problem solving on division of fractions

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Dividing Fractions Word Problems Worksheets

Toss off solutions to our pdf worksheets on dividing fractions word problems to foster a sense of excellence in identifying the dividend and the divisor and solving word problems on fraction division. Equipped with answer key, our worksheets get children in grade 5, grade 6, and grade 7 rattling their way through the division of fractions and mixed numbers in regular and themed problems. A flurry of everyday scenarios, our free worksheet for dividing fractions word problems is worth a shot!

Dividing Fractions and Whole Numbers Word Problems

Prepare the child through and through so they divide fractions and whole numbers with word problems. Let them take the reciprocal of the divisor and multiply it with the dividend, and they’re good to go!

• Download the set

Dividing Fractions by Cross Cancelling Word Problems

Exceed every learning expectation with our dividing fractions word problems worksheets! Apply cross cancellation after inverting the divisor, find products of what's left, and do write the correct units.

Dividing Mixed Numbers Word Problems

Give 5th grade and 6th grade students a good round of practice to hone their skills in fraction division. Convert mixed numbers into improper fractions, and proceed to divide them as usual.

Dividing Mixed Numbers and Fractions Word Problems

The road to mastery in word problems on dividing mixed numbers and fractions is made smooth with our printable worksheets. Read the problems, identify the dividends and divisors, and find the answers.

Themed Fraction Division Word Problems

If grade 6 and grade 7 learners are bent on proving they're real gifted at tackling fraction division, nothing can stop them! With our themed word problems pdfs, problem-solving is at its most exciting.

Related Worksheets

» Adding Fractions Word Problems

» Subtracting Fractions Word Problems

» Multiplying Fractions Word Problems

» Fraction Word Problems

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Dividing fractions word problems

Dividing fractions word problems arise in numerous situations. We will show you some examples. I recommend that you review the lesson about division of fractions before starting this lesson.

Dividing fractions word problems: a few examples

3 friends share 4/5 of a pizza. what fraction of pizza does each person get?

The amount to share is 4/5

Since the amount will be shared between 3 friends, the amount must be divided between 3 people.

So each person must get 4/5 divided by 3

(4 / 5) / 3 = (4 / 5) / (3 / 1) = 4 / 5 × 1 / 3 = (4 × 1) / (5 × 3)= 4 / 15

Each person will eat 4/15.

Indeed, 4 / 15 + 4 / 15 + 4 / 15 = 12 / 15 = 4/5 (divide 12 and 15 by 3 to get 4 / 5)

On June 21st, there were 9/10 of a billion stars visible to the naked eye.

On December 21st, there were 4/5 of a billion stars out visible to the naked eye.

How many times more stars were there visible on June 21st than December 21st?

9/10 divided by 4/5 = ?

Find the reciprocal of the divisor.

9/10 × 5/4 = ?

9/10 × 5/4 = 9/2 × 1/4

Solve 9/2 × 1/4 = 9/8

Simplify again

Did you have a hard time understanding the problems above? Did you not understand them at all? Take a look at this figure !

Do you need to master fractions once and for all? Check out my book about fractions .

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Dividing Fractions

Turn the second fraction upside down, then multiply.

There are 3 Simple Steps to Divide Fractions:

Example: 1 2   ÷   1 6.

Step 1. Turn the second fraction upside down (it becomes a reciprocal ):

1 6 becomes 6 1

Step 2. Multiply the first fraction by that reciprocal :

(multiply tops ...)

1 2  ×  6 1   =   1 × 6 2 × 1   =   6 2

(... multiply bottoms)

Step 3. Simplify the fraction:

6 2   =  3

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

To help you remember:

♫ "Dividing fractions, as easy as pie, Flip the second fraction, then multiply. And don't forget to simplify, Before it's time to say goodbye" ♫

20 divided by 5 is asking "how many 5s in 20?" (=4) and so:

1 2   ÷   1 6 is really asking:

how many 1 6 s in 1 2 ?

Now look at the pizzas below ... how many "1/6th slices" fit into a "1/2 slice"?

So now you can see why 1 2   ÷   1 6 = 3

In other words "I have half a pizza, if I divide it into one-sixth slices, how many slices is that?"

Another Example: 1 8   ÷   1 4

Step 1. Turn the second fraction upside down (the reciprocal ):

1 4   becomes   4 1

1 8   ×   4 1 = 1 × 4 8 × 1 = 4 8

4 8   =   1 2

Fractions and Whole Numbers

What about division with fractions and whole numbers?

Make the whole number a fraction, by putting it over 1.

Example: 5 is also 5 1

Then continue as before.

Example: 2 3   ÷  5

Make 5 into 5 1 :

2 3   ÷   5 1

5 1 becomes 1 5

2 3 × 1 5 = 2 × 1 3 × 5 = 2 15

The fraction is already as simple as it can be.

Answer = 2 15

Example: 3  ÷   1 4

Make 3 into 3 1 :

3 1   ÷   1 4

1 4 becomes 4 1

3 1 × 4 1 = 3 × 4 1 × 1 = 12 1

And Remember ...

You can rewrite a question like "20 divided by 5" into "how many 5s in 20"

So you can also rewrite "3 divided by ¼" into "how many ¼s in 3" (=12)

Why Turn the Fraction Upside Down?

Because dividing is the opposite of multiplying!

But for DIVISION we:

• divide by the top number
• multiply by the bottom number

Example: dividing by 5 / 2 is the same as multiplying by 2 / 5

So instead of dividing by a fraction, it is easier to turn that fraction upside down, then do a multiply.

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4.9: Dividing Fractions- Problems

• Last updated
• Save as PDF
• Page ID 10584

• Michelle Manes
• University of Hawaii

We’ve spent the last couple of chapters talking about dividing fractions: how to make sense of the operation, how to picture what’s going on, and how to do the computations. But all of this kind of begs the question: When would you ever want to divide fractions, anyway? How does that even come up?

It’s important that teachers are able to come up with situations and problems that model particular operations, which means you have to really understand what the operations mean and when they are used.

