number addition problem solving

Addition is ...

... bringing two or more numbers (or things) together to make a new total.

Example: When we add 2 and 3 we get 5 .

We can write it like this:

Write this down, with the answer, using numerals :

You should get:   4 + 3 = 7  

Have a Play

Drag the numerals to the two blue boxes see how addition works:

Swapping Places

Swapping the position of the numbers we are adding still gets the same result!

More Examples:

5 + 1 = 1 + 5 = 6

7 + 11 = 11 + 7 = 18

4 + 100 = 100 + 4 = 104

You get better at addition with practice, so we have:

Math Trainer - Addition (train your memory)

Kindergarten Worksheets (easy addition)

Addition Worksheets (normal and advanced)

Tips and Tricks

Learn more on our Addition Tips and Tricks page

Addition Table

We can also "look up" answers for simple addition using the Addition Table (but it is really best to learn to remember the answers).

Example: Find 3 + 5

• find the row starting with "3"

• move along to be under the column "5"

• and there is the number "8", so 3 + 5 = 8

Larger Numbers: Use Addition in Columns

Other names for Addition are Sum, Plus, Increase, Total

And the numbers to be added together are called the " Addends ":

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It's best to leave the range for 'sum' empty. If you fill in a step-size for the "sum" and for addend 1, and the script is not working right, please set the step-size for addend 2 to be 1.

Advanced options

3 addends 4 addends 5 addends 6 addends

Problem Solving on Addition

Problem solving on addition will help us to get the idea on how to solve the basic addition statement problems.

1.  Three boys were playing cricket. Two more boys came along and played cricket with them. How many boys altogether were playing cricket?

Number of boys were playing cricket = 3

Number of boys came along and played cricket with them = 2

Therefore, total number of boys were playing cricket = 3 + 2 = 5

2.  Harry had 5 stamps. Mother gave him 4 more. How many stamps in all did Harry have?

Number of stamps Harry had = 5

Number of stamps his mother gave him = 4

Therefore, total number of stamps he have = 5 + 4 = 9

3. Rachael had 6 stamps. Father gave her 2 stamps. How many stamps does Rachael have now?

Number of stamps Rachael had = 6

Number of stamps her father gave her = 4

Therefore, total number of stamps she have now = 6 + 4 = 10

4. In a classroom, there were 2 brown tables, 1 red table and 3 green tables. How many tables were there altogether?

Number of brown tables = 2

Number of red table = 1

Number of green tables = 3

Therefore, total number of tables in a classroom = 2 + 1 + 3 = 6

5. Jack spent 5 dollars for a pen, 3 dollars for a color box, 2 dollars for a pencil box. How much did he spend altogether?

Amount of money Jack spent for a pen = $5

Amount of money he spent for a color box = $3

Amount of money he spent for a pencil box = $2

Therefore, total amount of money he spend altogether = $5 + $3 + $2 = 10

6. There were 6 yellow hats, 2 red hats and 6 blue hats. How many hats were there?

Number of yellow hats = 6

Number of red hats = 2

Number of blue hats = 6

Therefore, total number of hats were there = 6 + 2 + 6 = 14

7. Alex had 4 books on cars, 5 on airplanes and 7 on boats. How many books did he have in all?

Number of books on cars Alex had = 4

Number of books on airplanes = 5

Number of books on boats = 7

Therefore, total number of books he have in all = 4 + 5 + 7 = 16

More examples on statement problem solving on addition:

8. In a game Mary had the best score. She made 8 in her first turn, 6 in her second and 5 in her third. What was her total score?

Number of score Mary had in her first turn = 8

Number of score in her second turn = 5

Number of score in her third turn = 7

Therefore, total number of score Mary had in a game = 8 + 5 + 7 = 20

9. Sarah had 25 cards. She got 7 cards more. How many cards did she have then?

Number of cards Sarah had = 25

Number of cards she got more = 7

Therefore, total number of cards she have then = 25 + 7 = 32

10. A farmer had 45 sheep before he bought 25 more. How many sheep did he have then?

Number of sheep a farmer had = 45

Number of sheep he bought more = 25

Therefore, total number of sheep he have then = 45 + 25 = 70

Word Problems on Addition:

11. A basket had 28 mangoes in it. 14 more mangoes are kept in the basket. How many mangoes are there in the basket now?

The basket had                 2 8    mangoes

Mangoes kept in       (+)   1 4                      

Now, there are                 4 2 mangoes in all

Thus, there are 42 mangoes in the basket now.

