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  • Fractions & decimals

Introduction to Fractions Workbook

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Fractions & Decimals Worksheets for Grade 3

Free fraction and decimals worksheets.

Our grade 3 fractions and decimals worksheets provide practice exercises on introductory fraction and decimal concepts , including identifying fractions, equivalent fractions, simplifying fractions and basic decimal addition and subtraction.  

year 3 maths worksheets fractions

Sample Grade 3 Fractions Worksheet

More fractions worksheets

Explore all of our fractions worksheets , from dividing shapes into "equal parts" to multiplying and dividing improper fractions and mixed numbers.

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year 3 maths worksheets fractions

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Year 3 Fractions

Click on an objective for related worksheets and resources.

Exercises and Materials for Teaching Math

Year 3 Fractions Worksheets PDF Free

year 3 maths worksheets fractions

Fractions addition 1

 Fractions addition 1

Fractions addition 1 printable math worksheet

Print here >

Fractions addition 2

 Fractions addition 2

Fractions addition 2 printable math worksheet

Fractions comaparisons

 Fractions comaparisons

Fractions comaparisons printable math worksheet

Fractions comparisons

 Fractions comparisons

Fractions comparisons printable math worksheet

Fractions half quater third

 Fractions half quater third

Fractions half quater third printable math worksheet

Fractions of circles

 Fractions of circles

Fractions of circles printable math worksheet

Fractions shown with circles squares

 Fractions shown with circles squares

Fractions shown with circles squares printable math worksheet

Fractions shown with pictures

 Fractions shown with pictures

Fractions shown with pictures printable math worksheet

All Grade 3 Worksheets >

Grade 3 Worksheets >

For children in Year 3, the most useful fractions worksheets are time saving, allowing students to complete tasks independently without any adult help. The questions on these worksheets will cover basic concepts like adding and subtracting fractions, ordering and comparing fractions, and comparing and ordering sets of objects. The key to these worksheets is to get children to review the required fractions skills until they are fully understood.

These worksheets will help your child compare and order fractions with the same denominator, as well as explain how they differ in magnitude. For example, if you give a fifth compared to a third, you would ask your child to explain how a fifth is larger than a third. Luckily, a fifth is much smaller than a third, which is the reason why simple fractions are more commonly used to practice.

If you're looking for a fractions worksheet that is both engaging and informative, look no further. Free math resources are a fantastic way to get kids excited about learning this new concept. Several websites have hundreds of printable handouts and exclusive pages in each subtopic. These test sheets are geared toward early learners, and will provide them with a comprehensive review of the basics. A great resource for year three fractions are the worksheets with Fraction Strips, a visual graphic tool that helps children understand fractions through pictures.

These worksheets cover a wide variety of fraction topics, including adding and subtracting fractions with different denominators, understanding 24 hours on an analogue clock with fractions, and finding the duration of events. They also focus on dividing fractions by whole numbers, as well as on division. Some of the year three worksheets involve pictures showing shaded portions. There are many worksheets for all of these topics, so you can be sure that you'll find something that will resonate with your students.

The questions are designed to be both simple and complex, and can be completed in as little time as 30 minutes per day. However, it is important to note that a Year 3 fractions worksheet should cover every topic related to a particular skill. If you want your child to learn how to add and subtract fractions of a dollar, it is essential to practice with the worksheets that involve the use of money.

The best worksheets for this subject include ones that help children learn the relationship between fractions and division.

As you can see, there are many worksheets that relate to the objectives of the curriculum. It's also a good idea to keep track of the progress of your child by noting down their score at each level. Tell us what your experience was using these worksheets.

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Fraction Worksheets for Year 3 (age 7-8)

Children coming into Year 3 should have a sound understanding of simple fractions, especially halves, quarters and thirds.  They should have had plenty of practical experience dividing shapes and sets of objects into quarters and thirds.

There are plenty of new concepts on fractions to be understood in Year 3,but it is still important to use practical work, using shapes and objects, to help with understanding.  A key step is to begin working with tenths and recognising that tenths arise from dividing an object into ten equal parts. Later this can be developed to dividing one-digit numbers or quantities by 10. This is crucial for understanding our decimal system and understanding that a fraction such as three tenths can also be represented as a decimal (0.3) and connects to dividing 3 by 10. Counting in tenths can also help enormously with this. We have a great selection of worksheets which deal with writing tenths, counting in tenths and converting tenths to decimals.

