# How to Divide Mixed NumbersSupport Page

Welcome to our How to Divide Mixed Numbers support page.

On this page, we have some support and worked examples on how to divide mixed numbers, or mixed fractions, including free support sheets and practice sheets.

## How to Divide Mixed Numbers

### How to Divide Mixed Numbers Support

Frazer says "To divide a mixed number by another fraction, follow these four easy steps..." Step 1

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

Convert any mixed numbers into improper fractions. Any integers (whole numbers) should be written as fractions with a denominator of 1.

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).

### Examples showing how to divide mixed numbers

#### Example 1) Work out $3 {1 \over 3} ÷ 1 {5 \over 6}$

Step 1)

We need to convert each of the mixed numbers into improper fractions.

$3 {1 \over 3} \; = \; {10 \over 3}$ and $1{ 5 \over 6} \; = \; {11 \over 6}$

Now we have: $3 {1 \over 3} ÷ 1 {5 \over 6} \; = \; {10 \over 3} ÷ {11 \over 6}$

Step 2)

We need to invert the dividend fraction and change the operator to multiplication.

This gives us: ${10 \over 3} ÷ {11 \over 6} \; = \; {10 \over 3} \times {6 \over 11}$

Step 3) Multiply the fractions

${10 \over 3} \times {6 \over 11} \; = \; {10 \times 6 \over 3 \times 11} \; = \; {60 \over 33}$

We can simplify the answer by dividing the numerator and denominator by 3.

${60 \over 33} \; = \; {60 ÷ 3 \over 33 ÷ 3} = {20 \over 11}$

Now convert back to a mixed number.

${20 \over 11} = 1 {9 \over 11}$

Final answer: $3 {1 \over 3} ÷ 1 {5 \over 6} \; = \; 1 {9 \over 11}$

#### Example 2) Work out $1 {3 \over 4} ÷ 2 {2 \over 5}$

Step 1)

We need to convert each of the mixed numbers into improper fractions.

$1 {3 \over 4} \; = \; {7 \over 4}$ and $2{ 2 \over 5} \; = \; {12 \over 5}$

Now we have: $1 {3 \over 4} ÷ 2 {2 \over 5} \; = \; {7 \over 4} ÷ {12 \over 5}$

Step 2)

We need to invert the dividend fraction and change the operator to multiplication.

This gives us: ${7 \over 4} ÷ {12 \over 5} \; = \; {7 \over 4} \times {5 \over 12}$

Step 3) Multiply the fractions

${7 \over 4} \times {5 \over 12} \; = \; {7 \times 5 \over 4 \times 12} \; = \; {35 \over 48}$

This fraction is already in simplest form.

Final answer: $1 {3 \over 4} ÷ 2 {2 \over 5} \; = \; {35 \over 48}$

#### Example 3) Work out $4 ÷ 2 {1 \over 3}$

Step 1)

We need to convert the mixed numbers into an improper fraction and put any integers over a denominator of 1.

$2 {1 \over 3} \; = \; {7 \over 3}$

Now we have: $4 ÷ 2 {1 \over 3} \; = \; {4 \over 1} ÷ {7 \over 3}$

Step 2)

We need to invert the dividend fraction and change the operator to multiplication.

This gives us: ${4 \over 1} ÷ {7 \over 3} \; = \; {4 \over 1} \times {3 \over 7}$

Step 3) Multiply the fractions

${4 \over 1} \times {3 \over 7} \; = \; {4 \times 3 \over 1 \times 7} \; = \; {12 \over 7}$

Step 4) Simplify and convert.

This fraction is already in simplest form.

Now convert back to a mixed number.

${12 \over 7} = 1 {5 \over 7}$

Final answer: $4 ÷ 2 {1 \over 3} \; = \; 1 {5 \over 7}$

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