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Here we will learn about converting improper fractions to mixed numbers including how to recognise improper fractions and mixed numbers.

There are also improper fractions and mixed numbers worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Proper fractions** and **improper fractions** are types of fractions.

A **proper fraction** is a fraction where the **numerator **(top number) is **smaller **than the **denominator **(bottom number).

Here are some examples of proper fractions:

\[\frac{1}{2} \quad \quad \frac{3}{4} \quad \quad \frac{17}{20}\]

An **improper **fraction is a fraction where the **numerator **(top number) is **larger **than the **denominator **(bottom number). They are sometimes called “top-heavy fractions”.

Here are some examples of improper fractions:

\[\frac{7}{2} \quad \quad \frac{13}{4} \quad \quad \frac{14}{5}\]

A** mixed number** has a **whole number part** and a** fractional part**.

Here is an example of a mixed number, it means 1 whole and 3 fifths.

\[1\frac{3}{5}\]

We can change improper fractions to mixed numbers and vice versa. To do this we know how many equal parts there are and how many of them make a whole.

There is 1 whole that is split into 5 equal pieces. 1 whole is equal to 5 fifths.

Altogether there are 8 fifths or 1 whole and 3 fifths.

\[\frac{8}{5}=1\frac{3}{5}\]

**See also:** Mixed number to improper fraction

In order to change an improper fraction to a mixed number:

- Work out how many times the denominator divides into the numerator.
- Work out the remainder.
- Write the mixed number with the whole number at the front and the remainder as the new numerator over the original denominator.

Get your free improper fraction to mixed number worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free improper fraction to mixed number worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEWrite the following improper fraction as a mixed number:

\[\frac{7}{3}\]

**Work out how many times the denominator divides into the numerator**.

The denominator of the fraction is

2**Work out the remainder**.

The remainder is

The denominator stays the same.

\[\frac{7}{3}=\frac{2\times3+1}{3}=2\frac{1}{3}\]

3**Write the mixed number with the whole number at the front and the remainder as the new numerator over the original denominator.**

\[\frac{7}{3}=2\frac{1}{3}\]

Write the following improper fraction as a mixed number:

\[\frac{17}{5}\]

**Work out how many times the denominator divides into the numerator**.

The denominator of the fraction is

**Work out the remainder**.

The remainder is

The denominator stays the same.

\[\frac{17}{5}=\frac{3\times5+2}{5}=3\frac{2}{5}\]

\[\frac{17}{5}=3\frac{2}{5}\]

Write the following improper fraction as a mixed number:

\[\frac{17}{7}\]

**Work out how many times the denominator divides into the numerator**.

The denominator of the fraction is

**Work out the remainder**.

The remainder is

\[\frac{7}{3}=\frac{2\times7+3}{7}=2\frac{3}{7}\]

\[\frac{17}{7}=2\frac{3}{7}\]

**The denominator (the bottom number) stays the same**

If the improper fraction has a denominator of 3 , then so will the mixed number and vice versa.

**Take care when using a calculator and mixed numbers**

When putting a mixed number into a calculator, you must use the “shift” button and then the fraction button so that you can input the mixed number properly.

**Sometimes the fraction will need to be written in its simplest terms**

An improper fraction may be written as a mixed number but the fraction part of the mixed number still needs to be written in its simplest terms.

\[\frac{22}{4}=\frac{5\times4+2}{4}=5\frac{2}{4}=5\frac{1}{2}\]

Improper fractions and mixed numbers is part of our series of lessons to support revision on fractions. You may find it helpful to start with the main fractions lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Write the following improper fraction as a mixed number:

\frac{5}{4}

1\frac{1}{4}

\frac{4}{5}

1\frac{1}{5}

1\frac{3}{4}

\frac{5}{4}=\frac{1\times4+1}{4}=1\frac{1}{4}

2. Write the following improper fraction as a mixed number:

\frac{8}{3}

1\frac{2}{3}

2\frac{1}{3}

2\frac{2}{3}

\frac{3}{8}

\frac{8}{3}=\frac{2\times3+2}{3}=2\frac{2}{3}

3. Write the following improper fraction as a mixed number:

\frac{23}{5}

4\frac{3}{5}

\frac{5}{23}

2\frac{3}{5}

3\frac{4}{5}

\frac{23}{5}=\frac{4\times5+3}{5}=4\frac{3}{5}

4. Write the following improper fraction as a mixed number:

\frac{20}{7}

2\frac{1}{6}

2\frac{6}{7}

\frac{7}{20}

2\frac{1}{7}

\frac{20}{7}=\frac{2\times7+6}{7}=2\frac{6}{7}

5. Write the following improper fraction as a mixed number:

\frac{41}{6}

6\frac{6}{5}

5\frac{5}{6}

6\frac{5}{6}

\frac{5}{6}

\frac{41}{6}=\frac{6\times6+6}{5}=6\frac{5}{6}

6. Write the following improper fraction as a mixed number:

\frac{115}{11}

\frac{5}{11}

5\frac{10}{11}

10\frac{4}{11}

10\frac{5}{11}

\frac{115}{11}=\frac{10\times11+5}{11}=10\frac{5}{11}

1. Write this improper fraction as a mixed number

\frac{25}{8}

**(1 mark)**

Show answer

\frac{25}{8}=\frac{3\times8+1}{8}=3\frac{1}{8}

3\frac{1}{8}

**(1)**

2. Work out

\frac{4}{9} + \frac{7}{9}

Circle your answer

\frac{11}{18} \quad \quad \frac{11}{81} \quad \quad 1\frac{4}{9} \quad \quad 1\frac{2}{9}

**(1 mark)**

Show answer

\frac{4}{9}+\frac{7}{9}=\frac{4+7}{9}=\frac{11}{9}=\frac{1\times9+2}{9}=1\frac{2}{9}

1\frac{2}{9}

**(1)**

3. Work out

\frac{3}{7}\times11

Give your answer as a mixed number

**(2 marks)**

Show answer

\frac{3}{7}\times11=\frac{33}{7}

**(1)**

\frac{33}{7}=\frac{4\times 7+5}{7}=4\frac{5}{7}

4\frac{5}{7}

**(1)**

You have now learned how to:

- Convert an improper fraction to a mixed number

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