Divide Whole Numbers by Fractions

Welcome to our support page to help you learn How to Divide Whole Numbers by Fractions page.

On this page, we have a range of free printable sheets to help your child learn to divide integers (or whole numbers) by fractions.

Take a look at our worked examples or have a go at our practice sheets!

We also have a calculator which will not only give you the answer, but also show you all the working out along the way!

If you need support to divide fractions by other fractions, use the link below.

Dividing Whole Numbers by Fractions

On this page, you will learn how to divide a whole number by a fraction, and also some practice worksheets designed to help your master this skill.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

We have split the sheets into two main sections:

  • Dividing Whole Numbers by Unit Fractions
  • Dividing Whole Numbers by Non-unit Fractions

Before your child tackles dividing whole numbers by fractions, they should be confident with multiplying fractions, and also converting mixed fractions to improper fractions and reducing fractions to simplest form.

Using these sheets will help your child to:

  • divide a whole number by a fraction;
  • apply their understanding of simplest form;
  • convert an improper fraction to a mixed number.

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Dividing Fractions Calculator

If you want to divide any fractions, you can use our Free Divide Fractions calculator.

The calculator will help you dividing whole numbers by fractions, or fractions by other fractions or mixed numbers.

The best thing about the calculator is that it also shows you all the working out along the way.

Divide Whole Numbers by Fractions Support

Frazer says "To divide a whole number by a fraction, follow these 4 easy steps."

Frazer the Fraction Salamander

Step 1

Change the whole number to a fraction by putting it over a denominator of 1.

If any of the fractions are mixed fractions (or mixed numbers), then convert them into improper fractions.

Step 2

Swap the numerator and denominator of the dividend fraction (the fraction after the ÷ sign) and change the operator to a 'x' instead of a '÷ '

Step 3

Multiply the numerators of the fractions together, and the denominators of the fractions together. This will give you the answer.

Step 4

Simplify the fraction.

For those of you who like to see the algebra:

Formula for dividing a whole number by a fraction.

\[a \div {b \over c} \; = \; {a \over 1} \times {c \over b} \; = \; {a \times c \over 1 \times b} \; = \; {ac \over b} \]

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Examples of Dividing Whole Numbers by Fractions

Example 1) Work out: \[ 6 \div {3 \over 4} \]

Step 1)

Put the integer over a denominator of 1.

So this gives us: \[ 6 \div {3 \over 4} \; = \; {6 \over 1} \div {3 \over 4} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[ {6 \over 1} \div {3 \over 4} \; = \; {6 \over 1} \times {4 \over 3}\]

Now multiply the fractions:

\[{6 \over 1} \times {4 \over 3} \; = \; {6 \times 4 \over 1 \times 3} \; = \; {24 \over 3} \]

Step 3)

Simplify the answer.

\[ {24 \over 3} \; = \; 8 \]

Final answer: \[ 6 \div {3 \over 4} \; = \; 8 \]


Example 2) Work out: \[ 4 \div {5 \over 9} \]

Step 1)

Put the integer over a denominator of 1.

So this gives us: \[ 4 \div {5 \over 9} \; = \; {4 \over 1} \div {5 \over 9} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[{4 \over 1} \div {5 \over 9} \; = \; {4 \over 1} \times {9 \over 5} \]

Now multiply the fractions:

\[{4 \over 1} \times {9 \over 5} \; = \; {4 \times 9 \over 1 \times 5} \; = \; {36 \over 5} \]

Step 3)

This fraction is already in simplest form, but we can convert it to a mixed number.

\[ {36 \over 5} \; = \; 7 {1 \over 5} \]

Final answer: \[ 4 \div {5 \over 9} \; = \; {36 \over 5} \; or \; 7 {1 \over 5} \]


Example 3) Work out: \[ 10 \div 2 {2 \over 3} \]

Step 1)

Convert the mixed number to an improper fraction and put the integer over a denominator of 1.

As an improper fraction: \[ 2 {2 \over 3} \; = \; {8 \over 3} \]

So this gives us: \[ 10 \div 2 {2 \over 3} \; = \; {10 \over 1} \div {8 \over 3} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[{10 \over 1} \div {8 \over 3} \; = \; {10 \over 1} \times {3 \over 8} \]

Now multiply the fractions:

\[{10 \over 1} \times {3 \over 8} \; = \; {10 \times 3 \over 1 \times 8} \; = \; {30 \over 8} \]

Step 3)

This fraction needs to be simplified and can also be written as a mixed number.

\[ {30 \over 8} \; = \; {15 \over 4} \; = \; 3 {3 \over 4} \]

Final answer: \[10 \div 2 {2 \over 3} \; = \; {15 \over 4} \; or \; 3 {3 \over 4} \]


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How to Divide Whole Numbers by Fractions Support Page

We have created a support page to help you understand how to divide whole numbers by fractions with some examples.

It is quick and easy to print, and has all the information on one page.

Dividing Whole Number by Unit Fractions

A unit fraction is a fraction which has a numerator of 1.

Dividing whole numbers by unit fractions is a Common Core objective for 5th grade.

Our sheets are carefully graded and get gradually harder.

Our first two worksheets have been designed to introduce this concept, and include using visual models to aid understanding.

Sheet 3 is for children who are confident with this process and need some practice.

Sheet 4 is trickier and involves finding the missing number or fraction in the equation.

Sheet 5 consists of a series of challenges which involve using the skill of dividing whole numbers by unit fractions.

Dividing Whole Numbers by Unit Fractions Worksheets

Dividing Whole Numbers by Fractions Worksheets

The first 3 sheets involve dividing whole numbers by proper fractions.

Sheets 4 & 5 involve dividing whole numbers by mixed numbers.

Dividing by Whole Numbers and Fractions

These sheets involve both dividing whole numbers by fractions and also dividing fractions by whole numbers.

The first two sheets involve dividing by proper and improper fractions.

Sheet 3 involves dividing by mixed numbers.

More Recommended Math Worksheets

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

Multiplying and Dividing Fractions Support Pages

The links below will take you to our support pages for multiplying and dividing fractions.

All the support pages contain detailed explanations and some worked examples.

Multiplying and Dividing Fractions Worksheets

The links below will take you to our worksheets for multiplying and dividing fractions.

The worksheets are all carefully graded and have different levels of support for students.

Converting Improper Fractions

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert an improper fraction to a mixed number.

Using these sheets will help your child to:

  • convert an improper fraction to a mixed number;
  • convert a mixed number to an improper fraction.

How to Convert to Simplest Form

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert a fraction to its simplest form.

Using these sheets will help your child to:

  • develop an understanding of equivalent fractions;
  • know when a fraction is in its simplest form;
  • convert a fraction to its simplest form.

Fractions Adding and Subtracting Generated Sheets

We have created a random generator for making your own adding and subtracting fractions worksheets.

You can change your fraction values, choose whether you want like or unlike denominators or change from proper to improper fractions.

Dividing Whole Numbers by Fractions Online Quiz

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' field which is optional. We collect this information so that if a class of students is taking a quiz, the individual results can be recorded along with the first name of the student.

We also collect the results from the quizzes which we use to help us to develop our resources.

For more information on the information we collect, please take a look at our Privacy Policy

If the error message 'File Unavailable' should appear in a pop-up window with a 'RELOAD' option in the bottom right corner of the screen:

  • Don't click the RELOAD link - it doesn't do anything
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  • the pop-up window should disappear and you should be able to see your results.
  • NB. This error is a Google error in the Google Quiz app - it is currently unresolved!

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 dividing whole numbers by fractions.

 

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