Other fractions are also introduced, such as fifths, and equivalence between fractions is developed with the help of pictures and diagrams. This leads on to ordering fractions with the same denominator. One of the quirks of fractions, which some children find hard to understand, is that as the denominator gets larger the size of the number gets smaller (e.g. one tenth is smaller than one fifth; one twentieth is smaller than one tenth and so on). We have some excellent ordering fractions pages for Year 3 to help consolidate this concept. As well as these, some of our most popular worksheets are the sets of finding fractions of numbers, with questions such as ‘What is one sixth of 30?’ Again, the link between fractions and division needs to be constantly reinforced.

As the year progresses children will be introduced to adding and subtracting fractions, but only with the same denominator and with totals up to one whole one. Simplifying fractions is important at this stage and children should be encouraged to write fractions in their simplest form. (e.g. two sixths can be simplified to one third).

All this will lead onto much more on decimals and fractions in Year 4, including hundredths and further work on equivalence. If you child is finding the Year 3 work difficult then it is important to go back to Year 2, or even Year 1, and see what is understood and what concepts have not been fully understood.

Understand fractions and equivalent fractions

Understanding fractions and work on the importance of equivalent fractions.

Preview of worksheet Complete the fraction sequences

Colour the correct fractions to match the sequences.

Preview of worksheet Ordering fractions

Order simple fractions.

Preview of worksheet Use fraction notation

Various fraction problems.

Preview of worksheet Equivalent fractions

Tricky work on equivalent fractions.

Preview of worksheet Order fractions

Order fractions with the same denominator.

Preview of worksheet Writing fractions

A little bit of revision on reading and writing fractions.

Understanding halves, quarters and thirds

Revision of work on halves, quarters and thirds.

Preview of worksheet Halves, quarters and thirds (1)

Finding halves, quarters and thirds of numbers of bees etc..

Preview of worksheet Halves, quarters and thirds (2)

More finding halves, quarters and thirds.

Preview of worksheet Halves, quarters and thirds (3)

More finding halves, quarters and thirds - fun colouring.

Preview of worksheet Halves and quarters word problems

Some tricky word problems using halves and quarters.

Preview of worksheet More than less than or equal to a half

Ordering fractions as more than, equal to or less than a half.

Understanding tenths

Understanding tenths and counting in tenths.

Preview of worksheet Fractions: tenths

Chocolate cakes to help with understanding tenths.

Preview of worksheet Colouring tenths

Colouring tenths of various shapes.

Preview of worksheet Recognise tenths

Introducing tenths by colouring one tenth; then finding six tenths, seven tenths etc of shapes. Finding out that five tenths is the same as a half.

Preview of worksheet More tenths

Writing tenths in words and as a fraction.

Preview of worksheet Finding tenths: animals

Finding tenths of various animals.

Preview of worksheet Tenths of numbers of objects

Finding tenths of numbers of objects.

Preview of worksheet Tenths as decimals

Looking at tenths as decimals and fractions.

Preview of worksheet Tenths: fractions as decimals

Matching fractions and decimals. ordering fractions and decimals.

Preview of worksheet Count on in tenths

Counting on in tenths.

Preview of worksheet Estimate tenths

Estimating tenths on a number line.

Find fractions of amounts and numbers

Finding fractions of amounts.

Preview of worksheet Fractions of shapes (quarters, thirds, fifths)

Shading quarters, thirds or fifths of various shapes.

Preview of worksheet Find fractions of shapes

Finding fractions of shapes. Makes a change from numbers!

Preview of worksheet Non unit fractions

A non-unit fraction is any fraction which does not have one as a numerator.

Preview of worksheet Fractions: pizzas

Find fractions of pizzas.

Preview of worksheet Fractions: fifths and sixths pizzas

More pizzas, this time concentrating on fifths and sixths.

Preview of worksheet Fractions: Tommy's allotment

Finding fractions of an allotment: equivalent fractions.

Preview of worksheet Find fractions of numbers

Finding fractions of numbers. Working with halves, quarters, thirds and tenths. Remember, to find one fifth, divide by 5.

Preview of worksheet Find fractions of numbers (2)

More finding fractions of numbers.

Preview of worksheet Solving word problems with fractions

Solving word problems involving fractions.

Adding and subtracting fractions

Begin to add and subtract fractions with the same denominator.

