times 9}{4}=\frac{63}{4}=15\frac{3}{4}$        

(d)  $\text{4 }\!\!\times\!\!\text{ 6}\frac{\text{1}}{\text{3}}$ 

$4\times 6\frac{1}{3}=4\times \frac{19}{3}=\frac{4\times 19}{3}=\frac{76}{3}=25\frac{1}{3}$ 

(e)  $\text{3}\frac{\text{1}}{\text{4}}\text{ }\!\!\times\!\!\text{ 6}$ 

$3\frac{1}{4}\times 6=\frac{13}{4}\times 6=\frac{13\times 3}{2}=\frac{39}{2}=19\frac{1}{2}$  

(f)  $\text{3}\frac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ 8}$ 

$3\frac{2}{5}\times 8=\frac{17}{5}\times 8=\frac{17\times 8}{5}=\frac{136}{5}=27\frac{1}{5}$

(a)  $\frac{\text{1}}{\text{2}}\,\text{of}\,\text{(i)}\,\text{2}\frac{\text{3}}{\text{4}}\,\text{(ii)}\,\text{4}\frac{\text{2}}{\text{9}}$             

(i) Calculating the value, \[\frac{\text{1}}{\text{2}}\,\text{of}\,\text{2}\frac{\text{3}}{\text{4}}\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ 2}\frac{\text{3}}{\text{4}}\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ }\frac{\text{11}}{\text{4}}\text{=}\frac{\text{11}}{\text{8}}\text{=1}\frac{\text{3}}{\text{8}}\] 

(ii) Calculating the value, \[\frac{\text{1}}{\text{2}}\,\text{of}\,\text{4}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ 4}\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ }\frac{\text{38}}{\text{9}}\text{=}\frac{\text{19}}{\text{9}}\text{=2}\frac{\text{1}}{\text{9}}\] 

(b)  $\frac{\text{5}}{\text{8}}\,\text{of}\,\text{(i)}\,\text{3}\frac{\text{5}}{\text{6}}\,\text{(ii)}\,\text{9}\frac{\text{2}}{\text{3}}$ 

(i) Calculating the value, \[\frac{\text{5}}{\text{8}}\,\text{of}\,\text{3}\frac{\text{5}}{\text{6}}\text{=}\frac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ 3}\frac{\text{5}}{\text{6}}\text{=}\frac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ }\frac{\text{23}}{\text{6}}\text{=}\frac{\text{115}}{\text{48}}\text{=2}\frac{\text{19}}{\text{48}}\] 

(ii) Calculating the value, \[\frac{\text{5}}{\text{8}}\,\text{of}\,\text{9}\frac{\text{2}}{\text{3}}\text{=}\frac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ 9}\frac{\text{2}}{\text{3}}\text{=}\frac{\text{5}}{\text{8}}\text{ }\!\!\times\!\!\text{ }\frac{\text{29}}{\text{3}}\text{=}\frac{\text{145}}{\text{24}}\text{=6}\frac{\text{1}}{\text{24}}\] 

8.  Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained $\text{5}$ liters of water. Vidya consumed $\frac{\text{2}}{\text{5}}$ of the water. Pratap consumed the remaining water.

(i). How much water did Vidya drink?

Ans:   Water consumed by Vidya is, $\text{=}\frac{\text{2}}{\text{5}}\,\text{of}\,\text{5}\,\text{litres=}\frac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ 5=2}\,\text{litres}$ 

Hence, Vidya drank $2$ litres of water from the bottle.

(ii). What fraction of the total quantity of water did Pratap drink?

Ans: Water consumed by Pratap \[\text{= }\left( \text{1-}\frac{\text{2}}{\text{5}} \right)\text{  }\]part of bottle

Pratap consumed $\frac{\text{3}}{\text{5}}\,\text{of}\,\text{5}\,\text{litres}\,\text{water=}\frac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ 5=3}\,\text{lites}$ 

Hence, Pratap drank $\frac{3}{5}$ part of the total quantity of water present in the bottle.

Exercise - 2.3

(i) $\frac{\text{1}}{\text{4}}\,\text{of}$ (a) $\frac{\text{1}}{\text{4}}$ (b) $\frac{\text{3}}{\text{5}}$ (c) $\frac{\text{4}}{\text{3}}$ 

(a) Calculating the value,

$\frac{\text{1}}{\text{4}}\,\text{of}\,\frac{\text{1}}{\text{4}}\text{=}\frac{\text{1}}{\text{4}}\text{ }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{4}}\text{=}\frac{\text{1 }\!\!\times\!\!\text{ 1}}{\text{4 }\!\!\times\!\!\text{ 4}}\text{=}\frac{\text{1}}{\text{16}}$ 

(b) Calculating the value,

$\frac{\text{1}}{\text{4}}\,\text{of}\,\frac{\text{3}}{\text{5}}\text{=}\frac{\text{1}}{\text{4}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{4}}\text{=}\frac{\text{1 }\!\!\times\!\!\text{ 3}}{\text{4 }\!\!\times\!\!\text{ 4}}\text{=}\frac{\text{3}}{\text{16}}$ 

(c) Calculating the value,

$\frac{\text{1}}{\text{4}}\,\text{of}\,\frac{\text{4}}{\text{3}}\text{=}\frac{\text{1}}{\text{4}}\text{ }\!\!\times\!\!\text{ }\frac{\text{4}}{\text{3}}\text{=}\frac{\text{1 }\!\!\times\!\!\text{ 4}}{\text{4 }\!\!\times\!\!\text{ 3}}\text{=}\frac{\text{1}}{\text{3}}$ 

(ii) \[\frac{\text{1}}{\text{7}}\,\text{of}\] (a) \[\frac{\text{2}}{\text{9}}\] (b) \[\frac{\text{6}}{\text{5}}\] (c) $\frac{\text{3}}{\text{10}}$ 

$\frac{\text{1}}{\text{7}}\,\text{of}\,\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1 }\!\!\times\!\!\text{ 2}}{\text{7 }\!\!\times\!\!\text{ 9}}\text{=}\frac{\text{2}}{\text{63}}$ 

$\frac{\text{1}}{\text{7}}\,\text{of}\,\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\frac{\text{6}}{\text{5}}\text{=}\frac{\text{1 }\!\!\times\!\!\text{ 6}}{\text{7 }\!\!\times\!\!\text{ 5}}\text{=}\frac{\text{6}}{\text{35}}$ 

$\frac{\text{1}}{\text{7}}\,\text{of}\,\frac{\text{2}}{\text{9}}\text{=}\frac{\text{1}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{10}}\text{=}\frac{\text{1 }\!\!\times\!\!\text{ 3}}{\text{7 }\!\!\times\!\!\text{ 10}}\text{=}\frac{3}{70}$ 

2. Multiply and reduce to lowest form (if possible):

(i) $\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ 2}\frac{\text{2}}{\text{3}}$ 

Ans: Multiplying and reducing to lowest form,  

$\frac{2}{3}\times 2\frac{2}{3}=\frac{2}{3}\times \frac{8}{3}=\frac{2\times 8}{3\times 3}=\frac{16}{9}=1\frac{7}{9}$ 

(ii) $\frac{\text{2}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\frac{\text{7}}{\text{9}}$

$\frac{2}{7}\times \frac{7}{9}=\frac{2\times 7}{7\times 9}=\frac{2}{9}$

(iii) $\frac{\text{3}}{\text{8}}\text{ }\!\!\times\!\!\text{ }\frac{\text{6}}{\text{4}}$ 

Ans: Multiplying and reducing to lowest form, 

$\frac{3}{8}\times \frac{6}{4}=\frac{3\times 6}{8\times 4}=\frac{3\times 3}{8\times 2}=\frac{9}{16}$

(iv) $\frac{\text{9}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{5}}$ 

$\frac{9}{5}\times \frac{3}{5}=\frac{9\times 3}{5\times 5}=\frac{27}{25}=1\frac{2}{25}$

(v) $\frac{\text{1}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\frac{\text{15}}{\text{8}}$ 

Ans: Multiplying and reducing to lowest form,

$\frac{1}{3}\times \frac{15}{8}=\frac{1\times 15}{3\times 8}=\frac{1\times 5}{1\times 8}=\frac{5}{8}$

(vi) $\frac{\text{11}}{\text{2}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{10}}$ 

$\frac{11}{2}\times \frac{3}{10}=\frac{11\times 3}{2\times 10}=\frac{33}{20}=1\frac{3}{20}$ 

(vii) $\frac{\text{4}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\frac{\text{12}}{\text{7}}$ 

$\frac{4}{5}\times \frac{12}{7}=\frac{4\times 12}{5\times 7}=\frac{48}{35}=1\frac{13}{35}$

3. Multiply the following fractions:

(i) $\frac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ 5}\frac{\text{1}}{\text{4}}$

Ans: Performing multiplication,

$\frac{2}{5}\times 5\frac{1}{4}=\frac{2}{5}\times \frac{21}{4}=\frac{2\times 21}{5\times 4}=\frac{1\times 21}{5\times 2}=\frac{21}{10}=2\frac{1}{10}$ 

(ii) $\text{6}\frac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\frac{\text{7}}{\text{9}}$ 

$6\frac{2}{5}\times \frac{7}{9}=\frac{32}{5}\times \frac{7}{9}=\frac{32\times 7}{5\times 9}=\frac{224}{45}=4\frac{44}{45}$

(iii) $\frac{\text{3}}{\text{2}}\text{ }\!\!\times\!\!\text{ 5}\frac{\text{1}}{\text{3}}$ 

$\frac{3}{2}\times 5\frac{1}{3}=\frac{3}{2}\times \frac{16}{3}=\frac{48}{6}=8$ 

(iv) $\frac{\text{5}}{\text{6}}\text{ }\!\!\times\!\!\text{ 2}\frac{\text{3}}{\text{7}}$ 

$\frac{5}{6}\times 2\frac{3}{7}=\frac{5}{6}\times \frac{17}{7}=\frac{85}{42}=2\frac{1}{42}$ 

(v) $\text{3}\frac{\text{2}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\frac{\text{4}}{\text{7}}$

$3\frac{2}{5}\times \frac{4}{7}=\frac{17}{7}\times \frac{4}{7}=\frac{68}{35}=1\frac{33}{35}$

(vi) $\text{2}\frac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ 3}$ 

$2\frac{3}{5}\times 3=\frac{13}{5}\times \frac{3}{1}=\frac{13\times 3}{5\times 1}=\frac{39}{5}=7\frac{4}{5}$

(vii) $\text{3}\frac{\text{4}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{5}}$ 

$3\frac{4}{7}\times \frac{3}{5}=\frac{25}{7}\times \frac{3}{5}=\frac{5\times 3}{7\times 1}=\frac{15}{7}=2\frac{1}{7}$

4. Which is greater:

(i) $\frac{\text{2}}{\text{7}}\,\text{of}\,\frac{\text{3}}{\text{4}}\,\text{or}\,\frac{\text{3}}{\text{5}}\,\text{of}\,\frac{\text{5}}{\text{8}}$

Ans: Calculating the greater term,

$\frac{\text{2}}{\text{7}}\,\text{of}\,\frac{\text{3}}{\text{4}}\,\text{or}\,\frac{\text{3}}{\text{5}}\,\text{of}\,\frac{\text{5}}{\text{8}}$                

$\Rightarrow \frac{\text{2}}{\text{7}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{4}}\,\text{or}\,\frac{\text{3}}{\text{5}}\text{ }\!\!\times\!\!\text{ }\frac{\text{5}}{\text{8}}$ 

$\Rightarrow \frac{\text{3}}{\text{14}}\,\text{or}\,\frac{\text{3}}{\text{8}}$

$\Rightarrow \frac{3}{14}<\frac{3}{8}$ 

Hence, $\frac{\text{3}}{\text{5}}\,\text{of}\,\frac{\text{5}}{\text{8}}$ is greater.

(ii) $\frac{\text{1}}{\text{2}}\,\text{of}\,\frac{\text{6}}{\text{7}}\,\text{or}\,\frac{\text{2}}{\text{3}}\,\text{of}\,\frac{\text{3}}{\text{7}}$ 

Calculating the greater term,

$\frac{\text{1}}{\text{2}}\,\text{of}\,\frac{\text{6}}{\text{7}}\,\text{or}\,\frac{\text{2}}{\text{3}}\,\text{of}\,\frac{\text{3}}{\text{7}}$                

$\Rightarrow \frac{\text{1}}{\text{2}}\text{ }\!\!\times\!\!\text{ }\frac{\text{6}}{\text{7}}\,\text{or}\,\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{7}}$ 

$\Rightarrow \frac{\text{6}}{\text{14}}\,\text{or}\,\frac{\text{2}}{\text{7}}$ $\Rightarrow \frac{\text{6}}{\text{14}}>\frac{\text{2}}{\text{7}}$ 

Hence, $\frac{\text{1}}{\text{2}}\,\text{of}\,\frac{\text{6}}{\text{7}}$ is greater.

