# Divide Whole Numbers by Fractions

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

### Divide Whole Numbers by Fractions Support

Frazer says "To divide a whole number by a fraction, 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 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)

${24 \over 3} \; = \; 8$

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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### More Recommended Math Worksheets

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

### Dividing Whole Numbers by Fractions Online Quiz

Our quizzes have been created using Google Forms.

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• NB. This error is a Google error in the Google Quiz app - it is currently unresolved!

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

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