Preview of worksheet Adding fractions: bar models

Use the bar models to help with adding fractions.

Preview of worksheet Add fractions

Adding fractions with visual clues.

Preview of worksheet Adding fractions (1)

Adding fractions with the same denominator.

Preview of worksheet Adding fractions (2)

More adding fractions with the same denominator.

Preview of worksheet Subtracting fractions (1)

Subtracting fractions with the same denominator.

Preview of worksheet Subtracting fractions (2)

More subtracting fractions with the same denominator.

Preview of worksheet Add and subtract fractions

A mixture of addition and subtraction of fractions with the same denominator.

Preview of worksheet 2014 programme of Study: Year 3 Fractions

The statutory requirements for fractions in Year 3.

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year 3 maths worksheets fractions

What your child will learn

Understand and count in tenths.

In Year 3, your child will learn to count in tenths. They will understand that finding a tenth is the same as dividing by ten (by dividing objects, sets of objects, and numbers into ten equal parts).

This will help them to keep seeing the connection between fractions and division. It is possible that your child will start to be introduced to decimals at this stage, too.

Find fractions of a set of objects

Your child will learn to find and write fractions of a given number of objects. For example:

Find     of 15.   First, your child can find   of 15 by dividing the total by the denominator : 15 ÷ 5 = 3.   Then, they can multiply this result by the numerator to find the correct fraction: If   of 15 is 3, then    of 15 is 3  × 2 = 6.     of 15 is therefore 6.

Your child will be able to do this with unit and non-unit fractions. They will learn that:

1/4

Use fractions as numbers

1/2

Your child will be able to do this with unit and non-unit fractions:

2/3

Show equivalent fractions using diagrams

1/2

They’ll show their understanding of equivalent fractions by drawing diagrams like this:

Diagram showing a half and two quarters. They are equivalent.

Your child will also learn to use objects and  fraction walls  to show equivalent fractions.

Add and subtract fractions with the same denominator

2/9

Compare and order fractions

Solve problems that involve all of the above.

Finally, your child will learn to put all this learning into practice by solving problems involving fractions.

They will be able to relate fractions to division, count in fractional steps (for example, counting up and down in tenths), compare fractions, understand  unit  and  non-unit fractions , understand equivalent fractions, find fractions of amounts, and add and subtract fractions with the same denominator.

How to help at home

There are lots of everyday ways you can help your child to understand fractions. Here are just a few ideas.

1. Make fraction snowflakes

Paper folding can be a great way to explore fractions.

Decorate a piece of paper or card and then ask your child to fold the paper into different equal parts. For example, they could fold the paper into fifths by creating five equal sections. Ask them to show you a fifth, two-fifths, three-fifths, four-fifths, and five-fifths, which they can see is equivalent to a whole.

Challenge your child by giving the paper a value and asking them to work out what the fractions would be worth. What would one fifth represent if the whole paper had a value of 10? As they fold, they may like to cut patterns into the paper to make a ‘snowflake’ and watch the pattern develop as they fold further.

2. Have fun with food

Cake, pizza, or any foods with a regular shape can help children understand what fractions are and how they work. Ask your child questions like, ‘If I cut our cake into 8 pieces, what fraction will each piece be?’

Foods that people eat lots of can help your child understand how to find fractions of amounts. For example:

‘We have 12 fish fingers in the packet. There are 4 of us. What fraction of the fish fingers can we each have? How many fish fingers would that be?’

Activity: Cupcake fractions

Cupcake fractions

3. Compare fractions together

In Year 3, your child will compare  unit fractions  and fractions with the same  denominator  by saying which fraction is bigger or smaller – and explaining how they know.

1/3

4. Fraction countdown

1/10

‘Would you prefer it if I cut this cake into ten equal pieces and gave you a piece, or if I cut the cut into two equal pieces and gave you a piece?’

Print out the  Fraction Match activity sheet and cut out each fraction card. Take a selection of cards and see if your child can put them all in order, either from largest to smallest or smallest to largest. Are there any equivalent fractions? See if your child can match them up.

Activity: Fraction Match

year 3 maths worksheets fractions

5. Make a fraction wall

Equivalent fractions are different fractions that have the same value. In Year 3, your child will learn about equivalent fractions with small denominators using drawings and diagrams.

1/2

Why not try making a fraction wall with your child? You could investigate using the computer to make your fraction wall by creating a table and splitting each row into the equal number of parts you need. For example, to represent fifths, you would have to split the whole row into five equal parts.

