how to use fractions to solve word problems

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

• Download the set

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

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28 Fraction Word Problems for Year 2 to Year 6 With Tips On Supporting Pupils’ Progress

Emma Johnson

Fraction word problems are an important piece in teaching fractions. Fractions are a key component of the National Curriculum throughout primary, with children introduced to the concept in Year 1 and continuously building upon their knowledge and understanding, through to Year 6 and beyond.

The abstract nature of fractions makes them one of the more difficult areas of maths for children to understand. It is essential that they are taught through the use of concrete resources and visual images, but also through a link to the real world. Word problems are a great way to help children develop this understanding and should be used alongside any fluency work the children do.

To help you with this, we have put together a collection of 20 word problems which can be used with children from Year 2 to Year 6.

Fraction word problems in the national curriculum

• Why are word problems important for children’s understanding of fractions?

How to teach fraction word problem solving in primary school

Fraction word problems for primary , fraction word problems for year 2, fraction word problems for year 3, fraction word problems for year 4, fraction word problems for year 5, fraction word problems for year 6, more word problems resources.

Fraction Lessons Resource Pack

Download this free pack of fraction lessons to support your students and help them to practice fractions problems.

Fractions in KS1

Pupils are first introduced to fractions in Year 1, where they begin to recognise a half and quarter of a shape or quantity. As they progress through Key Stage 1, they are introduced to a wider range of fractions.

In Year 2 pupils need to be able to recognise, find, name and write fractions \frac{1}{3}, \ \frac{1}{4}, \ \frac{2}{4} and \frac{3}{4} of lengths, shape, a set of objects or quantity.

Fractions in lower KS2

Once pupils move into Key Stage 2, there is an increased focus on fractions, with a significant period of time dedicated to developing students’ knowledge and building on previous learning from Year 3 through to Year 6.

In Year 3, pupils are taught to count in tenths; recognise, find and write fractions of a discrete set of objects; understand the term ‘unit’ and ‘non-unit’ fractions; recognise equivalent fractions, compare and order fractions and add/subtract fractions with the same denominator. At this stage, pupils also begin to solve simple problems involving fractions.

As pupils progress into Year 4, they are also introduced to the concept of decimals alongside the work on fractions. They build upon their understanding of equivalent fractions and adding/ subtracting fractions (still with the same denominator.

They also learn to count up and down in hundredths, recognise and write decimals equivalent to \frac{1}{4}, \ \frac{1}{2} and \frac{3}{4} and begin to solve problems with increasingly harder fractions.

Fractions in upper KS2

As pupils continue through the school, into upper Key Stage 2, they continue to build on their learning. They are introduced to mixed numbers and improper fractions. They are also introduced to the concept of percentages alongside fractions and decimals.

In Year 5, children build on the knowledge gained in Year 4, comparing and ordering fractions; recognising equivalent fractions; addition and subtraction of fractions (with different denominators, but multiples of the same number). Fractions appear in addition and subtraction word problems .

They are also introduced to the multiplication of fractions; converting between improper fractions and mixed numbers and the link between fractions, decimals and percentages. By Year 5 pupils will be completing more complex problems, including multi-step word problems and multiplication word problems .

In Year 6, pupils consolidate and build upon the knowledge of fractions they have gained so far. Pupils continue to add and subtract fractions (with different denominators and mixed numbers). They also develop their understanding of how to multiply fractions and begin to divide fractions by whole numbers, combining fraction and division word problems .

Pupils also continue to build upon their understanding of the equivalences between fractions, decimals and percentages and solve increasingly complex one-step, two-step and multi-step percentage word problems .

Why are word problems important for children’s understanding of fractions?

Word problems, alongside the use of concrete resources and visual images, help children to make sense of the abstract nature of fractions. 

For example, if children were presented with the question \frac{6}{8} ÷ 3, some might find this difficult to access. If children are given it as a word problem, alongside a visual image, it becomes much more accessible.