12. Aaron scored 33 runs in the first cricket match and 29 runs in the second. How many runs did he score in all?

Aaron scored                  3 3  runs in the first match

He scored                (+)  2 9  runs in the second match

He scored                       6 2  runs in all                      

Thus, he scored 62 runs in all.

2nd Grade Math Practice

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100 Single-Digit Addition Questions with No Regrouping (A)

Welcome to The 100 Single-Digit Addition Questions with No Regrouping (A) Math Worksheet from the Addition Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2020-10-16 and has been viewed 527 times this week and 2,200 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Addition problem search.

This is a word-search type of puzzle but with math problems hidden in the grid instead of words. The problems only read forward, and you can make it a little harder to search by selecting diagonals too.

Be careful not to overestimate your students’ ability to do this puzzle. It can be very frustrating if they are given a large puzzle with diagonals before they are ready.

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Addition Word Problem Worksheets

The addition word problem worksheets presented here involve performing addition operations with regrouping and without regrouping. Our extensive and well-researched word problem worksheets feature real-life scenarios that involve single-digit addition, two-digit addition, three-digit addition, and addition of large numbers. These pdf handouts are designed to provide ample practice for elementary school children. Free worksheets are included.

Single-digit Addition Word Problems

These printable practice worksheets involve simple addition of single-digit numbers. Read the word problems and perform addition operations to arrive at the answers.

• Download the set

Addition Word Problems: Sum up to 20

Featured in these worksheets are engaging word problems whose sums add up to 20. Addends may have a combination of single-digit and two-digit numbers.

Addition Problems: Two-digit and Single-digit

A number of real-life scenarios in the form of word problems featured in the addition worksheets here involve single digit and two-digit addends.

Two-digit Addition Problems - No Regrouping

The word problems in this section do not require regrouping or carrying. Find the answers to the word problems that feature two-digit addends.

Two-digit Addition Problems - With Regrouping

All two-digit addition word problems presented in this set of worksheets here require regrouping (carry over). Follow the place value columns to sum up the two-digit addends.

Theme based Word Problems

Presented here are worksheets with three colorful themes - Fall Season, Aquarium and Theme Park. Read the questions and solve the word problems. Answer keys are included.

Three-digit and Two-digit Addition

A total of 15 addition word problems spread over three PDF worksheets presented here require you to sum up three-digit addends with the two-digit addends.

Three-digit Addition Word Problems

Enhance your arithmetic skills. Read the word problems and sum up three-digit addends in these printable worksheets. Some problems may require regrouping. Answer key included in each worksheet.

Multi-digit Addition Word Problems: Adding Large Numbers

The word problems presented in the worksheets here feature large numbers with addends up to eight digits.

Related Worksheets

» Subtraction Word Problems

» Multiplication Word Problems

» Division Word Problems

» Math Word Problems

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3rd Grade Addition and Subtraction

Word problems.

Welcome to our 3rd Grade Addition and Subtraction Word Problems page. Here is our selection of free addition and subtraction word problem worksheets, which will help your child practice solving a range of addition and subtraction problems using 3-digit and 4-digit numbers.

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• 3 Digit Addition & Subtraction Word Problems
• 4 Digit Addition & Subtraction Word Problems
• 2-Step Addition & Subtraction Word Problems
• Easier Addition & Subtraction Worksheets
• More related resources
• Addition & Subtraction Word Problems up to 1000 Online Quiz

3-digit and 4-digit Word Problems

Each sheet consists of a range of 5 addition and subtraction word problems with numbers up to thousands.

There is a space on each sheet for working out, so that your child can write out the problem and solve it.

We have split the worksheets up into 3-digit word problems and 4-digit word problems.

Using these sheets will help your child to:

• add and subtract numbers with 3-digit and 4-digit numbers;
• solve addition and subtraction word problems with and without regrouping.
• recognise the language used in addition and subtraction - sum, total, difference, how many more, etc.
• solve problems involving more than 1 step.

3rd Grade Addition and Subtraction Word Problems

3-digit addition and subtraction word problems.

There are two versions of each sheet.

The first version (version A) contains problems where no regrouping is needed.

The second version (version B) contains similar problems but regrouping is needed to solve them.

Answers have been provided with each sheet, along with the calculation needed to solve the problem.

