Dividing Fractions by Whole Numbers

Welcome to our Dividing Fractions by Whole Numbers page.

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

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 Fractions by Whole Numbers

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

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

Before your child tackles dividing 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 fraction by a whole number;
  • apply their understanding of simplest form;
  • convert an improper fraction to a mixed number.

Dividing Fractions Calculator

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

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

Dividing Fractions by Whole Numbers Support

Frazer says "To divide a fraction by an integer, or whole numbers, 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 first 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 (Optional)

You may want to convert the fraction into its simplest form or convert it back to a mixed fraction (if it is an improper fraction).

For those of you who like to see the algebra:

Formula for dividing a fraction by a whole number

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

How to Divide a Fraction by a Whole Number Printable Sheet

Examples of Dividing Fractions by Whole Numbers

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

Step 1)

Put the integer over a denominator of 1.

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

Step 2)

Invert the dividend fraction and change the operation to multiplication.

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

Now multiply the fractions:

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

Step 3)

Simplify the answer by dividing the numerator and denominator by 3.

\[ {3 \over 24} \; = \; {3 ÷ 3 \over 24 ÷ 3} \; = \; {1 \over 8}\]

Final answer: \[{3 \over 4} \; ÷ \; 6 \; = \; {1 \over 8} \]


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

Step 1)

Put the integer over a denominator of 1.

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

Step 2)

Invert the dividend fraction and change the operation to multiplication.

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

Now multiply the fractions:

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

Step 3)

This fraction is already in simplest form.

Final answer: \[{5 \over 9} \; ÷ \; 4 \; = \; {5 \over 36} \]


Example 3) Work out: \[ 2 {2 \over 3} \; ÷ \; 7 \]

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: \[2 {2 \over 3} \; ÷ \; 7 \; = \; {8 \over 3} ÷ {7 \over 1} \]

Step 2)

Invert the dividend fraction and change the operation to multiplication.

So we now have \[{8 \over 3} \; ÷ \; {7 \over 1} \; = \; {8 \over 3} \times {1 \over 7}\]

Now multiply the fractions:

\[{8 \over 3} \times {1 \over 7} \; = \; {8 \times 1 \over 3 \times 7} \; = \; {8 \over 21} \]

Step 3)

This fraction is already in simplest form.

Final answer: \[2 {2 \over 3} \; ÷ \; 7 \; = \; {8 \over 21} \]


Dividing Fractions by Whole Numbers Worksheets

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.

Dividing Fractions by Whole Numbers 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.

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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

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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 dividing fractions by whole numbers.

 

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