# Dividing Mixed Fractions

Welcome to our Dividing Mixed Fractions page.

On this page, we have a range of free printable Fractions sheets on how to divide mixed fractions, including free support sheets and practice sheets.

## Dividing Mixed Fractions

### How to Divide Mixed Fractions Support

Frazer says "To divide a mixed fraction 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 fractions 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 of Dividing Mixed Fractions

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

Step 1)

We need to convert each of the mixed fractions 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 1) Work out $1 {3 \over 4} ÷ 2 {2 \over 5}$

Step 1)

We need to convert each of the mixed fractions 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 1) Work out $4 ÷ 2 {1 \over 3}$

Step 1)

We need to convert the mixed fractions 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: $4 ÷ 2 {1 \over 3} \; = \; 1 {5 \over 7}$

### More Recommended Math Resources

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

### How to Divide Fractions

Dividing Fractions by Whole Numbers

### How to Convert to Simplest Form

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