Alternatively, you can download our fraction wall below.

Fraction wall

year 3 maths worksheets fractions

6. Adding and subtracting fractions

Try adding and subtracting fractions with the same denominator with your child. Try to do this within a whole, i.e. make sure that the sum uses numbers less than one, including the answer.

Using drawings or diagrams can help your child visualise adding and subtracting fractions. For example:

 +   =    This could be calculated using a diagram like this:     Y our child will first split the whole into five equal parts. Your child can then shade one box to represent   and two boxes to represent  . They will then be able to see that the total is  .
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Week 11 Worksheets

  • Lesson 1 - Measure mass (2).pdf
  • Lesson 2 - Compare mass.pdf
  • Lesson 3 - Add and subtract mass.pdf
  • Lesson 4 - Measure capacity (2).pdf

Week 11 Answers

  • Lesson 1 Answers - Measure mass (2).pdf
  • Lesson 2 Answers - Compare mass.pdf
  • Lesson 3 Answers - Add and subtract mass.pdf
  • Lesson 4 Answers - Measure capacity (2).pdf

Week 10 Worksheets

  • Lesson 1 - Draw accurately.pdf
  • Lesson 2 - Recognise and describe 2D shapes.pdf
  • Lesson 3 - Recognise and describe 3D shapes.pdf
  • Lesson 4 - Telling the time to 5 minutes.pdf

Week 10 Answers

  • Lesson 1 Answers - Draw accurately.pdf
  • Lesson 2 Answers - Recognise and describe 2D shapes.pdf
  • Lesson 3 Answers - Recognise and describe 3D shapes.pdf
  • Lesson 4 Answers - Telling the time to 5 minutes.pdf

Week 9 Worksheets

  • Lesson 1 - Right angles in shapes.pdf
  • Lesson 2 - Compare angles.pdf
  • Lesson 3 - Horizontal and vertical.pdf
  • Lesson 4 - Parallel and perpendicular.pdf

Week 9 Answers

  • Lesson 1 Answers - Right angles in shapes.pdf
  • Lesson 2 Answers - Compare angles.pdf
  • Lesson 3 Answers - Horizontal and vertical.pdf
  • Lesson 4 Answers - Parallel and perpendicular.pdf

Week 8 Worksheets

  • Lesson 1 - Order fractions 2020.pdf
  • Lesson 2 - Add fractions 2020.pdf
  • Lesson 3 - Subtract fractions 2020.pdf
  • Lesson 4 - Problem solving with addition and subtraction of fractions.pdf

Week 8 Answers

  • Lesson 1 Answers - Order fractions 2020.pdf
  • Lesson 2 Answers - Add fractions 2020.pdf
  • Lesson 3 Answers - Subtract fractions 2020.pdf
  • Lesson 4 Answers - Problem solving with addition and subtraction of fractions.pdf

Week 8 Alternatives

  • Y3 Week 8 Alternative Plan.pdf
  • Lesson 1 - Add lengths 2019.pdf
  • Lesson 2 - Subtract lengths 2019.pdf
  • Lesson 3 - Measure perimeter 2019.pdf
  • Lesson 4 - Calculate perimeter 2019.pdf
  • Lesson 1 Answers - Add lengths 2019.pdf
  • Lesson 2 Answers - Subtract lengths 2019.pdf
  • Lesson 3 Answers - Measure perimeter 2019.pdf
  • Lesson 4 Answers - Calculate perimeter 2019.pdf

Week 7 Worksheets

  • Lesson 1 - Equivalent fractions (1) 2020.pdf
  • Lesson 2 - Equivalent fractions (2) 2020.pdf
  • Lesson 3 - Equivalent fractions (3) 2020.pdf
  • Lesson 4 - Compare fractions 2020.pdf

Week 7 Answers

  • Lesson 1 Answers - Equivalent fractions (1) 2020.pdf
  • Lesson 2 Answers - Equivalent fractions (2) 2020.pdf
  • Lesson 3 Answers - Equivalent fractions (3) 2020.pdf
  • Lesson 4 Answers - Compare fractions 2020.pdf