5. Saili plants \[\text{4}\] saplings in a row in her garden. The distance  between

two adjacent saplings is \[\frac{\text{3}}{\text{4}}\] m. Find the 

distance between the first and the last sapling. 

Ans: Given: Saili plants \[4\] saplings in a row where the distance between two 

adjacent saplings $=\frac{3}{4}$m.

The number of gaps in saplings \[=\text{ }3\] 

Hence, 

The distance between the first and the last saplings$\text{=3 }\!\!\times\!\!\text{ }\frac{\text{3}}{\text{4}}\text{=}\frac{\text{9}}{\text{4}}\text{m=2}\frac{\text{1}}{\text{4}}\text{m}$

Therefore, the distance between the first and the last saplings is $\text{2}\frac{\text{1}}{\text{4}}\,\text{m}$

6. Lipika reads a book for $\text{1}\frac{\text{3}}{\text{4}}$ hours every day. 

She reads the entire book in \[\text{6}\] days. how many hours in all were , required by her to read the book.

Ans: Given: Time taken for reading a book by Lipika $=1\frac{3}{4}$ hours.

Lipika reads the entire book in $6$ days

Calculating the Total hours taken by Lipika to read the entire book,

$=1\frac{3}{4}\times 6=\frac{7}{4}\times 6=\frac{21}{2}=10\frac{1}{2}$ hours.

Hence, it would take $10$ hours to read the book.

7. A car runs $\text{16}$ km using \[\text{1}\] litre of petrol. How much 

distance will it cover using   $\text{2}\frac{\text{3}}{\text{4}}$ litres of 

Ans: Given: A car covers the distance$\text{=16}\,\text{km}$ in $1$ litre of 

Calculating the distance covered by car in $2\frac{3}{4}$ litres of petrol,

Distance$\text{=2}\frac{\text{3}}{\text{4}}\,\text{of}\,\text{16}\,\text{km=}\frac{\text{11}}{\text{4}}\text{ }\!\!\times\!\!\text{ 16=44}\,\text{km}$

Therefore, car will cover a distance of $44$ km in $2\frac{3}{4}$ litres of petrol.

(i) Provide the number in the box , such that 

$\frac{\text{2}}{\text{3}}\text{ }\!\!\times\!\!\text{ }\text{=}\frac{\text{10}}{\text{30}}$  

Ans: The number inside the box should be $\frac{2}{3}\times =\frac{10}{30}$ 

(ii) The simplest form of the number obtained in $$ is _____.

Ans: The simplest form of the number obtained in 

$\frac{\text{5}}{\text{10}}\,\text{is}\,\frac{\text{1}}{\text{2}}$

(i) Provide the number in the box $$ , such that $\frac{3}{5}\times =\frac{24}{75}$ .

Ans: The number inside the box should be $\frac{3}{5}\times =\frac{24}{75}$ 

(ii) The simplest form of the number obtained in is______.

$\frac{\text{8}}{\text{15}}\,\text{is}\,\frac{\text{8}}{\text{15}}$

Exercise - 2.4

(i) $\text{12 }\!\!\div\!\!\text{ }\frac{\text{3}}{\text{4}}$ 

Ans: Calculating the value,

$12\div \frac{3}{4}=12\times \frac{4}{3}=16$

(ii) $\text{14 }\!\!\div\!\!\text{ }\frac{\text{5}}{\text{6}}$ 

$14\div \frac{5}{6}=14\times \frac{6}{5}=\frac{84}{5}=16\frac{4}{5}$ 

(iii) $\text{8 }\!\!\div\!\!\text{ }\frac{\text{7}}{\text{3}}$ 

Ans:  Calculating the value,

$8\div \frac{7}{3}=8\times \frac{3}{7}=\frac{24}{7}=3\frac{3}{7}$

(iv) $\text{4 }\!\!\div\!\!\text{ }\frac{\text{8}}{\text{3}}$ 

$4\div \frac{8}{3}=4\times \frac{3}{8}=\frac{3}{2}=1\frac{1}{2}$

(v) $\text{3 }\!\!\div\!\!\text{ 2}\frac{\text{1}}{\text{3}}$ 

$3\div 2\frac{1}{3}=3\div \frac{7}{3}=3\times \frac{3}{7}=\frac{9}{7}=1\frac{2}{7}$           

(vi) \[\text{5 }\!\!\div\!\!\text{ 3}\frac{\text{4}}{\text{7}}\] 

$5\div 3\frac{4}{7}=5\div \frac{25}{7}=5\times \frac{7}{25}=\frac{7}{5}=1\frac{2}{5}$

2. Find the reciprocal of each of the following fractions. Classify the 

reciprocals as proper fraction, improper fractions and whole numbers.

(i) $\frac{\text{3}}{\text{7}}$

Ans: Calculating the reciprocal and stating the type of the fraction,

Reciprocal of $\frac{\text{3}}{\text{7}}\text{=}\frac{\text{7}}{\text{3}}\to \text{Improper}\,\text{fraction}$  

(ii) $\frac{\text{5}}{\text{8}}$

Reciprocal of$\frac{\text{5}}{\text{8}}\text{=}\frac{\text{8}}{\text{5}}\to \text{Improper}\,\text{fraction}$

(iii) $\frac{\text{9}}{\text{7}}$

Reciprocal of $\frac{\text{9}}{\text{7}}\text{=}\frac{\text{7}}{\text{9}}\to \text{Proper}\,\text{fraction}$

(iv) $\frac{\text{6}}{\text{5}}$ 

Reciprocal of $\frac{\text{6}}{\text{5}}\text{=}\frac{\text{5}}{\text{6}}\to \text{Proper}\,\text{fraction}$

(v) $\frac{\text{12}}{\text{7}}$ 

Reciprocal of $\frac{\text{12}}{\text{7}}\text{=}\frac{\text{7}}{\text{12}}\to \text{Proper}\,\text{fraction}$  

(vi) $\frac{\text{1}}{\text{8}}$

Reciprocal of $\frac{\text{9}}{\text{7}}\text{=8}\to \text{Whole number}$

(vii) $\frac{\text{1}}{\text{11}}$ 

Reciprocal of $\frac{\text{1}}{\text{11}}\text{=11}\to \text{Whole number}$

(i) $\frac{\text{7}}{\text{3}}\text{ }\!\!\div\!\!\text{ 2}$ 

$\frac{7}{3}\div 2=\frac{7}{3}\times \frac{1}{2}=\frac{7\times 1}{3\times 2}=\frac{7}{6}=1\frac{1}{6}$

(ii) $\frac{\text{4}}{\text{9}}\text{ }\!\!\div\!\!\text{ 5}$

$\frac{4}{9}\div 5=\frac{4}{9}\times \frac{1}{5}=\frac{4\times 1}{9\times 5}=\frac{4}{45}$ 

(iii) $\frac{\text{6}}{\text{13}}\text{ }\!\!\div\!\!\text{ 7}$ 

$\frac{6}{13}\div 7=\frac{6}{13}\times \frac{1}{7}=\frac{6\times 1}{13\times 7}=\frac{6}{91}$ 

(iv) $\text{4}\frac{\text{1}}{\text{3}}\text{ }\!\!\div\!\!\text{ 3}$

Ans:  Calculating the value,

$4\frac{1}{3}\div 3=\frac{13}{3}\div 3=\frac{13}{3}\times \frac{1}{3}=\frac{13}{9}=1\frac{4}{9}$

(v) $\text{3}\frac{\text{1}}{\text{2}}\text{ }\!\!\div\!\!\text{ 4}$ 

$3\frac{1}{2}\div 4=\frac{7}{2}\div 4=\frac{7}{2}\times \frac{1}{4}=\frac{7}{8}$

(vi) $\text{4}\frac{\text{3}}{\text{7}}\text{ }\!\!\div\!\!\text{ 7}$ 

$4\frac{3}{7}\div 7=\frac{31}{7}\div 7=\frac{31}{7}\times \frac{1}{7}=\frac{31}{49}$

(i) $\frac{\text{2}}{\text{5}}\text{ }\!\!\div\!\!\text{ }\frac{\text{1}}{\text{2}}$

$\frac{2}{5}\div \frac{1}{2}=\frac{2}{5}\times \frac{2}{1}=\frac{2\times 2}{5\times 1}=\frac{4}{5}$ 

(ii) $\frac{\text{4}}{\text{9}}\text{ }\!\!\div\!\!\text{ }\frac{\text{2}}{\text{3}}$ 

$\frac{4}{9}\div \frac{2}{3}=\frac{4}{9}\times \frac{3}{2}=\frac{2}{3}$

(iii) $\frac{\text{3}}{\text{7}}\text{ }\!\!\div\!\!\text{ }\frac{\text{8}}{\text{7}}$

$\frac{3}{7}\div \frac{8}{7}=\frac{3}{7}\times \frac{7}{8}=\frac{3}{8}$

(iv) $\text{2}\frac{\text{1}}{\text{3}}\text{ }\!\!\div\!\!\text{ }\frac{\text{3}}{\text{5}}$ 

$2\frac{1}{3}\div \frac{3}{5}=\frac{7}{3}\div \frac{3}{5}=\frac{7}{3}\times \frac{5}{3}=\frac{35}{9}=3\frac{8}{9}$

(v) $\text{3}\frac{\text{1}}{\text{2}}\text{ }\!\!\div\!\!\text{ }\frac{\text{8}}{\text{3}}$ 

$3\frac{1}{2}\div \frac{8}{3}=\frac{7}{2}\div \frac{3}{8}=\frac{7}{2}\times \frac{3}{8}=\frac{7\times 3}{2\times 8}=\frac{21}{16}=1\frac{5}{16}$

(vi) $\frac{\text{2}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\frac{\text{1}}{\text{2}}$

$2\frac{1}{3}\div \frac{3}{5}=\frac{2}{5}\div 1\frac{1}{2}=\frac{2}{5}\div \frac{3}{2}=\frac{2}{5}\times \frac{2}{3}=\frac{2\times 2}{5\times 3}=\frac{4}{15}$

(vii) $\text{3}\frac{\text{1}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\frac{\text{2}}{\text{3}}$

Ans:   Calculating the value,

$3\frac{1}{5}\div 1\frac{2}{3}=\frac{16}{5}\div \frac{5}{3}=\frac{16}{5}\times \frac{3}{5}=\frac{16\times 3}{5\times 5}=\frac{48}{25}=1\frac{23}{25}$

(viii) $\text{2}\frac{\text{1}}{\text{5}}\text{ }\!\!\div\!\!\text{ 1}\frac{\text{1}}{\text{5}}$ 

$2\frac{1}{5}\div 1\frac{1}{5}=\frac{11}{5}\div \frac{6}{5}=\frac{11}{5}\times \frac{5}{6}=\frac{11}{6}=1\frac{5}{6}$

Exercise - 2.5

1. Which is greater:

(i) $\text{0}\text{.5}\,\text{or}\,\text{0}\text{.05}$

Ans: Finding the greater term,

$0.5>0.05$

(ii) $\text{0}\text{.7}\,\text{or}\,\text{0}\text{.5}$ 

$0.7>0.5$

(iii) \[\text{7 or 0}\text{.7}\] 

(iv) \[\text{1}\text{.37 or 1}\text{.49}\]

$1.37<1.49$

(v) \[\text{2}\text{.03 or 2}\text{.30}\]

$2.03<2.30$

(vi) \[\text{0}\text{.8 or 0}\text{.88}\]

$0.8<0.88$

2. Express as rupees using decimals:

(i) $\text{7}\,\text{paise}$

Ans:  Expressing the term as rupees,

$\text{7}\,\text{paise=Re}\text{.}\frac{\text{7}}{\text{100}}\text{=Re}\text{.0}\text{.07}$ 

(ii) \[\text{7 rupees 7 paise}\] 

Ans: Expressing the term as rupees,$\text{7}\,\text{rupees}\,\,\text{7}\,\,\text{paise=Rs}\text{.7+Re}\text{.}\frac{\text{7}}{\text{100}}\text{=Rs}\text{.7+Rs}\text{.0}\text{.07=Rs}\text{.7}\text{.07}$

(iii) \[\text{77 rupees 77 paise}\] 

Ans: Expressing the term as rupees,$\text{77}\,\text{rupees}\,\,\text{77}\,\,\text{paise=Rs}\text{.77+Re}\text{.}\frac{\text{77}}{\text{100}}\text{=Rs}\text{.77+Rs}\text{.0}\text{.77=Rs}\text{.77}\text{.77}$

(iv) \[\text{50 paise}\] 

Ans: Expressing the term as rupees,

$\text{50}\,\text{paise=Re}\text{.}\frac{\text{50}}{\text{100}}\text{=Re}\text{.0}\text{.50}$

(v) \[\text{235 paise}\] 

$\text{235}\,\text{paise=Re}\text{.}\frac{\text{235}}{\text{100}}\text{=Rs}\text{.2}\text{.35}$

(i) Express $\text{5}$ cm in metre and kilometer.

