# Divide Whole Numbers by Fractions

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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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## Dividing Whole Numbers by Fractions Worksheets

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### Dividing Whole Numbers by Fractions Online Quiz

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

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