Week 7 Alternatives

  • Y3 Week 7 Alternative Plan.pdf
  • Lesson 1 - Measure length 2019.pdf
  • Lesson 2 - Equivalent lengths - m and cm 2019.pdf
  • Lesson 3 - Equivalent lengths - mm and cm 2019.pdf
  • Lesson 4 - Compare lengths 2019.pdf
  • Lesson 1 Answers - Measure length 2019.pdf
  • Lesson 2 Answers - Equivalent lengths - m and cm 2019.pdf
  • Lesson 3 Answers - Equivalent lengths - mm and cm 2019.pdf
  • Lesson 4 Answers - Compare lengths 2019.pdf

Week 6 Worksheets

  • Lesson 1 - Tenths as decimals 2019.pdf
  • Lesson 2 - Fractions on a number line 2019.pdf
  • Lesson 3 - Fractions of a set of objects (1) 2019.pdf
  • Lesson 4 - Fractions of a set of objects (2) 2019.pdf

Week 6 Answers

  • Lesson 1 Answers - Tenths as decimals 2019.pdf
  • Lesson 2 Answers - Fractions on a number line 2019.pdf
  • Lesson 3 Answers - Fractions of a set of objects (1) 2019.pdf
  • Lesson 4 Answers - Fractions of a set of objects (2) 2019.pdf

Week 6 Alternatives

  • Year 3 Week 6 Alternative Plan.pdf
  • Lesson 1 - Add two 3-digit numbers - crossing 10 or 100 2019.pdf
  • Lesson 2 - Subtract 3-digit numbers from 3-digit numbers - no exchange 2019.pdf
  • Lesson 3 - Subtract a 3-digit number from a 3-digit number - exchange 2019.pdf
  • Lesson 4 - Estimate answers to calculations 2019.pdf
  • Lesson 1 Answers - Add two 3-digit numbers - crossing 10 or 100 2019.pdf
  • Lesson 2 Answers - Subtract 3-digit numbers from 3-digit numbers - no exchange 2019.pdf
  • Lesson 3 Answers - Subtract a 3-digit number from a 3-digit number - exchange 2019.pdf
  • Lesson 4 Answers - Estimate answers to calculations 2019.pdf

Week 5 Worksheets

  • Lesson 1 - Unit and non-unit fractions 2019.pdf
  • Lesson 2 - Making the whole 2019.pdf
  • Lesson 3 - Tenths 2019.pdf
  • Lesson 4 - Count in tenths 2019.pdf

Week 5 Answers

  • Lesson 1 Answers - Unit and non-unit fractions 2019.pdf
  • Lesson 2 Answers - Making the whole 2019.pdf
  • Lesson 3 Answers - Tenths 2019.pdf
  • Lesson 4 Answers - Count in tenths 2019.pdf

Week 5 Alternatives

  • Year 3 Week 5 Alternative Plan.pdf
  • Lesson 1 - Add and subtract 2-digit and 3-digit numbers - not crossing 10 or 100 2019.pdf
  • Lesson 2 - Add 2-digit and 3-digit numbers - crossing 10 or 100 2019.pdf
  • Lesson 3 - Subtract 2-digit numbers from 3-digit numbers - crossing 10 or 100 2019.pdf
  • Lesson 4 - Add two 3-digit numbers - not crossing 10 or 100 2019.pdf
  • Lesson 1 Answers - Add and subtract 2-digit and 3-digit numbers - not crossing 10 or 100 2019.pdf
  • Lesson 2 Answers - Add 2-digit and 3-digit numbers - crossing 10 or 100 2019.pdf
  • Lesson 3 Answers - Subtract 2-digit numbers from 3-digit numbers - crossing 10 or 100 2019.pdf
  • Lesson 4 Answers - Add two 3-digit numbers - not crossing 10 or 100 2019.pdf

Week 4 Worksheets

  • Y3 Lesson 1 The 4 and 8 times-tables 2019.pdf
  • Y3 Lesson 2 Multiply 2-digits by 1-digit (2) 2019.pdf
  • Y3 Lesson 3 Divide 2-digits by 1-digit (2) 2019.pdf
  • Y3 Lesson 4 Scaling 2019.pdf

Week 4 Answers

  • Lesson 1 Answers The 4 and 8 times-tables 2019.pdf
  • Lesson 2 Answers Multiply 2-digits by 1-digit (2) 2019.pdf
  • Lesson 3 Answers Divide 2-digits by 1-digit (2) 2019.pdf
  • Lesson 4 Answers Scaling 2019.pdf
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year 3 maths worksheets fractions

Fractions Maths Worksheets

Learning about fractions can be difficult, so we've made it easy for you to produce all of the fractions-related resources you need for your KS2 class right here. Develop understanding by progessing from Comparing Fractions and Finding Fractions of different numbers to the more complex Fraction Arithmetic

Fractions is a wide topic, and you can produce all of the possible fractions-related resources you need for your KS2 class right here.