Ans: Expressing $5$ cm in meter and kilometer,

$\because \,\,\text{100}\,\text{cm=1}\,\text{meter}$ 

$\therefore\,\,\text{1}\,\text{cm=}\frac{\text{1}}{\text{100}}\,\text{meter}\rightarrow \text{5}\,\text{cm=}\frac{\text{5}}{\text{100}}\text{=0}\text{.05}\,\text{meter}$  

And, $\because \,\,\text{1000}\,\text{meters=1}\,\text{kilometers}$ 

$\therefore     \,\,\text{1}\,\text{meter=}\frac{\text{1}}{\text{1000}}\,\text{kilometers}$$\Rightarrow \text{0}\text{.05}\,\text{meter=}\frac{\text{0}\text{.05}}{\text{1000}}\text{=0}\text{.00005}\,\,\text{kilometer}$

(ii) Express $\text{35}$ mm in cm, m and km.

Ans: Expressing $35$ mm in cm, m and km.

$\because \,\,\text{10}\,\text{mm=1}\,\text{cm}$ 

$\therefore \,\,\text{1}\,\text{mm=}\frac{\text{1}}{\text{10}}\,\text{cm}\Rightarrow \text{35}\,\text{mm=}\frac{\text{35}}{\text{10}}\text{=3}\text{.5}\,\text{cm}$ 

And, $\because \,\,\text{100}\,\text{cm=1}\,\text{meter}$ 

$\therefore \,\,\,\text{1}\,\text{cm=}\frac{\text{1}}{\text{100}}\,\text{meter}\Rightarrow \text{3}\text{.5}\,\text{cm=}\frac{\text{3}\text{.5}}{\text{100}}\text{=0}\text{.035}\,\text{meter}$ 

Also, $\because \,\,\text{1000}\,\text{meters=1}\,\text{kilometers}$ 

$\therefore \,\,\text{1}\,\text{meter=}\frac{\text{1}}{\text{1000}}\,\text{kilometer}$ $\Rightarrow \,\,\text{0}\text{.035}\,\text{meter=}\frac{\text{0}\text{.035}}{\text{1000}}\text{=0}\text{.000035}\,\text{kilometer}$ 

4. Express in kg:

(i) $\text{200}\,\text{g}$

Ans: Converting from grams to kilograms,

$\text{200}\,\text{g=}\left( \text{200 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{1000}} \right)\,\text{kg=0}\text{.2}\,\text{kg}$ 

(ii) $\text{3470}\,\text{g}$ 

$3470\,\text{g=}\left( \text{3470 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{1000}} \right)\,\text{kg=3}\text{.470}\,\text{kg}$

(iii) $\text{4}\,\text{kg}\,\text{8}\,\text{g}$ 

Ans: Converting from grams to kilograms,$\text{4}\,\text{kg}\,\text{8}\,\text{g=4}\,\text{kg}\,\text{+}\left( \text{8 }\!\!\times\!\!\text{ }\frac{\text{1}}{\text{1000}} \right)\,\text{kg=4}\,\text{kg+0}\text{.008}\,\text{kg=4}\text{.008}\,\text{kg}$

5. Write the following decimal numbers in the expanded form:

(i) $\text{20}\text{.03}$ 

Ans: Converting the decimal number in expanded form, 

$20.03=2\times 10+0\times 1+0\times \frac{1}{10}+3\times \frac{1}{100}$ 

(ii) $\text{2}\text{.03}$ 

Ans: Converting the decimal number in expanded form, $2.03=2\times 1+0\times \frac{1}{10}+3\times \frac{1}{100}$

(iii) $\text{200}\text{.03}$ 

Ans: Converting the decimal number in expanded form, $200.03=2\times 100+0\times 10+0\times 1+0\times \frac{1}{10}+3\times \frac{1}{100}$

(iv) $\text{2}\text{.034}$ 

Ans: Converting the decimal number in expanded form, $2.034=2\times 1+0\times \frac{1}{10}+3\times \frac{1}{100}+4\times \frac{1}{1000}$

6. Write the place value of \[\text{2}\] in the following decimal numbers:

(i) $\text{2}\text{.56}$

Ans: The place value of $2$ in $2.56$ $=2\times 1=2\,$ones

(ii) $\text{21}\text{.37}$ 

Ans: The place value of $2$ in $21.37=2\times 10=2$ tens

(iii) $\text{10}\text{.25}$ 

Ans: The place value of $2$ in $10.25=2\times \frac{1}{10}=2$ tenths

(iv) $\text{9}\text{.42}$

Ans:  The place value of $2$ in $9.42=2\times \frac{1}{100}=2$ hundredth

(v) $\text{63}\text{.352}$ 

Ans: The place value of $2$ in $63.352=2\times \frac{1}{1000}=2$ thousandth

7. Dinesh went from place\[\text{ }\!\!~\!\!\text{ A}\]to place \[\text{B}\] and 

from there to place\[\text{C}\]. 

\[\text{A}\] is \[\text{7}\text{.5}\] km from \[\text{B}\] and \[\text{B}\] is \[\text{12}\text{.7}\] km from\[\text{C}\].  Ayub went from

 place \[\text{A}\] to place \[\text{D}\] and from there to place\[\text{C}\]. \[\text{D}\] is \[\text{9}\text{.3}\] km from

 \[\text{A}\]and \[\text{C}\] is \[\text{11}\text{.8}\] km from\[\text{D}\] . Who travelled more and by how much?

Given: The distance travelled by Dinesh when he went from 

place \[\text{A}\] to place \[\text{B = 7}\text{.5 km}\] and from 

place\[\text{B to C = 12}\text{.7 km}\]

According to the figure,

The total distance covered by Dinesh \[\text{= AB + BC }\]

Substituting the values,

 \[\text{=7}\text{.5 + 12}\text{.7 = 20}\text{.2 km}\] 

The total distance covered by Ayub \[\text{= AD + DC }\]

Substituting the values, 

\[\text{=9}\text{.3 + 11}\text{.8 = 21}\text{.1 km}\]

Comparing the total distance covered by Ayub and Dinesh, 

\[\text{21}\text{.1 km  20}\text{.2 km}\]

Hence, Ayub covered \[\text{21}\text{.1 -- 20}\text{.2 = 0}\text{.9 km = 900m}\] more distance as compared to Dinesh.

8. Shyam bought \[\text{5 kg 300 g}\] apples and \[\text{3 kg 250 g}\] 

mangoes. Sarala bought \[\text{4 kg 800 g}\] oranges and \[\text{4 kg 150 g}\] 

bananas. Who bought more fruits?

Ans: Given: 

The total weight of fruits bought by Shyam\[\text{ = 5 kg 300 g + 3 kg 250 g = 8 kg 550 g}\]

And the total weight of fruits bought by Sarala\[\text{= 4 kg 800 g + 4 kg 150 g = 8 kg 950 g}\] 

Comparing the quantity of fruits bought by Shyam and Sarala,

\[\text{8}\,\text{kg}\,\text{550}\,\text{g8}\,\text{kg}\,\text{950}\,\text{g}\] 

Observe that quantity of fruits bought by Sarala is greater.

Hence, Sarala bought more fruits then Shyam.

9. How much less is \[\text{28 km}\]then \[\text{42}\text{.6 km}\]?

Given: The two distances are $\text{42}\text{.6}\,\text{km}\,\text{and}\,\text{28}\,\text{km}$

Finding the difference of $\text{42}\text{.6}\,\text{km}\,\text{and}\,\text{28}\,\text{km}$,

$\text{42}\text{.6-28}\text{.0=14}\text{.6}\,\text{km}$ 

Hence, $\text{14}\text{.6}\,\text{km}$ less is $\text{28}\,\text{km}$then 

$\text{42}\text{.6}\,\text{km}$.

Exercise 2.6

(i) $\text{0}\text{.2 }\!\!\times\!\!\text{ 6}$ 

\[0.2\times 6=1.2\]

(ii) $\text{8 }\!\!\times\!\!\text{ 4}\text{.6}$

\[8\times 4.6=36.8\]

(iii) $\text{2}\text{.71 }\!\!\times\!\!\text{ 5}$ 

\[2.71\times 5=13.55\]

(iv) $\text{20}\text{.1 }\!\!\times\!\!\text{ 4}$ 

\[20.1\times 4=80.4\]

(v) $\text{0}\text{.05 }\!\!\times\!\!\text{ 7}$ 

\[0.05\times 7=0.35\]

(vi) $\text{211}\text{.02 }\!\!\times\!\!\text{ 4}$ 

\[211.02\times 4=844.08\]

(vii) $\text{2 }\!\!\times\!\!\text{ 0}\text{.86}$ 

\[2\times 0.86=1.72\]

2. Find the area of rectangle whose length is \[\text{5}\text{.7 cm}\] and 

breadth is \[\text{3 cm}\text{.}\]

Ans: Given: The \[\text{Length of rectangle = 5}\text{.7 cm and Breadth of 

rectangle = 3 cm}\] 

Applying the area of rectangle formula,

\[\text{Area of rectangle = Length x Breadth}\] 

\[\text{= 5}\text{.7 x 3 = 17}\text{.1 c}{{\text{m}}^{2}}\]  

Hence, the area of rectangle is $\text{17}\text{.1}\,\text{c}{{\text{m}}^{\text{2}}}$.

(i) \[\text{1}\text{.3 }\!\!\times\!\!\text{ 10}\] 

$1.3\times 10=13.0$

(ii) \[\text{36}\text{.8 }\!\!\times\!\!\text{ 10}\] 

$36.8\times 10=368.0$

(iii) \[\text{153}\text{.7 }\!\!\times\!\!\text{ 10}\] 

$153.7\times 10=1537.0$

(iv) \[\text{168}\text{.07 }\!\!\times\!\!\text{ 10}\]

$168.07\times 10=1680.7$

(v) \[\text{31}\text{.1 }\!\!\times\!\!\text{ 100}\] 

$31.1\times 100=3110.0$

(vi) \[\text{156}\text{.1 }\!\!\times\!\!\text{ 100}\] 

$156.1\times 100=15610.0$

(vii) \[\text{3}\text{.62 }\!\!\times\!\!\text{ 100}\] 

$3.62\times 100=362.0$

(viii) \[\text{43}\text{.07 }\!\!\times\!\!\text{ 100}\] 

$43.07\times 100=4307.0$

(ix) \[\text{0}\text{.5 }\!\!\times\!\!\text{ 10}\] 

$0.5\times 10=5.0$ 

(x) \[\text{0}\text{.08 }\!\!\times\!\!\text{ 10}\] 

$0.08\times 10=0.80$ 

(xi) \[\text{0}\text{.9 }\!\!\times\!\!\text{ 100}\]

$0.9\times 100=90.0$

(xii) \[\text{0}\text{.03 }\!\!\times\!\!\text{ 1000}\] 

$0.03\times 1000=30.0$ 

4. A two-wheeler covers a distance of\[\text{ }\!\!~\!\!\text{ 55}\text{.3 

km}\] 

in one litre of petrol. How much distance will it cover in \[\text{10 litres}\] of 

Ans: Given: In one litre a two-wheeler covers a distance\[\text{ = 55}\text{.3 

Since distance covered in one litre by a two-wheeler\[\text{ = 55}\text{.3 km}\]

\[\therefore \,\,\text{In 10 litrs, a two- wheeler covers a distance = 55}\text{.3 x 10 = 553}\text{.0 km}\] 

Hence, $553$ km distance will be covered by two-wheeler in $10$ litres of petrol.