Think / Pair / Share

• Use one of our methods (draw a picture, rectangles, common denominator, missing factor) to compute \(1 \frac{3}{4} \div \frac{1}{2}\).
• Come up with a situation where you would want to compute \(1 \frac{3}{4} \div \frac{1}{2}\). (That is, write a word problem that would require you to do this computation to solve it.)

When to Multiply, When to Divide?

A common answer to

Come up with a situation where you would want to compute \(1 \frac{3}{4} \div \frac{1}{2}\).

Is something like this:

My recipe calls for \(1 \frac{3}{4} \div \frac{1}{2}\) cups of flour, but I only want to make half a recipe. How much flour should I use?

But that problem doesn’t ask you to divide fractions. It asks you to cut your recipe in half, which means dividing by 2 or multiplying by \(\frac{1}{2}\).

Why is it so hard to come up with division problems that use fractions? Maybe it’s because fractions are already the answer to a division problem, so you’re dividing and then dividing some more. Maybe it’s because they just make it look so complicated. In any case, it’s worth spending some time thinking about division problems that involve fractions and how to recognize and solve them.

One handy trick: Write a problem that involves division of whole numbers, and then see if you can change the numbers to fractions in a sensible way.

Example \(\PageIndex{1}\):

Here are some division problems involving whole numbers:

• I have 10 feet of ribbon. How many 2-inch pieces can I cut from it?
• I have a fancy old clock that rings once every 15 minutes. How many times will it ring over the course of 2 hours (120 minutes)?
• My fish tank needs 6 gallons of water, and my bucket holds 3 gallons. How many times will I need to fill my bucket in order to fill the tank?
• A recipe calls for 6 cups of flour, and my largest scoop measures exactly 2 cups. How many times should I use it?
• I ran 12 miles and went around the the same route 3 times. How long was the route?

Here are some very similar problems, rewritten to use fractions instead:

• I have \(1 \frac{3}{4}\) feet of ribbon. How many 6-inch (that’s \(\frac{1}{2}\) a foot) pieces can I cut from it?
• My watch alarm goes off every half hour, and I don’t know how to shut it off. How many times will it go off during the \(1 \frac{3}{4}\) hour movie?
• My fish tank needs \(1 \frac{3}{4}\) gallons of water, and my bucket holds \(\frac{1}{2}\) gallon. How many times will I need to fill my bucket in order to fill the tank?
• I want to measure \(1 \frac{3}{4}\) cups of flour for a recipe, but I only have a \(\frac{1}{2}\) cup measuring cup. How many times should I fill it?
• I ran \(1 \frac{3}{4}\) miles before I twisted my ankle. I only finished half the race. How long was the race course?

For each one of the fraction division questions, we can understand why it’s a division problem:

• I have \(1 \frac{3}{4}\) feet of ribbon. How many 6-inch (that’s \(\frac{1}{2}\) a foot) pieces can I cut from it? This means making equal groups of \(\frac{1}{2}\) foot each and asking how many groups. That’s quotative division.
• My watch alarm goes off every half hour, and I don’t know how to shut it off. How many times will it go off during the \(1 \frac{3}{4}\) hour movie? Again, we’re making equal groups of \(\frac{1}{2}\) hour each, and asking how many groups. Quotative division.
• My fish tank needs \(1 \frac{3}{4}\) gallons of water, and my bucket holds \(\frac{1}{2}\) gallon. How many times will I need to fill my bucket in order to fill the tank? Once again: we’re making equal groups of \(\frac{1}{2}\) gallon each, and asking how many groups (buckets).
• I want to measure \(1 \frac{3}{4}\) cups of flour for a recipe, but I only have a \(\frac{1}{2}\) cup measuring cup. How many times should I fill it? This is making equal groups of \(\frac{1}{2}\) cup and asking how many groups.
• I ran \(1 \frac{3}{4}\) miles before I twisted my ankle. I only finished half the race. How long was the race course? This one is a little different. This one is a little different. It’s the fraction version of partitive division.

Recall what partitive division asks: For \(20 \div 4\), we ask 20 is 4 groups of what size?

So for \(1 \frac{3}{4} \div \frac{1}{2}\), we ask: \(1 \frac{3}{4}\) is half a group of what size?

You try it.

• First write five different division word problems that use whole numbers. (Try to write at least a couple each of partitive and quotative division problems.)
• Then change the problems so that they are fraction division problems instead. You might need to rewrite the problem a bit so that it makes sense.
• Solve your problems!

Division of Fractions

Division means sharing an item equally. We have learned about the division of whole numbers, now let us see how to divide fractions. A fraction has two parts - a numerator and a denominator. Dividing fractions is almost the same as multiplying them. For the division of fractions, we multiply the first fraction by the reciprocal (inverse) of the second fraction. Let us learn more about the division of fractions in this article.

How to Divide Fractions?

We know that division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient . Now, when we do division of a fraction by another fraction, it is the same as multiplying the fraction by the reciprocal of the second fraction. The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator. Observe the following figure to learn a simple rule of dividing fractions.

In the subsequent sections, we will learn the division of fractions with fractions, whole numbers, decimals, and mixed numbers. In every case, we will be using the same rule of dividing fractions as given above. Let's begin!

Dividing Fractions by Fractions

We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,

⇒ x/y × b/a (reciprocal of a/b is b/a)

Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators .

5/8 ÷ 15/16 = 5/8 × 16/15 = 2/3

∴ The value of 5/8 ÷ 15/16 = 2/3.

Division of Fractions with Whole Numbers

For the division of fractions with whole numbers , we need to multiply the denominator of the given fraction with the given whole number . In the general form, if x/y is the fraction and a is the whole number, then x/y ÷ a = x/y × 1/a = x/ya.

Let us take an example and divide 2/3 with 4.

2/3 ÷ 4 = 2/3 × 1/4

Therefore, 2/3 ÷ 4 gives us 1/6. This is how we divide fractions with whole numbers.

