How to Divide Mixed Numbers
Support 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

Here you will find support on how to divide mixed fractions, and also some practice worksheets designed to help your child master this skill.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

Before your child tackles How to Divide Mixed Numbers, they should be confident with dividing and multiplying fractions, and also converting mixed numbers to improper fractions and reducing fractions to simplest form.

Using these sheets will help your child to:

  • divide one mixed number by another;
  • dividing an integer by a mixed number;
  • dividing a mixed number by an integer;
  • apply their understanding of simplest form;

How to Divide Mixed Numbers Support

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

Frazer the Fraction Salamander

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).

How to Divide Mixed Numbers Printable Sheet

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

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

Step 4) Simplify the answer

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

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

Step 4) Simplify the answer

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: \[ 4 ÷ 2 {1 \over 3} \; = \; 1 {5 \over 7} \]

Dividing Fractions Calculator

If you want to divide fractions, or mixed numbers, you can use our Free Divide Fractions calculator.

The calculator can divide fractions by whole numbers, or fractions by other fractions or mixed numbers.

The best thing about the calculator is that not only does it calculate the answer for you, it also shows the you the working out...step by step!

Dividing Mixed Numbers Worksheets

More Recommended Math Resources

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

How to Divide Fractions

Here is our support page to help your child understand how to divide a fraction by another fraction.

Dividing Fractions by Whole Numbers

Here you will find a selection of Fraction worksheets designed to help your child understand how to divide fractions by integers or whole numbers.

Using these sheets will help your child to:

  • divide a fraction by a whole number;

Converting Improper Fractions

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert an improper fraction to a mixed number.

Using these sheets will help your child to:

  • convert an improper fraction to a mixed number;
  • convert a mixed number to an improper fraction.

How to Convert to Simplest Form

Here you will find a selection of Fraction worksheets designed to help your child understand how to convert a fraction to its simplest form.

Using these sheets will help your child to:

  • develop an understanding of equivalent fractions;
  • know when a fraction is in its simplest form;
  • convert a fraction to its simplest form.
 

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