5.  Find:

(i) $\text{2}\text{.5 }\!\!\times\!\!\text{ 0}\text{.3}$

\[\text{2}\text{.5 x 0}\text{.3 = 0}\text{.75}\] 

(ii) $\text{0}\text{.1 }\!\!\times\!\!\text{ 51}\text{.7}$ 

\[\text{0}\text{.1 x 51}\text{.7 = 5}\text{.17}\]

(iii) $\text{0}\text{.2 }\!\!\times\!\!\text{ 316}\text{.8}$ 

\[\text{0}\text{.2 x 316}\text{.8 = 63}\text{.36}\]

(iv) $\text{1}\text{.3 }\!\!\times\!\!\text{ 1}\text{.3}$ 

\[\text{1}\text{.3 x 3}\text{.1 = 4}\text{.03}\]

(v) $\text{0}\text{.5 }\!\!\times\!\!\text{ 0}\text{.05}$ 

\[\text{0}\text{.5 x 0}\text{.05 = 0}\text{.025}\]

(vi) $\text{11}\text{.2 }\!\!\times\!\!\text{ 0}\text{.15}$ 

\[\text{11}\text{.2 x 0}\text{.15 = 1}\text{.680 }\]

(vii) $\text{1}\text{.07 }\!\!\times\!\!\text{ 0}\text{.02}$ 

\[\text{1}\text{.07 x 0}\text{.02 = 0}\text{.0214}\]

(viii) $\text{10}\text{.05 }\!\!\times\!\!\text{ 1}\text{.05}$

\[\text{10}\text{.05 x 1}\text{.05 = 10}\text{.5525}\]

(ix) $\text{101}\text{.01 }\!\!\times\!\!\text{ 0}\text{.01}$ 

\[\text{101}\text{.01 x 0}\text{.01 = 1}\text{.0101}\]

(x) $\text{100}\text{.01 }\!\!\times\!\!\text{ 1}\text{.1}$

\[\text{100}\text{.01 x 1}\text{.1 = 110}\text{.11 }\]

Exercise 2.7

(i) \[\text{0}\text{.4  }\!\!\div\!\!\text{  2}\] 

\[0.4\div 2=\frac{4}{10}\times \frac{1}{2}=\frac{2}{10}=0.2\]

(ii) \[\text{0}\text{.35  }\!\!\div\!\!\text{  5}\] 

\[0.35\div 5=\frac{35}{100}\times \frac{1}{5}=\frac{7}{100}=0.07\]

(iii) \[\text{2}\text{.48  }\!\!\div\!\!\text{  4}\] 

\[2.48\div 4=\frac{248}{100}\times \frac{1}{4}=\frac{62}{100}=0.62\]

(iv) \[\text{65}\text{.4  }\!\!\div\!\!\text{  6}\] 

\[65.4\div 6=\frac{654}{10}\times \frac{1}{6}=\frac{109}{10}=10.9\]

(v) \[\text{651}\text{.2  }\!\!\div\!\!\text{  4}\] 

\[651.2\div 4=\frac{6512}{10}\times \frac{1}{4}=\frac{1628}{10}=162.8\]

(vi) \[\text{14}\text{.49  }\!\!\div\!\!\text{  7 }\] 

\[14.49\div 7=\frac{1449}{100}\times \frac{1}{7}=\frac{207}{100}=2.07\]

(vii) \[\text{3}\text{.96  }\!\!\div\!\!\text{  4}\]

\[3.96\div 4=\frac{396}{100}\times \frac{1}{4}=\frac{99}{100}=0.99\]

(viii) \[\text{0}\text{.80  }\!\!\div\!\!\text{  5}\] 

\[0.80\div 5=\frac{80}{100}\times \frac{1}{5}=\frac{16}{100}=0.16\]

(i) \[\text{4}\text{.8  }\!\!\div\!\!\text{  10}\] 

Ans: Performing the given calculation,

$4.8\div 10=\frac{4.8}{10}=0.48$

(ii) \[\text{52}\text{.5  }\!\!\div\!\!\text{  10}\] 

$52.5\div 10=\frac{52.5}{10}=5.25$

(iii) \[\text{0}\text{.7  }\!\!\div\!\!\text{  10}\] 

$0.7\div 10=\frac{0.7}{10}=0.07$

(iv) \[\text{33}\text{.1  }\!\!\div\!\!\text{  10}\]

$33.1\div 10=\frac{33.1}{10}=3.31$

(v) \[\text{272}\text{.23  }\!\!\div\!\!\text{  10}\] 

$272.23\div 10=\frac{272.23}{10}=27.223$

(vi) \[\text{0}\text{.56  }\!\!\div\!\!\text{  10 }\] 

$0.56\div 10=\frac{0.56}{10}=0.056$

(vii) \[\text{3}\text{.97  }\!\!\div\!\!\text{  10}\] 

$3.97\div 10=\frac{3.97}{10}=0.397$

(i) \[\text{2}\text{.7  }\!\!\div\!\!\text{  100}\] 

Ans: Converting the terms in fraction form and calculating the value,

$2.7\div 100=\frac{27}{10}\times \frac{1}{100}=\frac{27}{1000}=0.027$ 

(ii) \[\text{0}\text{.3  }\!\!\div\!\!\text{  100 }\]

$0.3\div 100=\frac{3}{10}\times \frac{1}{100}=\frac{3}{1000}=0.003$

(iii) \[\text{0}\text{.78  }\!\!\div\!\!\text{  100}\] 

$0.78\div 100=\frac{78}{10}\times \frac{1}{100}=\frac{78}{1000}=0.0078$

(iv) \[\text{432}\text{.6  }\!\!\div\!\!\text{  100}\] 

$432.6\div 100=\frac{4326}{10}\times \frac{1}{100}=\frac{4326}{1000}=4.326$

(v) \[\text{23}\text{.6  }\!\!\div\!\!\text{  100}\] 

Ans: Converting the terms in fraction form and calculating the value,$23.6\div 100=\frac{236}{10}\times \frac{1}{100}=\frac{236}{1000}=0.236$

(vi) \[\text{98}\text{.53  }\!\!\div\!\!\text{  100}\] 

$98.53\div 100=\frac{9853}{10}\times \frac{1}{100}=\frac{9853}{1000}=0.9853$

(i) \[\text{7}\text{.9  }\!\!\div\!\!\text{  1000}\] 

$7.9\div 1000=\frac{79}{10}\times \frac{1}{1000}=\frac{79}{10000}=0.0079$ 

(ii) \[\text{26}\text{.3  }\!\!\div\!\!\text{  1000}\]

$26.3\div 1000=\frac{263}{10}\times \frac{1}{1000}=\frac{263}{10000}=0.0263$

(iii) \[\text{38}\text{.53  }\!\!\div\!\!\text{  1000}\] 

$38.53\div 1000=\frac{3853}{10}\times \frac{1}{1000}=\frac{3853}{10000}=0.03853$

(iv) \[\text{128}\text{.9  }\!\!\div\!\!\text{  1000}\] 

$128.9\div 1000=\frac{1289}{10}\times \frac{1}{1000}=\frac{1289}{10000}=0.1289$

(v) \[\text{0}\text{.5  }\!\!\div\!\!\text{  1000}\] 

$0.5\div 1000=\frac{5}{10}\times \frac{1}{1000}=\frac{5}{10000}=0.0005$

(i) \[\text{7  }\!\!\div\!\!\text{  3}\text{.5}\] 

$7\div 3.5=7\div \frac{35}{10}=7\times \frac{10}{35}=\frac{10}{5}=2$

(ii) \[\text{36  }\!\!\div\!\!\text{  0}\text{.2 }\]

$36\div 0.2=36\div \frac{2}{10}=36\times \frac{10}{2}=18\times 10=180$

(iii) \[\text{3}\text{.25  }\!\!\div\!\!\text{  0}\text{.5}\]  

Ans: Converting the terms in fraction form and calculating the value,$3.25\div 0.5=\frac{325}{100}\div \frac{5}{10}=\frac{325}{100}\times \frac{10}{5}=\frac{65}{10}=6.5$

(iv) \[\text{30}\text{.94  }\!\!\div\!\!\text{  0}\text{.7}\]

$30.94\div 0.7=\frac{3094}{100}\div \frac{7}{10}=\frac{3094}{100}\times \frac{10}{7}=\frac{442}{10}=44.2$

(v) \[\text{0}\text{.5  }\!\!\div\!\!\text{  0}\text{.25 }\] 

Ans: Converting the terms in fraction form and calculating the value,$0.5\div 0.25=\frac{5}{10}\div \frac{25}{100}=\frac{5}{10}\times \frac{100}{25}=\frac{10}{5}=2$

(vi) \[\text{7}\text{.75  }\!\!\div\!\!\text{  0}\text{.25}\] 

$7.75\div 0.25=\frac{775}{100}\div \frac{25}{100}=\frac{775}{100}\times \frac{100}{25}=31$

(vii) \[\text{76}\text{.5  }\!\!\div\!\!\text{  0}\text{.15}\] 

$76.5\div 0.15=\frac{765}{100}\div \frac{15}{100}=\frac{765}{10}\times \frac{100}{15}=51\times 10=510$

(viii) \[\text{37}\text{.8  }\!\!\div\!\!\text{  1}\text{.4}\]

$37.8\div 1.4=\frac{378}{10}\div \frac{14}{10}=\frac{378}{10}\times \frac{10}{14}=27$

(ix) \[\text{2}\text{.73  }\!\!\div\!\!\text{  1}\text{.3 }\] 

$2.73\div 1.3=\frac{273}{100}\div \frac{13}{10}=\frac{273}{100}\times \frac{10}{13}=\frac{21}{10}=2.1$

6. A vehicle covers a distance of \[\text{43}\text{.2 km}\] in

\[\text{2}\text{.4}\]litres of petrol. How much distance will it cover in one 

litre 

Ans: Given: \[\,\,\,\text{In 2}\text{.4 litres of petrol, distance covered by the vehicle = 43}\text{.2 km}\]

Since,\[\,\,\,\text{In 2}\text{.4 litres of petrol, distance covered by the vehicle = 43}\text{.2 km}\]

\[\therefore \,\,\text{In 1 litre of petrol, distance covered by the vehicle = 43}\text{.2  }\!\!\div\!\!\text{  2}\text{.4}\] 

Performing the required calculations,

$=\frac{432}{10}\div \frac{24}{10}=\frac{432}{10}\times \frac{24}{10}$ 

$\text{=18}\,\text{km}$ 

Hence, the vehicle can cover \[\text{18 km}\] distance in one litre of petrol.

NCERT Solutions for Class 7 Chapter 2 Maths PDF download

It is the best choice to download NCERT Solutions for Class 7 Maths Chapter 2 PDF available on Vedantu. Students can find all the solutions for solving problems in class 7 at their convenience. Several experts gave their best in preparing these solutions to find answers and compiled them all in our NCERT Solutions for Class 7 Maths Chapter 2 for all students to understand the concepts.

Key Concepts Covered in NCERT Solutions for CBSE Class 7 Maths Chapter 2 Fractions and Decimals

Some important concepts discussed in Chapter 2 Fractions and Decimals of NCERT Solutions Class 7 Maths are:

Addition and Subtraction of Fractions.

Multiplication of Fractions.

Multiplication of a Fraction by a Whole Number.

Multiplication of a Fraction by a Fraction.

Division of Fraction.

Division of Whole Number by a Fraction.

Reciprocal of Fraction.

Division of a Fraction by a Whole Number.

Division of Fraction by Another Fraction.

Multiplication of Decimal Numbers.

Multiplication of Decimal Numbers by 10, 100 and 1000.

Division of Decimal Numbers.

Division of Decimals by 10, 100 and 1000.

Division of a Decimal Number by a Whole Number.

Division of a Decimal Number by Another Decimal Number.

NCERT Solutions for Class 7 Chapter 2 Maths PDF Download

It is the best choice to download NCERT Solutions for Class 7 Maths Chapter 2 PDF available on Vedantu. Students can find all the solutions for solving the sums of this chapter at their convenience. Several experts gave their best in preparing these solutions to find answers and compiled them all in our NCERT Solutions for Class 7 Maths Chapter 2 for all students to understand the concepts. 

2.1 Introduction

In NCERT Solutions Class 7 Chapter 2 Maths, students will learn about fractions and decimals. In junior classes, students have learned about what is a fraction and its types: proper, improper, mixed fractions, etc. Now, in class 7, we are going to learn about multiplication and division of fractions. The concept of fractions mainly focuses on the ratios and proportions, how to distribute etc. At the same time, decimals are the accurate values obtained after the division.