Dividing Fractions with Decimals

We know that decimal numbers themselves are a fraction to base 10. We can represent the decimal in the fractional form and then perform the division. For dividing fractions with decimals, follow the steps given below:

• Convert the given decimal to a fraction.
• Divide both the fractions.

Consider the example, 4/5 ÷ 0.5. Here, 0.5 can be written in fractional form as 5/10 or 1/2. Now, divide 4/5 by 1/2. This implies, 4/5 ÷ 1/2 = 4/5 × 2/1 = 8/5. This is how we perform the division of fractions with decimals. Now let us learn how to divide fractions with mixed numbers.

Division of Fractions and Mixed Numbers

We have learned how to convert mixed fractions to improper fractions . For the division of fractions with mixed numbers , we have to convert the mixed fraction to an improper fraction first and then divide them as we divide two fractions. Consider the following example.

3/4 ÷ \(1\dfrac{1}{2}\)

So, the first step is to convert \(1\dfrac{1}{2}\) to an improper fraction . \(1\dfrac{1}{2}\) is the same as 3/2. Now, it can be solved in the following way:

⇒ 3/4 × 2/3

⇒ 6/12 = 1/2

Therefore, 3/4 ÷ \(1\dfrac{1}{2}\) = 1/2. If you want to divide a mixed number with a fraction, first convert the mixed number to an improper fraction and follow the same steps as shown above.

Division of Fractions Related Articles

Check these interesting articles related to the concept of division of fractions in math.

• Dividing Fractions Calculator
• Formula for Dividing Fractions
• Dividing Fractions with Whole Numbers

Division of Fractions Examples

Example 1: Find the value of 3/16 ÷ 15/32.

To divide 3/16 ÷ 15/32, we will be using the steps of the division of fractions. The first step is to keep the first fraction as it is. Then change the division sign to multiplication sign and at last, flip the second fraction to its reciprocal. This implies 3/16 × 32/15. After simplifying, we get (3 × 32) / (16 × 15) = 2/5.

∴ The value of 3/16 ÷ 15/32 = 2/5

Example 2: Tim has \(1\frac{1}{2}\) liters of juice in a jug. He has to pour the juice into cups. Each cup can hold 1/4 liters of juice. How many cups will he need to pour all the juice?

To solve this question, we will be using the concept of the division of fractions.

Number of cups needed = Total quantity of juice ÷ Capacity of 1 cup

= 3/2 ÷ 1/4 (as \(1\frac{1}{2}\) = 3/2)

= 3/2 × 4/1

Therefore, the number of cups required to pour the juice is 6.

Example 3: Use the steps of dividing fractions with whole numbers to find the value of 8/5 ÷ 5.

To divide a fraction with a whole number, we multiply the given whole number with the denominator of the fraction. Here, 8/5 ÷ 5 = 8/5 × 1/5 = 8/25.

Therefore, 8/5 ÷ 5 = 8/25.

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Practice Questions on Dividing Fractions

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FAQs on Dividing Fractions

What does division of fractions mean.

The division of fractions means breaking down a fraction into further parts. For example, if you take half (1/2) of a pizza and you further divide it into 2 equal parts, then each portion will be 1/4th of the whole pizza. Mathematically, we can express this reasoning as 1/2 ÷ 2 = 1/4.

What is Multiplication and Division of Fractions?

The multiplication of fractions means to add a fraction to itself repeatedly a specific number of times. The following steps are used to multiply fractions:

• Step 1: Multiply the numerators of both the fractions.
• Step 2: Multiply the denominators of both the fractions.
• Step 3: Simplify the fraction obtained after multiplication.

On the other hand, the division of fractions means to do equal grouping or equal sharing of a fraction. Dividing fractions is related to multiplication, as while dividing two fractions, we multiply the reciprocal of the second fraction to the first.

How to Visualize Division of Fractions?

To visualize the division of fractions, take a piece of paper and fold it into two equal parts. Cut 1/2 of the paper with scissors. Now, you will be left with 1/2 of the paper. Now, again divide that 1/2 portion into 2 equal parts. After this, you will be left with 1/4th of the paper. That is the answer of 1/2 ÷ 2. This is how you can visualize the concept of dividing fractions.

What is the Rule for Dividing Fractions?

The basic rule of dividing fractions is to keep, change, and flip. It means we have to keep the first fraction as it is, change the division sign to the multiplication sign, and flip the second fraction to its reciprocal. By following this simple rule, you can divide any two fractions.

What are the Steps to Dividing Fractions?

The following steps have to be followed in order to divide fractions:

• Step 1: Take the reciprocal of the second fraction.
• Step 2: Multiply it with the first fraction.
• Step 3: Reduce the resultant fraction to its lowest terms.

How to Teach Division of Fractions?

Division of fractions can be taught in many ways such as, by using models or applying the concept of multiplication of fractions. Some of the ways to teach how to divide fractions are listed below:

• Take circular or rectangular fraction models to demonstrate the concept of division of fractions to your learners.
• Use worksheets including pictures and word problems.
• Use materials from day-to-day lives like beans, leaves, pebbles, etc to show learners how to divide fractions.

How to Divide a Number by a Fraction?

To divide a whole number by a fraction, we multiply the whole number with the reciprocal of the given fraction. To divide a fraction by a fraction, we multiply the reciprocal of the second fraction with the first fraction.

How to do Division of Fractions with Whole Numbers?

Dividing fractions with whole numbers is a three-step process:

• Step 1: Keep the fraction as it is. For example, 3/4 ÷ 6.
• Step 2: Flip the whole number, which will make it a fraction of the format 1/a. In this case, 6 will become 1/6.
• Step 3: Change the sign into multiplication. We will get 3/4 × 1/6 = 3/24 = 1/8.

How to do Division of Fractions With Mixed Numbers?

For the division of fractions and mixed numbers, the following steps are used:

• Step 1: Keep the fraction as it is.
• Step 2: Convert the mixed number into an improper fraction and flip the second fraction.
• Step 3: Change the sign into multiplication between the fractions. Multiply and simplify them.