Free Fraction Arithmetic Worksheet Generator for KS1 and KS2.

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Free Comparing Fractions Worksheet Generator

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Year 3 Ordering Fractions Worksheets | KS2 Fractions | Primary Maths

Year 3 | Ordering Fractions Worksheets

Engage in the world of fractions with these friendly Year 3 ordering fractions worksheets ! Pupils are encouraged to arrange a set of given fractions from the smallest to the largest. Following that, they get to showcase their understanding by placing a group of fractions on a number line from 0 to 1, putting them in order. To add a personal touch, pupils are prompted to choose four fractions and then organise them on a number line from 0 to 1.

This worksheet serves as a fantastic tool to help children grasp the concept of ordering fractions and understand that a larger denominator doesn’t always mean a larger fraction. Enjoy the journey of ordering fractions!

Our Year 3 fractions primary worksheets are aligned with the KS2 national curriculum and can be combined with your ideas for learning activities, differentiation, homework and lesson plans.

You may also be interested in our Year 3 solving fraction problems worksheets .

Explore all of our Year 3 maths worksheets .

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Finding Non-Unit Fractions of Amounts

Finding Non-Unit Fractions of Amounts

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Classroom Owl Resources

Last updated

16 February 2024

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year 3 maths worksheets fractions

Transform Year 3 math lessons into engaging adventures with our Finding Non-Unit Fractions of Amounts PowerPoint and Worksheets Bundle! Tailored for Year 3 mathematics learners, this comprehensive resource includes a meticulously crafted lesson plan, PowerPoint presentation, purposeful independent worksheets, and a fun colouring activity. Specifically targeting the skill of finding non-unit fractions of amounts, this bundle provides a hands-on approach to reinforce mathematical understanding. Available on the TES website, our visually appealing and user-friendly materials make learning both enjoyable and impactful. Elevate your classroom experience and cultivate confident and proficient mathematicians with this all-in-one resource.

Included within this bundle: *Powerpoint Slides *Differentiated Worksheets *Colouring Activity

  • Lesson Plan

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Comparing Fractions Worksheet

Welcome to our Comparing Fractions Worksheets page. Here you will find our selection of worksheets to help you to learn and practice comparing two or more fractions.

Our worksheets introduce the concept of comparing fractions in a visual way using shapes to aid understanding.

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Here are the instructions how to enable JavaScript in your web browser .

Quicklinks to...

  • How to Compare Fractions?
  • All Comparing Fractions Worksheets
  • Comparing Fractions Worksheets with diagrams
  • Ordering Fractions Worksheets with diagrams
  • Comparing Fractions Worksheets without diagrams
  • Ordering Fractions Worksheets without diagrams
  • Comparing Fractions Riddles
  • More related Math resources

Comparing Fractions Online Quiz

Comparing fractions worksheets, how to compare fractions.

We can compare fractions using different ways.

  • using diagrams - this is a supported, easier way;
  • using knowledge of converting fractions to the same denominators which is harder.

One thing to remember is that if we are comparing two fractions without using diagrams, then it is much easier to do if they have the same denominator (or the same numerator).

Before you start comparing fractions, you should know about equivalent fractions.

Comparing fractions using diagrams Examples

Using diagrams can be a great way to help children understand about comparing fractions.

Also, if we are used to seeing fractions visually, this can really help us get an understanding of how much of a whole they represent.

You can see and compare how much of each diagram is shaded and see which fraction is bigger, or whether they are the same size.

Example 1) Compare \[ {3 \over 4} \; and \; {5 \over 6} \]

We can use diagrams to look at two fraction circles with the relevant fractions shaded.

comparing fractions example 1

These diagrams clearly show that: \[ {3 \over 4} \] is the smaller of the two fractions as less of the diagram is shaded.

So we now know \[ {3 \over 4} \; < \; {5 \over 6} \]

Example 2) Let us compare \[ {2 \over 8} \; and \; {1 \over 4} \].

comparing fractions example 2

These diagrams show the same amount shaded for each fraction, so the two fractions are equal.