2.2 Recollect

In NCERT Solutions Class 7 Maths Chapter 2, students need to think again on the topics they have learned so far in the previous classes. These include representation of fractions on the number line, ordering of fractions, addition and subtraction of fractions, decimals and their additions, how to keep a point, etc. These are reminded in the first two exercises.

2.3 Multiplication of Fractions

In this section, students can understand how to multiply two fractions. If students have values like a and b, they can say ab is the product of a and b. If the values are like p/q, a/b then, how can we multiply? To multiply these fractions, it has two different methods. One is by using a  whole number and the other is by using a portion.

2.3.1 Multiplication of Fractions Using the Whole Number

Here, let us see what Fraction tells us? It explains that a down part is a whole number (except zero) and the upper part is the integer. In a fraction, the down part is known as the denominator whereas the upper part is the numerator. We use a whole number to multiply fractions if they are the same. For instance, let's say we have p/q. Then we can multiply with the whole number as 3*p/q. It is also applicable for improper or mixed fractions. But students need to make them into simpler forms before multiplying.

2.3.1 Multiplication of Fractions Using the Fraction

In this section, students can learn how to multiply two fractions when they are dissimilar. Students use a fraction to multiply them. The formula for multiplying two fractions is,(product of numerators)/(product of denominators).

The resultant product is less than the two fractions if we multiply two proper fractions. On the other hand, the result is greater than the two fractions if we multiply two improper fractions.

2.4 Division of Fractions

Let's discuss the division of fractions. Students can divide a fraction by a whole number and a whole number by a fraction. Here is a particular case to keep in mind. If two fractions for which numerator and denominator are in reverse order, then they are called reciprocals to each other.  Their product is always 1.

In the same way, while dividing mixed fractions with a whole number, students need to change the mixed fraction into improper fractions. Then it is easy to divide and solve. Next, we have to learn to divide a fraction with another fraction by changing one of the fractions into its reciprocal form.

The three concepts are explained differently in the NCERT Solutions for Class 7 Maths Chapter 2 PDF book available on Vedantu for students to go through if necessary.

2.5 Recalling Decimals

Decimals are the proper forms to represent the results obtained from multiplication and division. Placing the point in between numbers plays a vital role. One can express the heights, distances, weights,  measuring values, interest rates, shares, and fractions, also using decimals. To change the place value of the point, we can multiply by 10,100,...... Let's have a glance at the addition and subtraction of decimals.

2.6 Multiplication of Decimals

In this section, students are going to practice the multiplication of decimals. Even though multiplication is easy, doubts might arise in students' minds while keeping a point. For this, we need to count the number of values after a decimal point in both the numbers and then keep the point before that number of places in the result. It plays a crucial role here. Another variation of Multiplication of Decimals is changing the place value of a decimal point by multiplying it with 10 multiples. It was already discussed by us earlier.

2.7 Division of Decimals

In this section, students will learn how to divide decimals and how many variations it has?  Students can understand the first one, which is explained in 2.7.1 in the PDF. Here let's divide the whole number with 10 multiples; it gives decimals. Similarly, let's divide decimals, we will get whole numbers. Next is the division of decimals with a whole number. Here the place value of the decimal point doesn't change in the result also. 

Students can refer to 2.7.2 in the PDF for further information. Finally,  2.7.3 contains the topic of the division of a decimal with other decimals. Here, students need to replace the decimal point to the right side with the same number of places in both. Then students can divide easily as it becomes the whole number.

NCERT Solutions for Class 7 Maths Chapter 2 Exercises

Ncert solutions for class 7 maths.

Chapter 1 - Integers

Chapter 3 - Data Handling

Chapter 4 - Simple Equations

Chapter 5 - Lines and Angles

Chapter 6 - The Triangle and Its Properties

Chapter 7 - Congruence of Triangles

Chapter 8 - Comparing Quantities

Chapter 9 - Rational Numbers

Chapter 10 - Practical Geometry

Chapter 11 - Perimeter and Area

Chapter 12 - Algebraic Expressions

Chapter 13 - Exponents and Powers

Chapter 14 - Symmetry

Chapter 15 - Visualizing Solid Shapes

Students can also refer to the following study material for Chapter 2 of Class 7 Maths:

Chapter 2 Fractions and Decimals: Important Questions

Chapter 2 Fractions and Decimals: Revision Notes

Chapter 2 Fractions and Decimals: Formulas

Chapter 2 Fractions and Decimals: RD Sharma Solutions

Chapter 2 Fractions and Decimals: NCERT Exemplar Solutions

Chapter 2 Fractions and Decimals: RS Aggarwal Solutions

Key Features of NCERT Solutions for Class 7 Maths Chapter 2

Practice makes a man perfect. It is perfectly apt for Mathematics. As much as students practice several problems, students will become experts and can solve problems easily and quickly. It helps to improve a student's thinking ability also. It also makes students score cent percent. NCERT Solutions for Class 7th Maths Chapter 2 Fractions and Decimals on Vedantu are an add-on for students' practice and goals. Students can choose the NCERT Solutions for Class 7 Maths for various reasons like:

It has several examples with answers in detail, which helps students to solve smartly.

An excellent explanation is available for every concept separately.

It builds confidence to attempt competitive exams at the national level.

Highly qualified trainers available online to prepare the PDFs.

Students should clear their doubts through live chats with instructors.

They provide the questions in the exam pattern so students can learn how to present in the exam also.

The first few exercises in the Class 7 Maths Chapter 2 Fractions and Decimals explain the addition and subtraction of fractions and decimals, as well as a review of fractions and decimals concepts studied in previous classes with appropriate examples.

The sample problems in class 7 NCERT solutions chapter 2 fractions and decimals are sufficient for students to gain a thorough understanding of applying arithmetic operations to fractions and decimals.

So, to score good marks in Maths easily, solve these NCERT Solutions  for CBSE Class 7 Maths Chapter 2 Fractions and Decimals regularly. It will help you understand all the concepts and you’ll be able to solve all the questions on your own. But, along with the NCERT Solutions do not forget to solve the sample papers and previous year's question papers.

FAQs on NCERT Solutions for Class 7 Maths Chapter 2 - Fractions And Decimals

1. What are the main topics and subtopics covered in chapter 2 of Class 7 Maths?

Topics and sub-topics discussed in Chapter 2 Fractions and Decimals of NCERT Solutions Class 7 Maths are: Addition and Subtraction of Fractions, Multiplication of Fraction, Multiplication of a Fraction by a Whole Number, Multiplication of a Fraction by a Fraction, Division of Fraction, Division of Whole Number by a Fraction, Reciprocal of Fraction, Division of a fraction by a Whole Number, Division of Fraction by Another Fraction, Multiplication of Decimal Numbers, Multiplication of Decimal Numbers by 10, 100 and 1000, Division of Decimal Numbers, Division of Decimals by 10, 100 and 1000, Division of a Decimal Number by a Whole Number and Division of a Decimal Number by Another Decimal Number.

2. How many questions are there in exercises of chapter 2 of Class 7 Maths?

There are a total of seven exercises given in the second chapter of Class 7 Maths. Exercise 2.1 has 8 questions, exercise 2.2 has 8 questions, exercise 2.3 has 8 questions, exercise 2.4 has 4 questions, exercise 2.5 has 9 questions, exercise 2.6 has 5 questions, and exercise 2.7 has 6 questions.

3. Why should I choose Vedantu’s Class 7 Maths Chapter 2 NCERT Solutions?

Vedantu’s Class 7 Maths NCERT Solutions titled Fractions and Decimals are highly useful while preparing for the final exam. NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals cover all the questions from the exercises of this chapter prepared by experienced Vedantu teachers. Our NCERT Solutions for Class 7 Maths have been designed to help you develop your knowledge base which will ultimately improve your exam performance.

All the necessary and important questions along with other study materials have been covered by us in order to make your revision much easier for the final exam.

4. What are the different types of fractions?

There are three main types of fractions: proper fractions, improper fractions, and mixed numbers.

Proper fractions: These are fractions whose numerator is smaller than the denominator. For example, 1/2 and 3/5 are proper fractions.

Improper fractions: These are fractions whose numerator is larger than or equal to the denominator. For example, 5/3 and 8/2 are improper fractions.

Mixed numbers: These are numbers that are made up of a whole number and a fraction. For example, 2 1/2 is a mixed number.

5. What are the different types of decimals?

There are two main types of decimals: terminating decimals and non-terminating decimals.

Terminating decimals: These are decimals that end after a finite number of digits. For example, 0.5 and 1.23 are terminating decimals.

Non-terminating decimals: These are decimals that do not end after a finite number of digits. For example, 1/3 and 1/2 are non-terminating decimals.

6. What are the uses of fractions and decimals?

Fractions and decimals are used in a variety of ways in mathematics and everyday life.

In mathematics, fractions and decimals are used to represent parts of a whole, to perform arithmetic operations, and to solve equations.

In everyday life, fractions and decimals are used to represent quantities such as money, time, and measurements.

NCERT Solutions for Class 7

Fractions Worksheets

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting... by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

Fraction Circles

Fraction circle manipulatives are mainly used for comparing fractions, but they can be used for a variety of other purposes such as representing and identifying fractions, adding and subtracting fractions, and as probability spinners. There are a variety of options depending on your purpose. Fraction circles come in small and large versions, labeled and unlabeled versions and in three different color schemes: black and white, color, and light gray. The color scheme matches the fraction strips and use colors that are meant to show good contrast among themselves. Do note that there is a significant prevalence of color-blindness in the population, so don't rely on all students being able to differentiate the colors.

Suggested activity for comparing fractions: Photocopy the black and white version onto an overhead projection slide and another copy onto a piece of paper. Alternatively, you can use two pieces of paper and hold them up to the light for this activity. Use a pencil to represent the first fraction on the paper copy. Use a non-permanent overhead pen to represent the second fraction. Lay the slide over the paper and compare the two circles. You should easily be able to tell which is greater or lesser or if the two fractions are equal. Re-use both sheets by erasing the pencil and washing off the marker.

Adding fractions with fraction circles will involve two copies on paper. Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work.

• Small Fraction Circles Small Fraction Circles in Black and White with Labels Small Fraction Circles in Color with Labels Small Fraction Circles in Light Gray with Labels Small Fraction Circles in Black and White Unlabeled Small Fraction Circles in Color Unlabeled Small Fraction Circles in Light Gray Unlabeled
• Large Fraction Circles Large Fraction Circles in Black and White with Labels Large Fraction Circles in Color with Labels Large Fraction Circles in Light Gray with Labels Large Fraction Circles in Black and White Unlabeled Large Fraction Circles in Color Unlabeled Large Fraction Circles in Light Gray Unlabeled

Fraction Strips

Fractions strips are often used for comparing fractions. Students are able to see quite easily the relationships and equivalence between fractions with different denominators. It can be quite useful for students to have two copies: one copy cut into strips and the other copy kept intact. They can then use the cut-out strips on the intact page to individually compare fractions. For example, they can use the halves strip to see what other fractions are equivalent to one-half. This can also be accomplished with a straight edge such as a ruler without cutting out any strips. Pairs or groups of strips can also be compared side-by-side if they are cut out. Addition and subtraction (etc.) are also possibilities; for example, adding a one-quarter and one-third can be accomplished by shifting the thirds strip so that it starts at the end of one-quarter then finding a strip that matches the end of the one-third mark (7/12 should do it).

Teachers might consider copying the fraction strips onto overhead projection acetates for whole class or group activities. Acetate versions are also useful as a hands-on manipulative for students in conjunction with an uncut page.

The "Smart" Fraction Strips include strips in a more useful order, eliminate the 7ths and 11ths strips as they don't have any equivalents and include 15ths and 16ths. The colors are consistent with the classic versions, so the two sets can be combined.

• Classic Fraction Strips with Labels Classic Fraction Strips in Black and White With Labels Classic Fraction Strips in Color With Labels Classic Fraction Strips in Gray With Labels
• Unlabeled Classic Fraction Strips Classic Fraction Strips in Black and White Unlabeled Classic Fraction Strips in Color Unlabeled Classic Fraction Strips in Gray Unlabeled
• Smart Fraction Strips with Labels Smart Fraction Strips in Black and White With Labels Smart Fraction Strips in Color With Labels Smart Fraction Strips in Gray With Labels

Modeling fractions

Fractions can represent parts of a group or parts of a whole. In these worksheets, fractions are modeled as parts of a group. Besides using the worksheets in this section, you can also try some more interesting ways of modeling fractions. Healthy snacks can make great models for fractions. Can you cut a cucumber into thirds? A tomato into quarters? Can you make two-thirds of the grapes red and one-third green?