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How to Solve Word Problems Involving Dividing Fractions

This article provides a step-by-step guide for solving math word problems that involve the division of fractions.

A step-by-step guide to word problems involving dividing fractions

The word problems of fractions are made of a few sentences involving a real-life scenario and you must use the mathematical calculation of fraction formulas to solve a problem.

Here are easy steps to solve word problems involving dividing fractions: Step 1: Use information and keywords to identify the problems. Step 2: Invert the second fraction and multiply instead of dividing. Step 3: Multiply the 2 numerators. Multiply the 2 denominators. If the problem contains mixed numbers, you must convert them to improper fractions first. Step 4: Simplify the fraction if possible.

Word Problems Involving Dividing Fractions – Example 1

Karolina uses \(\frac{6}{8}\) of a jar of cherry jam to make eight muffins. What fraction of the jar of cherry jam does each muffin contain?

Solution: Step 1: Divide the total amount of a used cherry jam by the number of muffins, \(\frac{6}{8}÷8\). Step 2: Write 8 as an improper fraction, \(\frac{6}{8}÷\frac{8}{1}\). Step 3: Invert the second fraction and multiply instead of dividing. \(\frac{6}{8}×\frac{1}{8}=\frac{6×1}{8×8}=\frac{6}{64}\) Step 4: Simplify the product. \(\frac{6}{64}=\frac{3}{32}\)

Word Problems Involving Dividing Fractions – Example 2

Alice uses \(\frac{4}{6}\) of a roll of wrapping paper to wrap five presents. What fraction of the roll wrapping paper does each present use?

Solution: Step 1: Divide the total amount of a roll of wrapping paper by the number of presents. \(\frac{4}{6}÷5\) Step 2: Write 5 as an improper fraction. \(\frac{4}{6}÷\frac{5}{1}\) Step 3: Invert the second fraction and multiply instead of dividing. \(\frac{4}{6}×\frac{1}{5}=\frac{4×1}{6×5}=\frac{4}{30}\) Step 4: Simplify the product. \(\frac{4}{30}=\frac{2}{15}\)

by: Effortless Math Team about 1 year ago (category: Articles )

Effortless Math Team

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Dividing Fractions – Definition with Examples

Created: December 19, 2023

Last updated: January 7, 2024

Division of fractions might appear intimidating to some young minds, but with the right guidance and resources, it can be easily grasped and mastered. At Brighterly , we are dedicated to helping children overcome their fear of math and to unlock their full potential. Our unique approach to teaching mathematics makes the subject both enjoyable and approachable, enabling children to embrace the beauty of dividing fractions and to confidently tackle more complex mathematical problems in the future.

To excel in the division of fractions, it is crucial to understand the underlying principles and the step-by-step process involved. With patience, practice, and the right guidance from our dedicated team of experts at Brighterly, children can excel in this fundamental area of mathematics and lay a strong foundation for their future endeavors.

What is Meant by Dividing Fractions?

Dividing fractions is a fundamental operation in mathematics where one fraction is divided by another. This concept is vital for young learners, as it lays the groundwork for tackling more advanced mathematical problems later on. In essence, dividing fractions is determining how many times one fraction can fit into another. At Brighterly, we strive to present this seemingly complex concept in an engaging and simplified manner, allowing children to develop a strong foundation in this area of mathematics.

How to Divide Fractions?

To divide fractions, one must employ a straightforward technique – multiplying by the reciprocal. The reciprocal of a fraction is obtained by inverting it, swapping the numerator and denominator. For instance, the reciprocal of 3/4 is 4/3. This method is an essential part of the Brighterly approach, making the division of fractions an easy-to-understand process for young learners.

Multiplication And Division Of Fractions Worksheets PDF

Multiplication And Division Of Fractions Worksheets

Division of Fractions Worksheets PDF

Division of Fractions Worksheets

If you are looking to improve your understanding of dividing fractions, then the math worksheets Brighterly are an excellent resource to consider. These worksheets are specifically designed to help you learn and reinforce your knowledge of this concept.

Steps to Divide Fractions

• Identify the problem: Note down the two fractions involved in the division problem.
• Determine the reciprocal: Find the reciprocal of the divisor (the second fraction).
• Perform multiplication: Multiply the dividend (the first fraction) by the reciprocal of the divisor.
• Simplify: If possible, simplify the resulting fraction for easier understanding.

Properties of Dividing Fractions

• Dividing by a fraction is equivalent to multiplying by its reciprocal, which simplifies the process.
• The division of fractions is commutative, meaning that the order in which the fractions are divided does not influence the result.
• The division of fractions is associative, implying that the grouping of the fractions does not affect the outcome.

Dividing Fractions by Fractions

To divide fractions by fractions, follow the steps outlined above. For example, let’s divide 1/2 by 3/4:

• Identify the problem: 1/2 ÷ 3/4
• Determine the reciprocal: The reciprocal of 3/4 is 4/3.
• Perform multiplication: 1/2 × 4/3 = 4/6
• Simplify: 4/6 simplifies to 2/3.

Division of Fractions with Whole Numbers

When dividing a fraction by a whole number, convert the whole number to a fraction before proceeding with the steps mentioned above. For instance, if you are dividing 2/3 by 4, convert 4 to 4/1 and continue with the division.

Dividing Fractions with Decimals

To divide fractions with decimals, first convert the decimal to a fraction, and then follow the steps for dividing fractions. For example, to divide 3/5 by 0.2, convert 0.2 to 1/5 and proceed with the division.

Division of Fractions and Mixed Numbers

When dividing fractions and mixed numbers, first convert the mixed numbers into improper fractions before following the steps for dividing fractions. For instance, if you are dividing 2 1/2 by 1 1/4, convert the mixed numbers to improper fractions (5/2 and 5/4) and proceed with the division.

By incorporating these techniques into the Brighterly approach, we help children develop a strong foundation in dividing fractions, paving the way for their future mathematical success.

