# Dividing Fractions by Whole Numbers

Welcome to our Dividing Fractions by Whole Numbers page.

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

### Dividing Fractions by Whole Numbers Support

Frazer says "To divide a fraction by an integer, or whole numbers, follow these 4 easy steps." 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

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

### 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: $2 {2 \over 3} \; ÷ \; 7 \; = \; {8 \over 21}$

### More Recommended Math Worksheets

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

### 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'.

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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 and give us insight into future resources to create.

This quick quiz tests your understanding and skill at dividing fractions by whole numbers.

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