• Modeling Fractions with Groups of Shapes Coloring Groups of Shapes to Represent Fractions Identifying Fractions from Colored Groups of Shapes (Only Simplified Fractions up to Eighths) Identifying Fractions from Colored Groups of Shapes (Halves Only) Identifying Fractions from Colored Groups of Shapes (Halves and Thirds) Identifying Fractions from Colored Groups of Shapes (Halves, Thirds and Fourths) Identifying Fractions from Colored Groups of Shapes (Up to Fifths) Identifying Fractions from Colored Groups of Shapes (Up to Sixths) Identifying Fractions from Colored Groups of Shapes (Up to Eighths) Identifying Fractions from Colored Groups of Shapes (OLD Version; Print Too Light)
• Modeling Fractions with Rectangles Modeling Halves Modeling Thirds Modeling Halves and Thirds Modeling Fourths (Color Version) Modeling Fourths (Grey Version) Coloring Fourths Models Modeling Fifths Coloring Fifths Models Modeling Sixths Coloring Sixths Models
• Modeling Fractions with Circles Modeling Halves, Thirds and Fourths Coloring Halves, Thirds and Fourths Modeling Halves, Thirds, Fourths, and Fifths Coloring Halves, Thirds, Fourths, and Fifths Modeling Halves to Sixths Coloring Halves to Sixths Modeling Halves to Eighths Coloring Halves to Eighths Modeling Halves to Twelfths Coloring Halves to Twelfths

Ratio and Proportion Worksheets

The equivalent fractions models worksheets include only the "baking fractions" in the A versions. To see more difficult and varied fractions, please choose the B to J versions after loading the A version. More picture ratios can be found on holiday and seasonal pages. Try searching for picture ratios to find more.

• Picture Ratios Autumn Trees Part-to-Part Picture Ratios ( Grouped ) Autumn Trees Part-to-Part and Part-to-Whole Picture Ratios ( Grouped )
• Equivalent Fractions Equivalent Fractions With Blanks ( Multiply Right ) ✎ Equivalent Fractions With Blanks ( Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply Right or Divide Left ) ✎ Equivalent Fractions With Blanks ( Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply Left ) ✎ Equivalent Fractions With Blanks ( Multiply Left or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Right ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide Left ) ✎ Equivalent Fractions With Blanks ( Multiply or Divide in Either Direction ) ✎ Are These Fractions Equivalent? (Multiplier 2 to 5) Are These Fractions Equivalent? (Multiplier 5 to 15) Equivalent Fractions Models Equivalent Fractions Models with the Simplified Fraction First Equivalent Fractions Models with the Simplified Fraction Second
• Equivalent Ratios Equivalent Ratios with Blanks Only on Right Equivalent Ratios with Blanks Anywhere Equivalent Ratios with x 's

Comparing and Ordering Fractions

Comparing fractions involves deciding which of two fractions is greater in value or if the two fractions are equal in value. There are generally four methods that can be used for comparing fractions. First is to use common denominators . If both fractions have the same denominator, comparing the fractions simply involves comparing the numerators. Equivalent fractions can be used to convert one or both fractions, so they have common denominators. A second method is to convert both fractions to a decimal and compare the decimal numbers. Visualization is the third method. Using something like fraction strips , two fractions can be compared with a visual tool. The fourth method is to use a cross-multiplication strategy where the numerator of the first fraction is multiplied by the denominator of the second fraction; then the numerator of the second fraction is multiplied by the denominator of the first fraction. The resulting products can be compared to decide which fraction is greater (or if they are equal).

• Comparing Proper Fractions Comparing Proper Fractions to Sixths ✎ Comparing Proper Fractions to Ninths (No Sevenths) ✎ Comparing Proper Fractions to Ninths ✎ Comparing Proper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper Fractions to Twelfths ✎

The worksheets in this section also include improper fractions. This might make the task of comparing even easier for some questions that involve both a proper and an improper fraction. If students recognize one fraction is greater than one and the other fraction is less than one, the greater fraction will be obvious.

• Comparing Proper and Improper Fractions Comparing Proper and Improper Fractions to Sixths ✎ Comparing Proper and Improper Fractions to Ninths (No Sevenths) ✎ Comparing Proper and Improper Fractions to Ninths ✎ Comparing Proper and Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper and Improper Fractions to Twelfths ✎ Comparing Improper Fractions to Sixths ✎ Comparing Improper Fractions to Ninths (No Sevenths) ✎ Comparing Improper Fractions to Ninths ✎ Comparing Improper Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper Fractions to Twelfths ✎

This section additionally includes mixed fractions. When comparing mixed and improper fractions, it is useful to convert one of the fractions to the other's form either in writing or mentally. Converting to a mixed fraction is probably the better route since the first step is to compare the whole number portions, and if one is greater than the other, the proper fraction portion can be ignored. If the whole number portions are equal, the proper fractions must be compared to see which number is greater.

• Comparing Proper, Improper and Mixed Fractions Comparing Proper, Improper and Mixed Fractions to Sixths ✎ Comparing Proper, Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Ninths ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Proper, Improper and Mixed Fractions to Twelfths ✎
• Comparing Improper and Mixed Fractions Comparing Improper and Mixed Fractions to Sixths ✎ Comparing Improper and Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Improper and Mixed Fractions to Ninths ✎ Comparing Improper and Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Improper and Mixed Fractions to Twelfths ✎
• Comparing Mixed Fractions Comparing Mixed Fractions to Sixths ✎ Comparing Mixed Fractions to Ninths (No Sevenths) ✎ Comparing Mixed Fractions to Ninths ✎ Comparing Mixed Fractions to Twelfths (No Sevenths; No Elevenths) ✎ Comparing Mixed Fractions to Twelfths ✎

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We've probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won't cut it. Try using some visuals to reinforce this important concept. Even though we've included number lines below, feel free to use your own strategies.

• Ordering Fractions with Easy Denominators on a Number Line Ordering Fractions with Easy Denominators to 10 on a Number Line Ordering Fractions with Easy Denominators to 24 on a Number Line Ordering Fractions with Easy Denominators to 60 on a Number Line Ordering Fractions with Easy Denominators to 100 on a Number Line
• Ordering Fractions with Easy Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with Easy Denominators to 10 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 24 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 60 + Negatives on a Number Line Ordering Fractions with Easy Denominators to 100 + Negatives on a Number Line
• Ordering Fractions with All Denominators on a Number Line Ordering Fractions with All Denominators to 10 on a Number Line Ordering Fractions with All Denominators to 24 on a Number Line Ordering Fractions with All Denominators to 60 on a Number Line Ordering Fractions with All Denominators to 100 on a Number Line
• Ordering Fractions with All Denominators on a Number Line (Including Negative Fractions) Ordering Fractions with All Denominators to 10 + Negatives on a Number Line Ordering Fractions with All Denominators to 24 + Negatives on a Number Line Ordering Fractions with All Denominators to 60 + Negatives on a Number Line Ordering Fractions with All Denominators to 100 + Negatives on a Number Line

The ordering fractions worksheets in this section do not include a number line, to allow for students to use various sorting strategies.

• Ordering Positive Fractions Ordering Positive Fractions with Like Denominators Ordering Positive Fractions with Like Numerators Ordering Positive Fractions with Like Numerators or Denominators Ordering Positive Fractions with Proper Fractions Only Ordering Positive Fractions with Improper Fractions Ordering Positive Fractions with Mixed Fractions Ordering Positive Fractions with Improper and Mixed Fractions
• Ordering Positive and Negative Fractions Ordering Positive and Negative Fractions with Like Denominators Ordering Positive and Negative Fractions with Like Numerators Ordering Positive and Negative Fractions with Like Numerators or Denominators Ordering Positive and Negative Fractions with Proper Fractions Only Ordering Positive and Negative Fractions with Improper Fractions Ordering Positive and Negative Fractions with Mixed Fractions Ordering Positive and Negative Fractions with Improper and Mixed Fractions

Simplifying & Converting Fractions Worksheets

Rounding fractions helps students to understand fractions a little better and can be applied to estimating answers to fractions questions. For example, if one had to estimate 1 4/7 × 6, they could probably say the answer was about 9 since 1 4/7 is about 1 1/2 and 1 1/2 × 6 is 9.

• Rounding Fractions with Helper Lines Rounding Fractions to the Nearest Whole with Helper Lines Rounding Mixed Numbers to the Nearest Whole with Helper Lines Rounding Fractions to the Nearest Half with Helper Lines Rounding Mixed Numbers to the Nearest Half with Helper Lines
• Rounding Fractions Rounding Fractions to the Nearest Whole Rounding Mixed Numbers to the Nearest Whole Rounding Fractions to the Nearest Half Rounding Mixed Numbers to the Nearest Half

Learning how to simplify fractions makes a student's life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

• Simplifying Fractions Simplify Fractions (easier) Simplify Fractions (harder) Simplify Improper Fractions (easier) Simplify Improper Fractions (harder)
• Converting Between Improper and Mixed Fractions Converting Mixed Fractions to Improper Fractions Converting Improper Fractions to Mixed Fractions Converting Between (both ways) Mixed and Improper Fractions
• Converting Between Fractions and Decimals Converting Fractions to Terminating Decimals Converting Fractions to Terminating and Repeating Decimals Converting Terminating Decimals to Fractions Converting Terminating and Repeating Decimals to Fractions Converting Fractions to Hundredths
• Converting Between Fractions, Decimals, Percents and Ratios with Terminating Decimals Only Converting Fractions to Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Fractions to Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Decimals to Fractions, Percents and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Part Ratios ( Terminating Decimals Only) Converting Percents to Fractions, Decimals and Part-to- Whole Ratios ( Terminating Decimals Only) Converting Part-to-Part Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Part-to-Whole Ratios to Fractions, Decimals and Percents ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios ( Terminating Decimals Only) Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios ( Terminating Decimals Only)
• Converting Between Fractions, Decimals, Percents and Ratios with Terminating and Repeating Decimals Converting Fractions to Decimals, Percents and Part-to- Part Ratios Converting Fractions to Decimals, Percents and Part-to- Whole Ratios Converting Decimals to Fractions, Percents and Part-to- Part Ratios Converting Decimals to Fractions, Percents and Part-to- Whole Ratios Converting Percents to Fractions, Decimals and Part-to- Part Ratios Converting Percents to Fractions, Decimals and Part-to- Whole Ratios Converting Part-to-Part Ratios to Fractions, Decimals and Percents Converting Part-to-Whole Ratios to Fractions, Decimals and Percents Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios Converting Various Fractions, Decimals, Percents and Part-to- Part Ratios with 7ths and 11ths Converting Various Fractions, Decimals, Percents and Part-to- Whole Ratios with 7ths and 11ths

Multiplying Fractions

Multiplying fractions is usually less confusing operationally than any other operation and can be less confusing conceptually if approached in the right way. The algorithm for multiplying is simply multiply the numerators then multiply the denominators. The magic word in understanding the multiplication of fractions is, "of." For example what is two-thirds OF six? What is a third OF a half? When you use the word, "of," it gets much easier to visualize fractions multiplication. Example: cut a loaf of bread in half, then cut the half into thirds. One third OF a half loaf of bread is the same as 1/3 x 1/2 and tastes delicious with butter.