Solved Examples on Dividing Fractions

To better understand the division of fractions, let’s explore some solved examples, using the Brighterly approach to make the process engaging and clear for young learners.

Example 1: Divide 3/4 by 2/3:

3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8

Example 2: Divide 5/6 by 4:

5/6 ÷ 4 = 5/6 × 1/4 = 5/24

Example 3: Divide 7/9 by 1/3:

7/9 ÷ 1/3 = 7/9 × 3/1 = 21/9 = 7/3

Practice Questions on Dividing Fractions

Challenge yourself with these practice questions, designed to help reinforce the concepts and techniques we’ve covered. Remember to apply the Brighterly approach to make the process more enjoyable and engaging.

• Divide 7/8 by 1/2
• Divide 3/5 by 0.4
• Divide 2 3/4 by 1 1/2
• Divide 4/9 by 5/6
• Divide 5/7 by 2/3

Fraction Division Worksheet

Division Fractions Worksheet

By working through these examples and practice questions, young learners can develop a strong understanding of dividing fractions, setting them up for success in more advanced mathematical concepts. At Brighterly, we believe that every child has the potential to excel in mathematics, and our mission is to help them achieve this potential by making the learning process engaging and enjoyable.

Developing a strong grasp of the division of fractions is an indispensable skill for children as they embark on their mathematical journey. By embracing the Brighterly approach, young learners can follow the straightforward steps and gain a deep understanding of the properties of dividing fractions, empowering them to tackle these problems effortlessly and with confidence.

At Brighterly, we believe that every child has the potential to excel in mathematics, and our mission is to nurture this potential by making math accessible, engaging, and enjoyable. By mastering the division of fractions, children can build a strong foundation in mathematics, preparing them for more advanced topics and empowering them to approach future challenges with enthusiasm and determination.

Frequently Asked Questions on Dividing Fractions

Why do we multiply by the reciprocal when dividing fractions.

Multiplying by the reciprocal is a helpful trick that simplifies the division process. This method is based on the principle that dividing by a number is the same as multiplying by its reciprocal. By using this technique, we can transform the division of fractions into a multiplication problem, making it easier for young learners to understand and solve. At Brighterly, we incorporate this approach to make the concept of dividing fractions more accessible and engaging for children.

Can you divide fractions with different denominators?

Yes, you can divide fractions with different denominators by following the steps mentioned above. When dividing fractions, there is no need to find a common denominator, as is the case when adding or subtracting fractions. This is because the process of dividing fractions involves multiplying by the reciprocal, which does not require the fractions to have the same denominator. At Brighterly, we emphasize this distinction to help children differentiate between various fraction operations and develop a solid understanding of each.

How do you divide fractions with mixed numbers?

To divide fractions with mixed numbers, first, convert the mixed numbers into improper fractions. Improper fractions have a larger numerator than the denominator, making them easier to work with when dividing fractions. Once you’ve converted the mixed numbers to improper fractions, follow the steps for dividing fractions as described above. By breaking down the process into manageable steps, Brighterly helps young learners build confidence and master the skill of dividing fractions with mixed numbers.

• Math Drills – Dividing Fractions Worksheets
• Purplemath – Dividing Fractions
• Wikipedia – Fraction (mathematics)

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Word Problems on Fraction

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

1.  4/7 of a number is 84. Find the number. Solution: According to the problem, 4/7 of a number = 84 Number = 84 × 7/4 [Here we need to multiply 84 by the reciprocal of 4/7]

= 21 × 7 = 147 Therefore, the number is 147.

2.  Rachel took \(\frac{1}{2}\) hour to paint a table and \(\frac{1}{3}\) hour to paint a chair. How much time did she take in all?

3. If 3\(\frac{1}{2}\) m of wire is cut from a piece of 10 m long wire, how much of wire is left?

Total length of the wire = 10 m

Fraction of the wire cut out = 3\(\frac{1}{2}\) m = \(\frac{7}{2}\) m

Length of the wire left = 10 m – 3\(\frac{1}{2}\) m

            = [\(\frac{10}{1}\) - \(\frac{7}{2}\)] m,    [L.C.M. of 1, 2 is 2]

            = [\(\frac{20}{2}\) - \(\frac{7}{2}\)] m,    [\(\frac{10}{1}\) × \(\frac{2}{2}\)]

            = [\(\frac{20 - 7}{2}\)] m

            = \(\frac{13}{2}\) m

            = 6\(\frac{1}{2}\) m

4. One half of the students in a school are girls, 3/5 of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

Fraction of girls studying in school = 1/2

Fraction of girls studying in lower classes = 3/5 of 1/2

                                                            = 3/5 × 1/2

                                                            = (3 × 1)/(5 × 2)

                                                            = 3/10

Therefore, 3/10 of girls studying in lower classes.

5.  Maddy reads three-fifth of 75 pages of his lesson. How many more pages he need to complete the lesson? Solution: Maddy reads = 3/5 of 75 = 3/5 × 75

= 45 pages. Maddy has to read = 75 – 45. = 30 pages. Therefore, Maddy has to read 30 more pages. 6.  A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd? Solution: A herd of cows gives 4 litres of milk each day. Each cow gives one-third of total milk each day = 1/3 of 4 Therefore, each cow gives 4/3 of milk each day. Total no. of cows = 4 ÷ 4/3                          = 4 × ¾                          = 3 Therefore there are 3 cows in the herd.

Questions and Answers on Word problems on Fractions:

1. Shelly walked \(\frac{1}{3}\) km. Kelly walked \(\frac{4}{15}\) km. Who walked farther? How much farther did one walk than the other?

2. A frog took three jumps. The first jump was \(\frac{2}{3}\) m long, the second was \(\frac{5}{6}\) m long and the third was \(\frac{1}{3}\) m long. How far did the frog jump in all?

3. A vessel contains 1\(\frac{1}{2}\) l of milk. John drinks \(\frac{1}{4}\) l of milk; Joe drinks \(\frac{1}{2}\) l of milk. How much of milk is left in the vessel?