The above calculation as a word problem :

 ‘3 children shared \ \it{\frac{6}{8}} of a pizza, how much did each child get?’

Children can see and understand the concept of 3 children sharing 6 slices of pizza, compared to just seeing the written calculation.

As with all word problems, the first thing children need to do is read the question carefully and make sure they understand what is being asked. They then have to decide what calculation is needed and whether they can represent it pictorially.

Here is an example:

Ben has a bag of 48 sweets.

He gives \frac{3}{8} of his bag to his brother

How many sweets does he have left?

How to solve:

What do you already know?

• There are 48 sweets altogether. 
• The denominator is 8, so we know we need to divide the 48 by 8. This will tell us how many sweets in \frac{1}{8} .
• The numerator is 3, therefore we need to multiply the answer by 3, to tell us how many sweets are \frac{3}{8} .
• The last step of the problem is to find out how many sweets Ben has left.
• We can either calculate \frac{5}{8} , as we know Ben must have \frac{5}{8} left, or we subtract the number of sweets in \frac{3}{8} from the total of 48.

How can this be drawn/represented pictorially?

• We can draw a bar model, split into 8 sections. 
• The 48 sweets are then shared between the 8 sections (each worth \frac{1}{8} ). 
• We can see that \frac{3}{8} of the 48 sweets equals 18 sweets. 
• We can then either subtract 18 from 48, to work out how many sweets were left. 48 – 18 = 30
• Alternatively, we can calculate how many sweets are in \frac{5}{8} , which is 30.

Word problems are tied in throughout Third Space Learning’s online one-to-one tuition programmes. Tutors work with students to break down word problems and identify the operations needed to solve problems.

The following section lays out the types of fraction word problems that you can expect to see by year group in primary school. 

At Third Space Learning we incorporate word problems into our one-to-one online tutoring . With each lesson designed to suit the needs of each individual student, our tutoring programme aims to deepen mathematical understanding and confidence in maths. 

Fraction word problems are a great way to strengthen students’ conceptual understanding of fractions and grow their problem solving skills. Take a look at our article on fraction games to help with this.

• What Is A Unit Fraction: Explain For Primary School
• What Is An Improper Fraction: Explained For Primary School
• Fractions: A Comprehensive Guide
• How To Teach Fractions Key Stage 2: Maths Bootcamp
• How To Simplify Fractions: A Comprehensive Guide

Word problems in Year 2 involve recognising and naming simple fractions and beginning to understand the concept of equivalence.

Maisie was having a birthday party.

She invited 16 friends. Half of her friends were from her class and a half were from the other Year 2 class. 

How many friends did she invite from each class?

Answer: 8 friends

\frac{1}{2} of 16 = 8

Ahmed baked 12 cookies. 

He ate \frac{1}{4} of them.

How many cookies did Ahmed eat?

\frac{1}{4} of 12 = 3

Sara says ‘I ate \frac{1}{2} a pizza and my friend ate \frac{2}{4} . My friend had more than me, as she had 2 pieces’.

Is she correct? Explain why you have chosen your answer.

Answer: Sara is not correct

\frac{1}{2} is the same as \frac{2}{4}

Tom and Zeyn shared a chocolate bar.

They both had a quarter of the chocolate bar. 

How much was left?

Answer : \frac{1}{2} of the chocolate bar

\frac{2}{4} are equivalent to \frac{1}{2}

Word problems for Year 3 include proper fractions, fractions of amounts, simple equivalent fractions and adding and subtracting fractions with the same denominator. 

Sophie ate \frac{1}{4} of her chocolate bar. 

If the bar had 20 squares, how many squares did Sophie eat?

Answer : 5 squares

\frac{1}{4} of 20 = 20 ÷ 4 = 5

Hamza and Khalifa shared a pizza.

Hamza ate two fourths of the pizza and Khalifa ate one fourth.

How much pizza was left?

Answer : \frac{1}{4}

There are 24 hours in a day.