We have found out that \[ {2 \over 8} \; = \; {1 \over 4} \].

Comparing fractions without diagrams Examples

If there are no diagrams to help us, then we can use our knowledge of fractions to help us.

There are several examples given here which use different ways to compare the size of the fractions.

Example 1) Compare \[ {1 \over 2} \; and \; {3 \over 7} \]

If we are comparing a fraction with a half, it is usually quite quick and easy to tell whether it is bigger or not.

If a fraction is equivalent to a half, then the numerator is equal to half the denominator.

In this case, half of 7 = 3.5, so if the numerator was 3.5 the two fractions would be equal, or equivalent.

However, this numerator is equal to 3, which is smaller than 3.5, so the fraction is less than a half.

So this tells us \[ {1 \over 2} \; > \; {3 \over 7} \]

Example 2) Compare \[ {2 \over 5} \; and \; {3 \over 10} \]

We cannot directly compare these two fractions until their denominators are the same!

You will notice that in this case, one of the denominators is a multiple of the other: 10 is double 5.

So all we need to do is double the numerator and denominator of the first fraction to give us an equivalent fraction with the same denominator as the second fraction.

\[ {2 \over 5} = {2 \times 2 \over 5 \times 2} = {4 \over 10} \]

We can now compare the two fractions directly by looking at the numerators as the denominators are now the same.

4 is bigger than 3 so \[ {4 \over 10} \; > \; {3 \over 10}\]

So we have found out that \[ {2 \over 5} \; > \; {3 \over 10} \]

Example 3) Compare \[ {4 \over 9} \; and \; {3 \over 5} \]

These fractions are not multiples of each other but we can see that by comparing them each to a half, one is clearly bigger and the other is smaller.

If we look at \[ {4 \over 9} \] we can see that it is less than a half because the numerator is less than half of the denominator.

If we look at \[ {3 \over 5} \] we can see that it is more than a half because the numerator is greater than half of the denominator.

This tells us that \[ {4 \over 9} \; < \; {3 \over 5} \]

Example 4) Compare \[ {3 \over 7} \; and \; {3 \over 10} \]

You will notice that these fractions do not have the same denominator but they do have the same numerator.

This really helps us to compare them, because it means that if we think of fraction diagrams the circles have been split into different numbers of parts, but both fractions have the same number shaded in.

If we consider unit fractions, where the numerator is 1.

We know that: \[ {1 \over 7} \; > \; {1 \over 10} \] because the whole has been split into fewer pieces.

This tells us that \[ {3 \over 7} \; > \; {3 \over 10} \] because we are just shading in three pieces of each circle, and each of the sevenths is bigger than each of the tenths as the diagram below shows.

comparing fractions example 3

Example 5) Compare \[ {3 \over 7} \; and \; {2 \over 5} \]

If we look at both of these fractions, we can see (using the method above) that they are both smaller than a half.

We now need to convert them both to fractions with the same denominator (or a common denominator) so we can compare them.

The best way to do this is to multiply the denominators together to tell us the denominator we need.

In this case 7 x 5 = 35, so we need a common denominator of 35.

To get a denominator of 35, we need to multiply the numerator and denominator of the first fraction by 5, and multiply the numerator and denominator of the 2nd fraction by 7.

This gives us: \[ {3 \over 7} \; = \; {3 \times 5 \over 7 \times 5} \; = \; {15 \over 35} \]

and \[ {2 \over 5} \; = \; {2 \times 7 \over 5 \times 7} \; = \; {14 \over 35} \]

Now that the fractions have the same denominator, we can compare the two numerators.

We can clearly see that \[ {15 \over 35} \; > \; {14 \over 35} \]

This tells us that: \[ {3 \over 7} \; > \; {2 \over 5} \]

Here you will find a selection of Fraction worksheets designed to help your child learn to compare and order fractions.

The sheets are carefully graded so that the easiest supported sheets come first, and the most difficult sheets come later on.

We have split the sheets into 5 sections with the first two section looking at comparing and ordering visual fractions using diagrams.

For the sheets in the third and fourth sections, children need to understand how to convert fractions to fractions with like denominators.

The 5th section is applying your knowledge and skills of comparing fractions to solving some comparing fraction riddles.

Using these sheets will help your child to:

  • understand how to compare fractions using diagrams;
  • practice comparing and ordering a range of fractions;
  • use equivalence to compare two fractions.