●   Multiplication is Repeated Addition.

●  Multiplication of Fractional Number by a Whole Number.

●  Multiplication of a Fraction by Fraction.

●  Properties of Multiplication of Fractional Numbers.

●  Multiplicative Inverse.

●  Worksheet on Multiplication on Fraction.

●  Division of a Fraction by a Whole Number.

●  Division of a Fractional Number.

●  Division of a Whole Number by a Fraction.

●  Properties of Fractional Division.

●  Worksheet on Division of Fractions.

●  Simplification of Fractions.

●  Worksheet on Simplification of Fractions.

●  Word Problems on Fraction.

●  Worksheet on Word Problems on Fractions.

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Home / United States / Math Classes / 5th Grade Math / Problem Solving using Fractions

Problem Solving using Fractions

Fractions are numbers that exist between whole numbers. We get fractions when we divide whole numbers into equal parts. Here we will learn to solve some real-life problems using fractions. ...Read More Read Less

Table of Contents

What are Fractions?

Types of fractions.

• Fractions with like and unlike denominators
• Operations on fractions
• Fractions can be multiplied by using
• Let’s take a look at a few examples

Solved Examples

• Frequently Asked Questions

Equal parts of a whole or a collection of things are represented by fractions . In other words a fraction is a part or a portion of the whole. When we divide something into equal pieces, each part becomes a fraction of the whole.

For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction  \(\frac{1}{2}\) . 

Similarly, if it is divided into 4 equal parts, then each part is one fourth of the whole, that can be represented by the fraction \(\frac{1}{4}\) .

Proper fractions

A fraction in which the numerator is less than the denominator value is called a  proper fraction.

For example ,  \(\frac{3}{4}\) ,  \(\frac{5}{7}\) ,  \(\frac{3}{8}\)   are proper fractions.

Improper fractions 

A fraction with the numerator higher than or equal to the denominator is called an improper fraction .

Eg \(\frac{9}{4}\) ,  \(\frac{8}{8}\) ,  \(\frac{9}{4}\)   are examples of improper fractions.

Mixed fractions

A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction.

We express improper fractions as mixed numbers.

For example ,  5\(\frac{1}{3}\) ,  1\(\frac{4}{9}\) ,  13\(\frac{7}{8}\)   are mixed fractions.

Unit fraction

A unit fraction is a fraction with a numerator equal to one. If a whole or a collection is divided into equal parts, then exactly 1 part of the total parts represents a unit fraction .

Fractions with Like and Unlike Denominators

Like fractions are those in which two or more fractions have the same denominator, whereas unlike fractions are those in which the denominators of two or more fractions are different.

For example,  

\(\frac{1}{4}\)  and  \(\frac{3}{4}\)  are like fractions as they both have the same denominator, that is, 4.

\(\frac{1}{3}\)  and  \(\frac{1}{4}\)   are unlike fractions as they both have a different denominator.

Operations on Fractions

We can perform addition, subtraction, multiplication and division operations on fractions.

Fractions with unlike denominators can be added or subtracted using equivalent fractions. Equivalent fractions can be obtained by finding a common denominator. And a common denominator is obtained either by determining a common multiple of the denominators or by calculating the product of the denominators.

There is another method to add or subtract mixed numbers, that is, solve the fractional and whole number parts separately, and then, find their sum to get the final answer.

Fractions can be Multiplied by Using:

Division operations on fractions can be performed using a tape diagram and area model. Also, when a fraction is divided by another fraction then we can solve it by multiplying the dividend with the reciprocal of the divisor. 

Let’s Take a Look at a Few Examples

Addition and subtraction using common denominator

( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )

We apply the method of equivalent fractions. For this we need a common denominator, or a common multiple of the two denominators 6 and 5, that is, 30.

\(\frac{1}{6} ~+ ~\frac{2}{5}\)

= \(\frac{5~+~12}{30}\)  

=  \(\frac{17}{30}\) 

( \(\frac{5}{2}~-~\frac{1}{6}\) )

= \(\frac{12~-~5}{30}\)

= \(\frac{7}{30}\)

Examples of Multiplication and Division

Multiplication:

(\(\frac{1}{6}~\times~\frac{2}{5}\))

= (\(\frac{1~\times~2}{6~\times~5}\))                                       [Multiplying numerator of fractions and multiplying denominator of fractions]

=  \(\frac{2}{30}\)

(\(\frac{2}{5}~÷~\frac{1}{6}\))

= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\))                                     [Multiplying dividend with the reciprocal of divisor]

= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))

= \(\frac{12}{5}\)

Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)

Let’s add \(\frac{7}{8}\)  and  \(\frac{2}{3}\)   using equivalent fractions. For this we need to find a common denominator or a common multiple of the two denominators 8 and 3, which is, 24.

\(\frac{7}{8}\) + \(\frac{2}{3}\)

= \(\frac{21~+~16}{24}\)    

= \(\frac{37}{24}\)

Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)

Solution:  

Let’s subtract  \(\frac{12}{17}\) from \(\frac{11}{13}\)   using equivalent fractions. For this we need a common denominator or a common multiple of the two denominators 13 and 17, that is, 221.

\(\frac{11}{13}\) – \(\frac{12}{17}\)

= \(\frac{187~-~156}{221}\)

= \(\frac{31}{221}\)

Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)

Multiply the numerators and multiply the denominators of the 2 fractions.

\(\frac{15}{13}~\times~\frac{18}{17}\)

= \(\frac{15~~\times~18}{13~~\times~~17}\)

= \(\frac{270}{221}\)

Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)

Divide by multiplying the dividend with the reciprocal of the divisor.

\(\frac{25}{33}~\div~\frac{41}{45}\)

= \(\frac{25}{33}~\times~\frac{41}{45}\)                            [Multiply with reciprocal of the divisor \(\frac{41}{45}\) , that is, \(\frac{45}{41}\)  ]

= \(\frac{25~\times~45}{33~\times~41}\)

= \(\frac{1125}{1353}\)

Example 5: 

Sam was left with   \(\frac{7}{8}\)  slices of chocolate cake and    \(\frac{3}{7}\)  slices of vanilla cake after he shared the rest with his friends. Find out the total number of slices of cake he had with him. Sam shared   \(\frac{10}{11}\)  slices from the total number he had with his parents. What is the number of slices he has remaining?