Maise worked out that she spends \frac{1}{8} of her day on Saturday, doing exercise.

How long does she spend exercising on a Saturday?

Answer: 3 hours

\frac{1}{8} of 24 hours = 24 ÷ 8 = 3

There are 30 children in the class.

\frac{2}{5} of the children are wearing jumpers.

How many children are wearing jumpers?

Answer: 12 children

\frac{1}{5} of 30 = 30 ÷ 5 = 6

\frac{2}{5} of 20 = 12

Word problems for year 4 include equivalent fractions, fractions of quantities (including non-unit fractions and adding/subtracting fractions with the same denominator. Money word problems often appear in Year 4.

Abdullah spent \frac{1}{3} of his pocket money for the month on a new game.

He receives £18 per month.

How much did he spend on the game?

Answer : £6

\frac{1}{3} of 18 = £6

Bethan had a bag of sweets.

She gave \frac{2}{7} of the bag to her mum and ate \frac{3}{7} of herself.

What fraction of the bag was left?

Answer : \frac{2}{7}

Jamal ate \frac{6}{18} of a chocolate bar.

Mason ate \frac{1}{3}

Mason said that Jamal ate more than him. Do you agree? Explain your answer.

Answer : No – they both ate the same.

\frac{1}{3} is equivalent to \frac{6}{18}

\frac{2}{7} of a piece of ribbon is 10cm.

How long is the whole piece of ribbon?

Answer: 35cm

\frac{2}{7} = 10

\frac{1}{7} = 5

\frac{7}{7} = 5 x 7 = 35

Word problems for Year 5 include more complex equivalent fractions, problems involving mixed numbers and improper fractions, adding and subtracting fractions (with different denominators) and multiplying fractions.

There are 60 pupils in Year 5.

Eden carried out a survey on favourite foods.

\frac{1}{5} of the children said pizza, \frac{2}{6} said burgers and \frac{3}{10} said hot dogs.

How many pupils did she survey altogether?

Answer: 50 pupils

\frac{1}{5} of 60 = 12

\frac{2}{6} 0f 60 = 20

\frac{3}{10} = 18

The Johnson family are driving to the zoo.

They have driven \frac{5}{9} of their journey, which is 45 miles.

How much further do they have to drive, to reach their holiday home?

Answer: 20 miles left to drive

\frac{5}{9} = 45, therefore \frac{1}{9} = 45 ÷ 9 = 5. 

\frac{5}{9} = 5 x 5 = 25 miles

\frac{9}{9} = 9 x 5 = 45 miles

45 – 25 = 20

Macy is taking part in the school maths challenge. 

She is given a word problems worksheet containing 36 questions.

Macy gets \frac{7}{9} of the questions correct.

How many does she get wrong?

Answer: 8 questions wrong

\frac{1}{9} of 36 = 4

\frac{7}{9} = 28

\frac{2}{9} = 8

Oliver and Zac are making smoothies.

They make 800 ml of smoothies.

\frac{2}{5} is made from apples, \frac{3}{7} from strawberries and the rest from orange juice.

How many ml of orange juice do they add to the apples and strawberries?

Answer: 180ml orange juice

\frac{2}{5} of 800: \frac{1}{5} = 160ml, \frac{2}{5} = 320 ml apple juice

\frac{3}{8} of 800: \frac{1}{8} = 100, \frac{3}{8} = 300 ml strawberry juice

800 – 620 = 180ml 

Word problems for year 6 include adding and subtracting fractions with different denominators and mixed numbers, multiplying fractions, dividing fractions by whole numbers and finding equivalent fractions, decimals and percentages.

Children in a Year 6 Class at Oak Tree Middle School are answering a set of ratio questions. 

There are 10 questions and 28 children completing the activity. 

If the children got \frac{6}{7} of the total number of questions correct between them. 

How many did they get wrong?