The following sheets are all 1-step addition or subtraction word problems.

• 3-Digit Addition and Subtraction Word Problems Sheet 1A (no regrouping)
• PDF version
• 3-Digit Addition and Subtraction Word Problems Sheet 1B
• 3-Digit Addition and Subtraction Word Problems Sheet 2A (no regrouping)
• 3-Digit Addition and Subtraction Word Problems Sheet 2B

4-digit Addition and Subtraction Word Problems

The word problems all involve either addition or subtraction (both with and without regrouping).

• 4-Digit Addition and Subtraction Word Problems Sheet 1
• 4-Digit Addition and Subtraction Word Problems Sheet 2

Harder 2-Step Addition and Subtraction Word Problems

These problems are trickier than those above.

Each problem involved two steps to solve, and may involve just addition, just subtraction or both operators.

There are 4 problems on each sheet, and more space to work out the solutions.

• 2-Step Addition Subtraction Problems up to 3-digits Sheet 1
• 2-Step Addition Subtraction Problems up to 4-digits Sheet 1

Looking for some easier worksheets?

Take a look at our Subtraction word problems for first graders.

On this page, your child will learn to work out basic subtraction word problems with numbers to 20.

• 2nd Grade Addition and Subtraction Word Problems (up to 100)

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More 3rd Grade Addition and Subtraction Worksheets

Here you will find some more of our Addition and Subtraction Worksheet generators for creating your own bespoke addition and subtraction worksheets.

• Addition Subtraction Fact Worksheets (randomly generated)
• Column Addition and Subtraction Worksheets (randomly generated)

More 3rd Grade Math Word Problems

Using the 3rd Grade Math worksheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• develop their knowledge of fractions;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems.

These sheets involve solving one or two more challenging longer problems.

• 3rd Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

• Math Word Problems for kids 3rd Grade

These sheets involve solving 3-digit and 4-digit addition word problems.

• Addition Word Problems 3rd Grade (3- and 4-digits)

These sheets involve solving 3-digit and 4-digit subtraction problems.

• Subtraction Word Problems 3rd Grade

These sheets involve solving a range of multiplciation problems.

• Multiplication Word Problem Worksheets 3rd Grade

These sheets involve solving a range of division problems.

• Division Worksheets Grade 3 Word Problems

Addition and Subtraction Word Problems to 1000 Online Quiz

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This quick quiz tests your knowledge and skill at solving addition and subtraction word problems within 1000.

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Addition and Subtraction KS1

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

What's in a Name?

What do you notice about these squares of numbers? What is the same? What is different?

Sort Them Out (1)

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Number Balance

Can you hang weights in the right place to make the the number balance balanced?

What Was in the Box?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Arranging Additions and Sorting Subtractions

Order these four calculations from easiest to hardest. How did you decide?

Domino Sorting

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

One Big Triangle

Make one big triangle so the numbers that touch on the small triangles add to 10.

Subtraction Slip

Can you spot the mistake in this video? How would you work out the answer to this calculation?

Pairs of Numbers

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Butterfly Flowers

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

Equivalent Pairs

Can you match pairs of cards which show the same amount?

Number Lines

A resource to try once children are familiar with number lines, and they have begun to use them for addition. It could be a good way to talk about subtraction. Leah and Tom each have a number line. Can you work out where their counters will land?

Two Spinners

What two-digit numbers can you make with these two dice? What can't you make?

The Add and Take-away Path

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

What Could It Be?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Find all the numbers that can be made by adding the dots on two dice.

Unit Differences

This challenge is about finding the difference between numbers which have the same tens digit.

Cuisenaire Counting

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

Jumping Squares

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Ladybirds in the Garden

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Secret Number

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

Eggs in Baskets

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Birthday Cakes

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Find the Difference

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Dicey Addition

Who said that adding couldn't be fun?

This is an adding game for two players. Can you be the first to reach the target?

Doing and Undoing

An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting.

Sitting Round the Party Tables

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

How Do You See It?

Here are some short problems for you to try. Talk to your friends about how you work them out.

What could the half time scores have been in these Olympic hockey matches?

Strike it Out

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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[FREE] Fun Math Games & Activities Packs

Always on the lookout for fun math games and activities in the classroom? Try our ready-to-go printable packs for students to complete independently or with a partner!

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

To multiply fractions, multiply the numerators and multiply the denominators.

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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