To find the total number of slices of cake he had after sharing we need to add the slices of each cake he had,

=   \(\frac{7}{8}\) +   \(\frac{3}{7}\)   

=   \(\frac{49~+~24}{56}\)

=   \(\frac{73}{56}\)

To find out the remaining number of slices Sam has   \(\frac{10}{11}\)  slices need to be deducted from the total number,

= \(\frac{73}{56}~-~\frac{10}{11}\)

=   \(\frac{803~-~560}{616}\)

=   \(\frac{243}{616}\)

Hence, after sharing the cake with his friends, Sam has  \(\frac{73}{56}\) slices of cake, and after sharing with his parents he had  \(\frac{243}{616}\)  slices of cake left with him.

Example 6: Tiffany squeezed oranges to make orange juice for her juice stand. She was able to get 25 ml from one orange. How many oranges does she need to squeeze to fill a jar of   \(\frac{15}{8}\) liters? Each cup that she sells carries 200 ml and she sells each cup for 64 cents. How much money does she make at her juice stand?

First  \(\frac{15}{8}\) l needs to be converted to milliliters.

\(\frac{15}{8}\)l into milliliters =  \(\frac{15}{8}\) x 1000 = 1875 ml

To find the number of oranges, divide the total required quantity by the quantity of juice that one orange can give.

The number of oranges required for 1875 m l of juice =  \(\frac{1875}{25}\) ml = 75 oranges

To find the number of cups she sells, the total quantity of juice is to be divided by the quantity of juice that 1 cup has

=  \(\frac{1875}{200}~=~9\frac{3}{8}\) cups

We know that, the number of cups cannot be a fraction, it has to be a whole number. Also each cup must have 200ml. Hence with the quantity of juice she has she can sell 9 cups,   \(\frac{3}{8}\) th  of a cup cannot be sold alone.

Money made on selling 9 cups = 9 x 64 = 576 cents

Hence she makes 576 cents from her juice stand.

What is a mixed fraction?

A mixed fraction is a number that has a whole number and a fractional part. It is used to represent values between whole numbers.

How will you add fractions with unlike denominators?

When adding fractions with unlike denominators, take the common multiple of the denominators of both the fractions and then convert them into equivalent fractions. 

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Problems on Division of Fractional Numbers | Division of Fractions Word Problems with Answers

Problems on Divison of Fractional Numbers are provided with the various types of problems. Follow this complete concept and learn more about the division of the Fractional Numbers topic. Here on this page, we will explain different methods which are given to solve a single problem. So, let us check out different problems with explanations for the division of Fractional Number Problems.

Also, Check:

• Problems on Multiplication of Fractional Numbers
• Properties of Multiplication of Fractional Numbers

Fraction – Definition

A fractional number is nothing but a section, portion, or part of any given quantity. Fractions are usually represented in the form of \(\frac { m }{ n } \), where m  is called a numerator, and n is known as a denominator.

How to Divide Fractional Numbers?

We have to convert the given second fraction into its reciprocal and then multiply it with the given first fraction. Next, we just need to simplify the fraction to its lowest terms.

Problems on Division of Fractional Numbers

All the below-mentioned solved problems on dividing fractions numbers will help you to get every piece of detailed information and also helps you to score better marks in the exam. So let’s see few problems.

Division of a Fraction with a Whole Number

Solve the equation dividing a faction number \(\frac { 6 }{ 5 } \) with a whole number 10

First, we need to convert our given whole number 10 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 10 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 10 }{ 1 } \) which gives \(\frac { 1 }{ 10 } \)

Now we have to multiply both fractions \(\frac { 6 }{ 5 } * \frac { 1 }{ 10 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 6 * 1 }{ 5 * 10 } \)

Which gives \(\frac { 30 }{ 10 } \).

The result of dividing a facrtion \(\frac { 6 }{ 5 } \) with a whole number 10 is \(\frac { 30 }{ 10 } \).

Fractional number \(\frac { 30 }{ 10 } \) can be simplifed into lowest terms as \(\frac { 3 }{ 1 } \) since both these integers can be divided by 2.

Solve the equation dividing a faction number \(\frac { 2 }{ 4 } \) with a whole number 6

First, we need to convert our given whole number 6 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 6 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 6 }{ 1 } \) which gives \(\frac { 1 }{ 6 } \)

Now we have to multiply both fractions \(\frac { 2 }{ 4 } * \frac { 1 }{ 6 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 2 * 1 }{ 4 * 6 } \)

Which gives \(\frac { 2 }{ 24 } \).

The result of dividing a facrtion \(\frac { 2 }{ 4 } \) with a whole number 6 is \(\frac { 2 }{ 24 } \).

Fractional number \(\frac { 2 }{ 24 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 12 } \) since both these integers can be divided by 2.

Answer: \(\frac { 1 }{ 12 } \)

Division of a Whole Number with a Fractional Number.

Solve the equation dividing a whole number 5 with a factional number \(\frac { 3 }{ 15 } \)

First, we need to convert our given whole number 5 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 5 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 5 }{ 1 } \) which gives \(\frac { 1 }{ 5 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 5 } * \frac { 3 }{ 15 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 3 }{ 5 * 15 } \)

Which gives \(\frac { 3 }{ 75 } \)

The result of dividing a whole number 5 with a fractional number \(\frac { 3 }{ 15 } \) is \(\frac { 3 }{ 75 } \).

Fractional number \(\frac { 3 }{ 75 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 25 } \) since both these integers can be divided by 3.