Answer: 40 questions wrong

28 x 10 = 280 questions

\frac{1}{7} of 280 = 40 

\frac{6}{7} = 40 x 6 = 240

Amber and her 5 friends are sharing 4 pizzas for her birthday party.

The pizzas are split into sixths. 

If they each eat the same amount of pizza, how many slices does each person at the party get?

Answer: 4 slices

This is a dividing fractions word problem

\frac{24}{6} ÷ 6 = \frac{4}{6}

A group of friends win a quarter of the total lottery prize for the week.

There are 4 friends and each friend shares an equal fraction of the quarter.

What fraction of the total lottery prize does each friend get?

Answer: \frac{1}{16} of the prize fund

Each friend gets \frac{1}{4} of the \frac{1}{4} prize fund

There are 30 children in the class

\frac{7}{10} of the pupils in the class are girls.

\frac{3}{7} of the girls have their ears pierced.

How many girls have their ears pierced?

Answer: 9 girls have their ears pierced

\frac{1}{10} = 3, \ \frac{7}{10} = 21 girls

\frac{1}{7} of 21 = 3. \ \frac{3}{7} = 3 x 3 = 9

Third Space Learning offers a wide range of practice word problems for all primary year groups and covering a large number of topics, including; time word problems , ratio word problems , fraction questions , addition word problems and subtraction word problems .

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Fractions Operations Word problems

April 05, 2024

Fractions are an important part of the curriculum of each grade and we spend a lot of time teaching the concept of fractions, their operations, and more. They are used in various aspects of everyday life, from cooking recipes to financial transactions. Word problems with fractions create scenarios of real life and show the students how fractions and their operations are necessary to know and understand. We know the benefits of using word problems in our instructions, however, I have the feeling that when it comes to fractions we focus more on computation and less on problem-solving activities. The reason is that for many students the concept of fractions is a challenging one and it takes time and practice to make sure they fully comprehend it. Apart from knowing how to solve fraction operations, the students need to know which operation/operations to use based on the information of the word problem. Below are some more benefits of using word problems when teaching fraction operations.

Real-world Application

Fractions word problems help students understand the practical application of fractions in real-life scenarios. Whether it’s splitting a bill, measuring ingredients for a recipe, or determining the distance traveled, fractions are everywhere. By solving word problems, students can relate mathematical concepts to everyday life, making learning more relevant and engaging.

Critical Thinking and Problem-Solving Skills

Word problems require students to read, comprehend, and analyze the problem before applying mathematical concepts to find a solution. This process enhances critical thinking and problem-solving skills, which are valuable not only in math but across all subjects and in daily life. Students learn to break down complex problems into manageable parts, identify relevant information, and apply appropriate methods to solve problems.

Improved Communication Skills

Solving word problems often requires students to explain their thought process, and reasoning, either in writing or verbally. This practice improves mathematical communication skills, helping students to clearly and effectively articulate their ideas and solutions. Being able to communicate about math is essential for academic success and is a valuable skill in the workforce.

Building Confidence

Word problems can be challenging, but overcoming these challenges can significantly boost a student’s confidence in their math abilities. As students become more proficient in solving fractions’s word problems, they develop a growth mindset, understanding that effort and persistence can improve their skills. This confidence can positively affect their attitude towards math and learning in general.

Word problems that make fraction operations interesting often involve scenarios that students can relate to or find engaging. Here are a few types of word problems that can make learning about fractions more fun and relevant:

Cooking and Recipes

Problems that involve adjusting recipes are great for practicing fractions. For example, if a cookie recipe is for 4 dozen cookies but you only want to make 1 dozen, how do you adjust the ingredients? These problems can be relatable for students who enjoy cooking or baking, making fractions more interesting by applying them to real-life situations.

Sports and Games

Using fractions to describe scores, statistics, or probabilities in sports can make math more engaging for students interested in athletics. For instance, a word problem might ask what fraction of a basketball team’s points were scored by a certain player, or what the probability is of rolling a fraction on a specially designed dice in a game.