• Multiplying Two Proper Fraction Multiplying Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ ✎ Multiplying Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Proper Fractions with No Simplifying (Printable Only) Multiplying Two Proper Fractions with All Simplifying (Printable Only) Multiplying Two Proper Fractions with Some Simplifying (Printable Only)
• Multiplying Proper and Improper Fractions Multiplying Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying Proper and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying Two Improper Fractions Multiplying Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Improper Fractions with No Simplifying (Printable Only) Multiplying Two Improper Fractions with All Simplifying (Printable Only) Multiplying Two Improper Fractions with Some Simplifying (Printable Only)
• Multiplying Proper and Mixed Fractions Multiplying Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying Two Mixed Fractions Multiplying Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Two Mixed Fractions with No Simplifying (Printable Only) Multiplying Two Mixed Fractions with All Simplifying (Printable Only) Multiplying Two Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying Whole Numbers and Proper Fractions Multiplying Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
• Multiplying Whole Numbers and Improper Fractions Multiplying Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying Whole Numbers and Mixed Fractions Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying Proper, Improper and Mixed Fractions Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying 3 Fractions Multiplying 3 Proper Fractions (Fillable, Savable, Printable) ✎ Multiplying 3 Proper and Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying Proper and Improper Fractions and Whole Numbers (3 factors) (Fillable, Savable, Printable) ✎ Multiplying Fractions and Mixed Fractions (3 factors) (Fillable, Savable, Printable) ✎ Multiplying 3 Mixed Fractions (Fillable, Savable, Printable) ✎

Dividing Fractions

Conceptually, dividing fractions is probably the most difficult of all the operations, but we're going to help you out. The algorithm for dividing fractions is just like multiplying fractions, but you find the inverse of the second fraction or you cross-multiply. This gets you the right answer which is extremely important especially if you're building a bridge. We told you how to conceptualize fraction multiplication, but how does it work with division? Easy! You just need to learn the magic phrase: "How many ____'s are there in ______? For example, in the question 6 ÷ 1/2, you would ask, "How many halves are there in 6?" It becomes a little more difficult when both numbers are fractions, but it isn't a giant leap to figure it out. 1/2 ÷ 1/4 is a fairly easy example, especially if you think in terms of U.S. or Canadian coins. How many quarters are there in a half dollar?

• Dividing Two Proper Fractions Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Proper Fractions with No Simplifying (Printable Only) Dividing Two Proper Fractions with All Simplifying (Printable Only) Dividing Two Proper Fractions with Some Simplifying (Printable Only)
• Dividing Proper and Improper Fractions Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
• Dividing Two Improper Fractions Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Improper Fractions with No Simplifying (Printable Only) Dividing Two Improper Fractions with All Simplifying (Printable Only) Dividing Two Improper Fractions with Some Simplifying (Printable Only)
• Dividing Proper and Mixed Fractions Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
• Dividing Two Mixed Fractions Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Two Mixed Fractions with No Simplifying (Printable Only) Dividing Two Mixed Fractions with All Simplifying (Printable Only) Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
• Dividing Whole Numbers and Proper Fractions Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
• Dividing Whole Numbers and Improper Fractions Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
• Dividing Whole Numbers and Mixed Fractions Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
• Dividing Proper, Improper and Mixed Fractions Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
• Dividing 3 Fractions Dividing 3 Fractions Dividing 3 Fractions (Some Whole Numbers) Dividing 3 Fractions (Some Mixed) Dividing 3 Mixed Fractions

Multiplying and Dividing Fractions

This section includes worksheets with both multiplication and division mixed on each worksheet. Students will have to pay attention to the signs.

• Multiplying and Dividing Two Proper Fractions Multiplying and Dividing Two Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Proper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Proper and Improper Fractions Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Two Improper Fractions Multiplying and Dividing Two Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Improper Fractions (Printable Only)
• Multiplying and Dividing Proper and Mixed Fractions Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Two Mixed Fractions Multiplying and Dividing Two Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Two Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Two Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Whole Numbers and Proper Fractions Fractions Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Proper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Proper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Whole Numbers and Improper Fractions Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Improper Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Improper Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Whole Numbers and Mixed Fractions Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Whole Numbers and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Whole Numbers and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing Proper, Improper and Mixed Fractions Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying and Dividing Proper, Improper and Mixed Fractions with No Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with All Simplifying (Printable Only) Multiplying and Dividing Proper, Improper and Mixed Fractions with Some Simplifying (Printable Only)
• Multiplying and Dividing 3 Fractions Multiplying/Dividing Fractions (three factors) Multiplying/Dividing Mixed Fractions (3 factors)

Adding Fractions

Adding fractions requires the annoying common denominator. Make it easy on your students by first teaching the concepts of equivalent fractions and least common multiples. Once students are familiar with those two concepts, the idea of finding fractions with common denominators for adding becomes that much easier. Spending time on modeling fractions will also help students to understand fractions addition. Relating fractions to familiar examples will certainly help. For example, if you add a 1/2 banana and a 1/2 banana, you get a whole banana. What happens if you add a 1/2 banana and 3/4 of another banana?

• Adding Two Proper Fractions with Equal Denominators and Proper Fraction Results Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Equal Denominators and Mixed Fraction Results Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Equal Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Similar Denominators and Proper Fraction Results Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Similar Denominators and Mixed Fraction Results Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Similar Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Unlike Denominators and Proper Fraction Results Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Proper Fractions Result, and Some Simplifying (Printable Only)
• Adding Two Proper Fractions with Unlike Denominators and Mixed Fraction Results Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and No Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and All Simplifying (Printable Only) Adding Two Proper Fractions with Unlike Denominators, Mixed Fractions Result, and Some Simplifying (Printable Only)
• Adding Proper and Improper Fractions with Equal Denominators Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
• Adding Proper and Improper Fractions with Similar Denominators Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
• Adding Proper and Improper Fractions with Unlike Denominators Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)

A common strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. Another strategy which requires a little less brainpower is to look at the whole numbers and fractions separately. Add the whole numbers first. Add the fractions second. If the resulting fraction is improper, then it needs to be converted to a mixed number. The whole number portion can be added to the original whole number portion.

• Adding Two Mixed Fractions with Equal Denominators Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
• Adding Two Mixed Fractions with Similar Denominators Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Similar Denominators and Some Simplifying Adding Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
• Adding Two Mixed Fractions with Unlike Denominators Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) Adding Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)

Subtracting Fractions

There isn't a lot of difference between adding and subtracting fractions. Both require a common denominator which requires some prerequisite knowledge. The only difference is the second and subsequent numerators are subtracted from the first one. There is a danger that you might end up with a negative number when subtracting fractions, so students might need to learn what it means in that case. When it comes to any concept in fractions, it is always a good idea to relate it to a familiar or easy-to-understand situation. For example, 7/8 - 3/4 = 1/8 could be given meaning in the context of a race. The first runner was 7/8 around the track when the second runner was 3/4 around the track. How far ahead was the first runner? (1/8 of the track).

• Subtracting Two Proper Fractions with Equal Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Two Proper Fractions with Similar Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Two Proper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Two Proper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Equal Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Similar Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Unlike Denominators and Proper Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Proper Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Equal Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Equal Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Similar Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Similar Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Proper and Improper Fractions with Unlike Denominators and Mixed Fraction Results Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and No Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and All Simplifying (Printable Only) Subtracting Proper and Improper Fractions with Unlike Denominators, Mixed Fractions Results, and Some Simplifying (Printable Only)
• Subtracting Mixed Fractions with Equal Denominators Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Equal Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Equal Denominators, and Some Simplifying (Printable Only)
• Subtracting Mixed Fractions with Similar Denominators Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Similar Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Similar Denominators, and Some Simplifying (Printable Only)
• Subtracting Mixed Fractions with Unlike Denominators Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Mixed Fractions with Unlike Denominators, and No Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and All Simplifying (Printable Only) Subtracting Mixed Fractions with Unlike Denominators, and Some Simplifying (Printable Only)

Adding and Subtracting Fractions

Mixing up the signs on operations with fractions worksheets makes students pay more attention to what they are doing and allows for a good test of their skills in more than one operation.

• Adding and Subtracting Proper and Improper Fractions Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
• Adding and Subtracting Mixed Fractions Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ Adding and Subtracting Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only) Adding and Subtracting Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only) Adding/Subtracting Three Fractions/Mixed Fractions

All Operations Fractions Worksheets

• All Operations with Two Proper Fractions with Equal Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Equal Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
• All Operations with Two Proper Fractions with Similar Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Similar Denominators, Proper Fractions Results and Some Simplifying (Printable Only)
• All Operations with Two Proper Fractions with Unlike Denominators and Proper Fraction Results All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and No Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Proper Fractions Results and All Simplifying (Printable Only) All Operations with Two Proper Fractions with Unlike Denominators, Mixed Fractions Results and Some Simplifying (Printable Only)
• All Operations with Proper and Improper Fractions with Equal Denominators All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Equal Denominators and Some Simplifying (Printable Only)
• All Operations with Proper and Improper Fractions with Similar Denominators All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Similar Denominators and Some Simplifying (Printable Only)
• All Operations with Proper and Improper Fractions with Unlike Denominators All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Proper and Improper Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Proper and Improper Fractions with Unlike Denominators and Some Simplifying (Printable Only)
• All Operations with Two Mixed Fractions with Equal Denominators All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Equal Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Equal Denominators and Some Simplifying (Printable Only)
• All Operations with Two Mixed Fractions with Similar Denominators All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Similar Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Similar Denominators and Some Simplifying (Printable Only)
• All Operations with Two Mixed Fractions with Unlike Denominators All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Fillable, Savable, Printable) ✎ All Operations with Two Mixed Fractions with Unlike Denominators and No Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and All Simplifying (Printable Only) All Operations with Two Mixed Fractions with Unlike Denominators and Some Simplifying (Printable Only)
• All Operations with 3 Fractions All Operations with Three Fractions Including Some Improper Fractions All Operations with Three Fractions Including Some Negative and Some Improper Fractions

Operations with Negative Fractions Worksheets

Although some of these worksheets are single operations, it should be helpful to have all of these in the same location. There are some special considerations when completing operations with negative fractions. It is usually very helpful to change any mixed numbers to an improper fraction before proceeding. It is important to pay attention to the signs and know the rules for multiplying positives and negatives (++ = +, +- = -, -+ = - and -- = +).

• Adding with Negative Fractions Adding Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Adding Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Adding Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
• Subtracting with Negative Fractions Subtracting Negative Proper Fractions with Unlike Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Unlike Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Sixths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Mixed Fractions with Unlike Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Subtracting Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Subtracting Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
• Multiplying with Negative Fractions Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Sixths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Mixed Fractions with Denominators Up to Twelfths, Proper Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Multiplying Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Multiplying Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)
• Dividing with Negative Fractions Dividing Negative Proper Fractions with Denominators Up to Sixths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Twelfths, Mixed Fractions Results and Some Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Mixed Fractions with Denominators Up to Twelfths, Mixed Fractions Results and No Simplifying (Fillable, Savable, Printable) ✎ Dividing Negative Proper Fractions with Denominators Up to Sixths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Proper Fractions with Denominators Up to Twelfths, Proper Fraction Results and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Sixths and Some Simplifying (Printable Only) Dividing Negative Mixed Fractions with Denominators Up to Twelfths and Some Simplifying (Printable Only)

Order of Operations with Fractions Worksheets

The order of operations worksheets in this section actually reside on the Order of Operations page, but they are included here for your convenience.

• Order of Operations with Fractions 2-Step Order of Operations with Fractions 3-Step Order of Operations with Fractions 4-Step Order of Operations with Fractions 5-Step Order of Operations with Fractions 6-Step Order of Operations with Fractions
• Order of Operations with Fractions (No Exponents) 2-Step Order of Operations with Fractions (No Exponents) 3-Step Order of Operations with Fractions (No Exponents) 4-Step Order of Operations with Fractions (No Exponents) 5-Step Order of Operations with Fractions (No Exponents) 6-Step Order of Operations with Fractions (No Exponents)
• Order of Operations with Positive and Negative Fractions 2-Step Order of Operations with Positive & Negative Fractions 3-Step Order of Operations with Positive & Negative Fractions 4-Step Order of Operations with Positive & Negative Fractions 5-Step Order of Operations with Positive & Negative Fractions 6-Step Order of Operations with Positive & Negative Fractions

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Grade 7 - The Number System

Standard 7.NS.A.2b - Practice finding the fraction represented in a word problem.

Included Skills:

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

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NCERT Books and Solutions for all classes

Assignments Class 7 Mathematics Fractions And Decimals Pdf Download

Students can refer to Assignments for Class 7 Mathematics Fractions And Decimals available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Fractions And Decimals Class 7 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT Books for Class 7 Mathematics Fractions And Decimals for the current academic session. All Assignments for Mathematics Fractions And Decimals Grade 7 have been designed by expert faculty members and have been designed based on the type of questions asked in standard 7 class tests and exams. All Free printable Assignments for NCERT CBSE Class 7, practice worksheets, and question banks have been designed to help you understand all concepts properly. Practicing questions given in CBSE NCERT printable assignments for Class 7 with solutions and answers will help you to further improve your understanding. Our faculty have used the latest syllabus for Class 7. You can click on the links below to download all Pdf assignments for class 7 for free. You can get the best collection of Kendriya Vidyalaya Class 7 Mathematics Fractions And Decimals assignments and questions workbooks below.