Answer: \(\frac { 1 }{ 25 } \)

Solve the equation dividing a whole number 2 with a factional number \(\frac { 5 }{ 4 } \)

First, we need to convert our given whole number 2 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 2 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 2 }{ 1 } \) which gives \(\frac { 1 }{ 2 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 2 } * \frac { 5 }{ 4 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 5 }{ 2 * 4 } \)

Which gives \(\frac { 5 }{ 6 } \)

The result of dividing a whole number 2 with a fractional number \(\frac { 5 }{ 4 } \) is \(\frac { 5 }{ 6 } \)

The answer remains the same since 5 and 6 do not have common factorials so it can be simplified further.

Answer: \(\frac { 5 }{ 6 } \).

Dividing a Fractional Number with another Fractional Number

Solve the equation dividing these factional number \(\frac { 5 }{ 4 } \) and \(\frac { 2 }{ 3 } \).

First, we need to find the reciprocal of the second fractional number \(\frac { 2 }{ 3 } \) which gives \(\frac { 3 }{ 2 } \)

Now we have to multiply both fractions \(\frac { 5 }{ 4 } * \frac { 3 }{ 2 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 5 * 3 }{ 4 * 2 } \)

Which gives \(\frac { 15 }{ 8 } \)

The result of dividing a fractional number \(\frac { 5 }{ 4 } \)with another fractional number \(\frac { 2 }{ 3 } \) is \(\frac { 15 }{ 8 } \)

The answer remains the same since 15 and 8 do not have common factorials so it can be simplified further.

Answer: \(\frac { 15 }{ 8 } \).

Solve the equation dividing these factional number \(\frac { 9 }{ 4 } \) and \(\frac { 2 }{ 3 } \).

Now we have to multiply both fractions \(\frac { 9 }{ 4 } * \frac { 3 }{ 2 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 9 * 3 }{ 4 * 2 } \)

Which gives \(\frac { 27 }{ 8 } \)

The result of dividing a fractional number \(\frac { 9 }{ 4 } \)with another fractional number \(\frac { 2 }{ 3 } \) is \(\frac { 27 }{ 8 } \)

The answer remains the same since 27 and 8 do not have common factorials so it can be simplified further.

Answer: \(\frac { 27 }{ 8 } \)

Division of a Whole Number with a Mixed Fractional Number

Solve the equation dividing a whole number 4 with a mixed factional number 2\(\frac { 9 }{ 13 } \)

First, we need to convert our given whole number 4 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 4 }{ 1 } \)

Now we need to find the reciprocal of \(\frac { 4 }{ 1 } \) which gives \(\frac { 1 }{ 4 } \)

We have to convert the given mixed fractional number into the simple fractional number 2\(\frac { 9 }{ 13 } \) becomes \(\frac { 35 }{ 13 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 4 } * \frac { 35 }{ 13 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 35 }{ 4 * 13 } \)

Which gives \(\frac { 35 }{ 52 } \)

The result of dividing a whole number 2 with a fractional number 2\(\frac { 9 }{ 13 } \) is \(\frac { 35 }{ 52 } \)

The answer remains the same since 35 and 52 do not have common factorials so it can be simplified further.

Answer: \(\frac { 35 }{ 52 } \).

Solve the equation dividing a whole number 6 with a mixed factional number 2\(\frac { 2 }{ 3 } \)

We have to convert the given mixed fractional number into the simple fractional number 2\(\frac { 2 }{ 3 } \) becomes \(\frac { 8 }{ 3 } \)

Now we have to multiply both fractions \(\frac { 1 }{ 6 } * \frac { 8 }{ 3 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 1 * 8 }{ 6 * 3 } \)

Which gives \(\frac { 8 }{ 18 } \)

The result of dividing a whole number 6 with a fractional number 2\(\frac { 2 }{ 3 } \) is \(\frac { 8 }{ 18 } \)

Fractional number \(\frac { 8 }{ 18 } \) can be simplifed into lowest terms as \(\frac { 4 }{ 9 } \) since both these integers can be divided by 2.

Answer: \(\frac { 4 }{ 9 } \).

Division of a Mixed Fractional Number with a Whole Number

Solve the equation dividing mixed factional number 3\(\frac { 1 }{ 4 } \) with a whole number 3.

We have to convert the given mixed fractional number into the simple fractional number 3\(\frac { 1 }{ 4 } \) becomes \(\frac { 13 }{ 4 } \)

Now to convert our given whole number 3 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 3 }{ 1 } \)

Let us find the reciprocal of \(\frac { 3 }{ 1 } \) which gives \(\frac { 1 }{ 3 } \)

Now we have to multiply both fractions \(\frac { 13 }{ 4 } * \frac { 1 }{ 3 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 13 * 1 }{ 4 * 3 } \)

Which gives \(\frac { 13 }{ 3 } \)

The result of dividing a mixed fractional number 3\(\frac { 1 }{ 4 } \) with a whole number 3 is \(\frac { 13 }{ 3 } \)

The answer remains the same since 13 and 3 do not have common factorials so it can be simplified further.

Answer: \(\frac { 13 }{ 3 } \).

Problem 10:

Solve the equation dividing mixed factional number 2\(\frac { 2 }{ 3 } \) with a whole number 8.

Now to convert our given whole number 8 into a fractional number by simply just adding 1 as its denominator. which gives \(\frac { 8 }{ 1 } \)

Let us find the reciprocal of \(\frac { 8 }{ 1 } \) which gives \(\frac { 1 }{ 8 } \)

Now we have to multiply both fractions \(\frac { 8 }{ 3 } * \frac { 1 }{ 8 } \)

As we already know we can simplify this by multiplying numerators and denominators with each other \(\frac { 8 * 1 }{ 3 * 8 } \)

Which gives \(\frac { 8 }{ 24 } \)

The result of dividing a mixed fractional number 2\(\frac { 2 }{ 3 } \) with a whole number 8 is \(\frac { 8 }{ 24 } \)

Fractional number \(\frac { 8 }{ 24 } \) can be simplifed into lowest terms as \(\frac { 1 }{ 3 } \) since both these integers can be divided by 2.

Answer: \(\frac { 1 }{ 3 } \).

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