Shopping and Money

Problems involving discounts, sales tax, and budgeting can make fractions come alive. Asking students to calculate the final price of an item after a 1/5 off discount or to figure out how to split a budget for a project into various fractions for different expenses connects math with practical money management skills.

Nature and Science

Word problems that involve fractions in the context of natural phenomena or scientific experiments can be fascinating. For example, consider a problem that asks students to calculate what fraction of a day certain animals sleep based on given data or to measure ingredients for a science experiment.

Art and Music

Integrating fractions with art and music can also make for compelling problems. Students could be asked to find what fraction of a painting’s area is covered by a certain color or to determine the fraction of notes that are quarter notes in a piece of music. These problems can help students see the beauty and application of fractions in creative fields.

Travel and Adventure

Word problems that involve calculating distances, fuel usage, or time spent on different parts of a journey can capture the imagination. For example, if you travel 3/4 of your journey by train and the rest by bus, what fraction of your time was spent on the bus if the whole trip took 8 hours?

Construction and Design

Asking students to calculate the materials needed for building a model or designing a garden, using fractions to measure distances or quantities, can make math feel like a creative and constructive endeavor. For example, designing a flower bed where 1/2 of the area is roses, 1/4 is tulips, and the rest is daisies.

I have created a collection of Fraction Operations-word problems with their solutions. The collection includes 69 word-problems starting with addition problems (like and unlike) then subtraction followed by multiplication and division problems. After that, there are mixed operations word problems and some challenging problems. The solutions are included.

Find the google slides collection here

Find the print cards collection here

Find the worksheet collection here

Find the bundle here

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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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Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

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Fraction: Two-Step Word Problems

Related Topics & Worksheets: More Fractions Worksheets Fraction Games

Objective: I can solve two-step word problems involving addition and subtraction of fractions & mixed numbers.

“Fraction Word Problems” Worksheets: Fraction Word Problems (Add, Subtract) 2-Step Fraction Word Problems (Add, Subtract)

1-Step Mixed Number Word Problems (Add, Subtract) 2-Step Mixed Number Word Problems (Add, Subtract)

Solving two-step fraction word problems involves breaking down the problem into smaller steps and using fraction operations to find the solution.

Steps to Solve Two-Step Fraction Word Problems:

• Read and Understand the Problem:
• Carefully read the word problem to understand what it is asking. Identify the quantities, units of measurement, and any other relevant details.
• Determine what information is given in the problem and what is known.
• Identify what the problem is asking you to find. This may involve finding intermediate values or the final solution.
• Decide on a strategy to solve the problem. This may involve breaking the problem into smaller steps, using fraction operations, or applying other problem-solving techniques.
• Follow your plan and perform the necessary calculations to solve each step of the problem. Use fraction operations such as addition, subtraction, multiplication, and division as needed.
• After solving each step, check your answer to ensure it makes sense and matches the problem’s requirements.
• If the problem involves multiple steps, combine the results from each step to find the final solution.
• Clearly state your final answer in the context of the problem.

Printable Fraction Word Problems

(Answers on the second page.) Fraction Word Problems Worksheet #1 Fraction Word Problems Worksheet #2 Fraction Word Problems Worksheet #3

Online Fraction Word Problems

Solve the following word problems. Percy spent 1/4 of his money on a food and another 3/10 of his money on a drink. a. What fraction of his money did he spend in total? b. What fraction of Percy’s money was left? Sally has a piece of cloth. She used 1/3 of the cloth to make a pillow cover and another 4/7 of the cloth to make a tablecloth. a. What fraction of the cloth was used altogether for the pillow cover and tablecloth? b. What fraction of the cloth was left over? A container is 1/3 full of water and 1/4 full of oil. What fraction of the container is empty? Kathy spent 5/8 of her money on books and another 1/6 of her money on stationeries. What fraction of Kathy’s money was left? Carl used 2/9 of piece of string to tie a parcel and another 1/4 of the string to tie a box. What fraction of the string was left?

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