These sheets are suitable for 4th and 5th graders.

Want to test yourself to see how well you have understood this skill?

  • Try our NEW quick quiz at the bottom of this page.

Section 1 - Comparing Fractions Worksheet with diagrams

These sheets are all about using fraction diagrams to compare two fractions.

  • Comparing Fractions Worksheet with diagrams 1
  • PDF version
  • Comparing Fractions Worksheet with diagrams 2
  • Comparing Fractions Worksheet with diagrams 3
  • Comparing Fractions Worksheet with diagrams 4

Section 2 - Ordering Fractions Worksheet with diagrams

These sheets are similar to those in the section above, but you have to put 4 fractions in order from smallest to largest using diagrams for support.

  • Ordering Fractions using diagrams sheet 1
  • Ordering Fractions using diagrams sheet 2

Section 3 - Comparing Fractions Worksheet without diagrams

These sheets are all about using fraction knowledge and converting fractions to the same denominator to compare two fractions.

This first sheet just compares simple fractions with the same denominator or the same numerator, or equivalent to a half.

  • Comparing Fractions Worksheet 1
  • Comparing Fractions Worksheet 2
  • Comparing Fractions Worksheet 3
  • Comparing Fractions Worksheet 4

Section 4 - Ordering Fractions Worksheets without diagrams

These sheets are similar to those in the section above, but you have to put 5 fractions in order from smallest to largest.

  • Ordering Fractions Sheet 1
  • Ordering Fractions Sheet 2
  • Ordering Fractions Sheet 3
  • Ordering Fractions Sheet 4

Section 5 - Comparing Fractions Riddles

A great opportunity to test your fraction comparing skills and fraction knowledge to solve a range of fraction riddles!

These sheets are graded, with the easiest one first.

  • Comparing Fractions Riddles Sheet 1
  • Comparing Fractions Riddles Sheet 2
  • Comparing Fractions Riddles Sheet 3

More Recommended Math Worksheets

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

Equivalent Fractions

Equivalent fractions are fractions which have the same value as each other.

Before you can compare fractions, you should have a good understanding of what equivalent fractions are.

The printable fraction page below contains more support, examples and practice using equivalent fractions.

  • Finding Equivalent Fractions support page
  • Equivalent Fractions Worksheets

Simplifying Fractions

Take a look at our Simplifying Fractions Practice Zone or try our worksheets for finding the simplest form for a range of fractions.

You can choose from proper fractions, improper fractions or both.

You can print out your results or benchmark your scores against future achievements.

Good for practising equivalent fractions as well as converting to simplest form.

Great for using with a group of children as well as individually.

  • Simplify Fractions Practice Zone
  • Simplifying Fractions Worksheet page
  • Least Common Multiple Calculator

Our Least Common Multiple Calculator will find the lowest common multiple of 2 or more numbers.

It will tell you the smallest multiple to convert the denominators of the fractions you are comaring into.

There are also some worked examples.

least common multiple calculator image

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

Improper Fractions

We have a support page to help students understand how what improper fractions are and how to conver them.

We also have a wide range of Improper Fraction Worksheets, some of which use visual fractions to aid understanding and some sheets which are more abstract.

Convert Improper Fractions Image

  • How to Convert Improper Fractions
  • Improper Fraction Worksheets

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

We do not collect any personal data from our quizzes, except in the 'First Name' and 'Group/Class' fields which are both optional and only used for teachers to identify students within their educational setting.

We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your understanding and skill at comparing two or more fractions.

Fun Quiz Facts

  • This quiz was attempted 771 times in the last academic year.
  • The average (mean) score was 13.3 out of 20 marks.
  • Can you beat the mean score?

How to Print or Save these sheets 🖶

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    Transform Year 3 math lessons into engaging adventures with our Finding Non-Unit Fractions of Amounts PowerPoint and Worksheets Bundle! Tailored for Year 3 mathematics learners, this comprehensive resource includes a meticulously crafted lesson plan, PowerPoint presentation, purposeful independent worksheets, and a fun colouring activity.

  24. Comparing Fractions Worksheet

    Section 3 - Comparing Fractions Worksheet without diagrams. These sheets are all about using fraction knowledge and converting fractions to the same denominator to compare two fractions. This first sheet just compares simple fractions with the same denominator or the same numerator, or equivalent to a half. Comparing Fractions Worksheet 1.