Class 7 Mathematics Fractions And Decimals Assignments Pdf Download

CBSE NCERT KVS Assignments for Mathematics Fractions And Decimals Class 7 have been provided below covering all chapters given in your CBSE NCERT books. We have provided below a good collection of assignments in Pdf for Mathematics Fractions And Decimals standard 7th covering Class 7 questions and answers for Mathematics Fractions And Decimals. These practice test papers and workbooks with question banks for Class 7 Mathematics Fractions And Decimals Pdf Download and free CBSE Assignments for Class 7 are really beneficial for you and will support in preparing for class tests and exams. Standard 7th students can download in Pdf by clicking on the links below.

Subjectwise Assignments for Class 7 Mathematics Fractions And Decimals

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• CBSE Notes For Class 7
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• Chapter 2: Fractions And Decimals

Fractions and Decimals Class 7 Notes: Chapter 2

Introduction: fractions.

The word fraction derives from the Latin word “Fractus” meaning broken . It represents a part of a whole , consisting of a number of equal parts out of a whole. E.g : slices of a pizza.

For more information on Introduction to Fractions, watch the below video.

To know more about Fractions, visit here .

Representation of Fractions

A fraction is represented by 2 numbers on top of each other, separated by a line. The number on top is the numerator and the number below is the denominator . Example : 3 4   which basically means 3 parts out of 4 equal divisions.

For more information on Representation of Fractions, watch the below video.

Fractions on the Number Line

In order to represent a fraction on a number line, we divide the line segment between two whole numbers into n equal parts , where n is the denominator. Example : To represent 1/5  or 3/5 , we divide the line between 0 and 1 in 5 equal parts. Then the numerator gives the number of divisions to mark.

Multiplication of Fractions

Multiplication of a fraction by a whole number : Example 1: 7 ×(1/3)  = 7/3 Example 2 : 5 ×(7/45)  =  35/45 , Dividing numerator and denominator by 5, we get  7/9

Multiplication of a fraction by a fraction is basically product of numerators/product of denominators

Fraction as an Operator ‘Of’

The ‘of’ operator basically implies multiplication .

Example: 1/6  o f   18 = (1/6) × 18 = 18/6  =  3 or, 1/2  o f   11 = (1/2)  ×  11  = 11/2  To know more about Multiplication of Fractions, visit here .

Division of Fractions

Reciprocal of a fraction.

Reciprocal of any number n is written as 1 n Reciprocal of a fraction is obtained by interchanging the numerator and denominator. Example: Reciprocal of 2/5 is 5/2 Although zero divided by any number means zero itself, we cannot find reciprocals for them, as a number divided by 0 is undefined . Example : Reciprocal of 0/7  ≠   7/0

Division of a whole number by a fraction : we multiply the whole number with the reciprocal of the fraction. Example : 63 ÷( 7/5) =  63 × (5/7) =  9 × 5  =  45

Division of a fraction by a whole number : we multiply the fraction with the reciprocal of the whole number. Example : (8/11) ÷ 4  = (8/11) ×( 1/4) = 2/11

Division of a fraction  by another fraction  : We multiply the dividend with the reciprocal of the divisor. Example : (2/7)  ÷   (5/21) = (2/7)  ×   (21/5) = 6/5 To know more about Reciprocal and Division of Fractions, visit here .

Types of Fractions

Proper fractions represent a part of a whole. The numerator is smaller than the denominator. Example: 1/4, 7/9, 50/51. Proper fractions are greater than 0 and less than 1

Improper fractions have a numerator that is greater than or equal to the denominator. Example: 45/6, 6/5. Improper fractions are greater than 1 or equal to 1.

Conversion of fractions : An improper fraction can be represented as mixed fraction and  a mixed fraction can represented as improper. In the above case, if you multiply the denominator 5 with the whole number 8 add the numerator 3 to it, you get back 43 5

Like fractions : Fractions with the same denominator are called like fractions. Example: 5/7 ,   3/7. Here we can compare them as (5/7)  > ( 3/7)

Unlike fractions : Fractions with different denominators are called unlike fractions. Example: 5/3, 9/2. To compare them, we find the L.C.M of the denominator. Here the L.C.M is 6 So, (5/3)×(2/2) , (9/2)×(3/3) ⇒ 10/6, 27/6 ⇒ 27/6  > 10/7

For more information on Types of Fractions, watch the below videos.

To know more about “Types of Fractions”, visit here .

Introduction: Decimal

Decimal numbers are used to represent numbers that are smaller than the unit 1 . Decimal number system is also known as base 10 system since each place value is denoted by a power of 10.

A decimal number refers to a number consisting of the following two parts: (i) Integral part (before the decimal point) (ii) Fractional Part (after the decimal point). These both are separated by a decimal separator(.) called the decimal point .

A decimal number is written as follows: Example 564.8 or 23.97. The numbers to the left of the decimal point increase with the order of 10, while the numbers to the right of the point increase with the decrease order of 10. The above example 564.8 can be read as ‘five hundred and sixty four and eight tenths’ ⇒ 5 × 100  +  6 × 10  +  4 × 1  +  8 ×(1/10)

A fraction can be written as a decimal and vice-versa. Example 3/2   =  1.5 or 1.5  = 15/10  = 3/2

For more information on Fractions and Decimals, watch the below video.

To know more about Decimals, visit here .

Multiplication of Decimals

Multiplication of decimal numbers with whole numbers : Multiply them as whole numbers. The product will contain the same number of digits after the decimal point as that of the decimal number. E.g : 11.3 × 4  =  45.2

Multiplication of decimals with powers of 10 : If a decimal is multiplied by a power of 10, then the decimal point shifts to the right by the number of zeros in its power. E.g : 45.678 × 10  =  456.78  (decimal point shifts by 1 place to the right) or, 45.678 × 1000  =  45678 (decimal point shifts by 3 places to the right)

Multiplication of decimals with decimals :

Multiply the decimal numbers without decimal points and then give decimal point in the answer as many places same as the total number of places right to the decimal points in both numbers.

Division of Decimals

Dividing a decimal number by a whole number : Example: 45.2/55 Step 1 . Convert the Decimal number into Fraction: 45.25 = 4525/100 Step 2 . Divide the fraction by the whole number: ( 4525/100) ÷ 5  = ( 4525/100)  × (1/5)  =  9.05

Dividing a decimal number by a decimal number : Example 1: 45.25/0.5 Step 1.  Convert both the decimal numbers into fractions: 45.25  = 4525/100   and 0.5  = 5/10 Step 2.  Divide the fractions: (4525/100) ÷ (5/10) = (4525/100) × (10/5) =  90.5 Example 2:

Dividing a decimal number by powers of 10  : If a decimal is divided by a power of 10, then the decimal point shifts to the left by the number of zeros present in the power of 10. Example: 98.765 ÷ 100 = 0.98765  Infinity

When the denominator in a fraction is very very small (almost tending to 0), then the value of the fraction tends towards infinity . E.g: 999999/0.000001 = 999999000001  ≈ a very large number, which is considered to be ∞

To know more about Multiplication and Division of Decimals, visit here .

Frequently Asked Questions on CBSE Class 7 Maths Notes Chapter 2 Fractions and Decimals

What is a decimal.

A decimal is a fraction written in a special form.

What is a decimal fraction?

In algebra, a decimal fraction is a fraction whose denominator is 10 or a multiple of 10 like 100, 1,000, 10,000, etc.

What does reciprocal mean?

In Mathematics, reciprocal means an expression which when multiplied by another expression, gives one (1) as the result.

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Test Grade Calculator

How to calculate test score, test grade calculator – how to use it, test grade calculator – advanced mode options.

This test grade calculator is a must if you're looking for a tool to help set a grading scale . Also known as test score calculator or teacher grader , this tool quickly finds the grade and percentage based on the number of points and wrong (or correct) answers. Moreover, you can change the default grading scale and set your own. Are you still wondering how to calculate test scores? Scroll down to find out – or simply experiment with this grading scale calculator.

If this test grade calculator is not the tool you're exactly looking for, check out our other grading calculators like the grade calculator .

Prefer watching rather than reading? We made a video for you! Check it out below:

To calculate the percentile test score, all you need to do is divide the earned points by the total points possible . In other words, you're simply finding the percentage of good answers:

percentage score = (#correct / #total) × 100

As #correct + #wrong = #total , we can write the equation also as:

percentage score = 100 × (#total - #wrong) / #total

Then, all you need to do is convert the percentage score into a letter grade . The default grading scale looks as in the table below:

If you don't like using the +/- grades, the scale may look like:

• An A is 90% to 100%;
• A B is 80% to 89%;
• A C is 70% to 79%;
• A D is 60% to 69%; and finally
• F is 59% and below – and it's not a passing grade

Above, you can find the standard grading system for US schools and universities. However, the grading may vary among schools, classes, and teachers. Always check beforehand which system is used in your case.

Sometimes the border of passing score is not 60%, but, e.g., 50 or 65%. What then? We've got you covered – you can change the ranges of each grade! Read more about it in the last section of this article: Advanced mode options .

🙋 You might also be interested in our semester grade calculator and the final grade calculator .

Our test score calculator is a straightforward and intuitive tool!

Enter the number of questions/points/problems in the student's work (test, quiz, exam – anything). Assume you've prepared the test with 18 questions.

Type in the number the student got wrong . Instead – if you prefer – you can enter the number of gained points. Let's say our exemplary student failed to answer three questions.

Here we go! Teacher grader tool shows the percentage and grade for that score. For our example, the student scored 83.33% on a test, which corresponds to a B grade.

Underneath you'll find a full grading scale table . So to check the score for the next students, you can type in the number of questions they've got wrong – or just use this neat table.

That was a basic version of the test grade calculator. But our teacher grader is a much more versatile and flexible tool!

You can choose more options to customize this test score calculator. Just hit the Advanced mode button below the tool, and two more options will appear:

Increment by box – Here, you can change the look of the table you get as a result. The default value is 1, meaning the student can get an integer number of points. But sometimes it's possible to get, e.g., half-points – then you can use this box to declare the increment between the next scores.

Percentage scale – In this set of boxes, you can change the grading scale from the default one. For example, assume that the test was challenging and you'd like to change the scale so that getting 50% is already a passing grade (usually, it's 60% or even 65%). Change the last box, Grade D- ≥ value, from default 60% to 50% to reach the goal. You can also change the other ranges if you want to.

And what if I don't need +/- grades ? Well, then just ignore the signs 😄

How do I calculate my test grade?

To calculate your test grade:

• Determine the total number of points available on the test.
• Add up the number of points you earned on the test.
• Divide the number of points you earned by the total number of points available.
• Multiply the result by 100 to get a percentage score.

That's it! If you want to make this easier, you can use Omni's test grade calculator.

Is 27 out of 40 a passing grade?

This depends mainly on the grading scale that your teacher is using. If a passing score is defined as 60% (or a D-), then 27 out of 40 would correspond to a 67.5% (or a D+), which would be a passing grade. However, depending on your teacher’s scale, the passing score could be higher or lower.

What grade is 7 wrong out of 40?

This is a B-, or 82.5% . To get this result:

Use the following percentage score formula: percentage score = 100 × (#total - #wrong) / #total

Here, #total represents the total possible points, and #wrong , the number of incorrect answers.

Substitute your values: percentage score = 100 × (40 - 7) / 40 percentage score = 82.5%

Convert this percentage into a letter grade. In the default grading scale, 82.5% corresponds to a B-. However, grading varies — make sure to clarify with teachers beforehand.

Is 75 out of 80 an A?

Yes , a score of 75 out of 80 is an A according to the default grading scale. This corresponds to a percentage score of 93.75%.

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CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 7 Mathematics Assignments

We have provided below free printable Class 7 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 7 Mathematics . These Assignments for Grade 7 Mathematics cover all important topics which can come in your standard 7 tests and examinations. Free printable Assignments for CBSE Class 7 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 7 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 7 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 7. Students can click on the links below and download all Pdf Assignments for Mathematics class 7 for free. All latest Kendriya Vidyalaya Class 7 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 7 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 7 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 7th. Our expert faculty have covered Class 7 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 7 Mathematics and CBSE Assignments for Mathematics Class 7 will be really helpful for standard 7th students to prepare for the class tests and school examinations. Class 7th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 7 Mathematics Download in Pdf

More assignments for class 7 mathematics.

Advantages of Class 7 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 7, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 7 .
• All Mathematics assignments for Class 7 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 7 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 7 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 7 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 7 which you can download in Pdf

We provide here Standard 7 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 7, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 7 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 7 for all subjects. You can download them all and use them offline without the internet.

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