# Improper‌ ‌Fractions‌ ‌to‌ ‌Mixed‌ ‌Numbers‌

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.

## What are improper fractions and mixed numbers?

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.

$\frac{8}{5}=1\frac{3}{5}$

## How to convert improper fractions to mixed numbers

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

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

## Converting improper fractions to mixed numbers examples

### Example 1: change an improper fraction to a mixed number

Write the following improper fraction as a mixed number:

$\frac{7}{3}$

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

The denominator of the fraction is 3 and the numerator of the fraction is 7.

3 divides into 7 twice. This gives the whole number 2.

2Work out the remainder.

The remainder is 1. This gives the numerator for the fractional part.
The denominator stays the same.

$\frac{7}{3}=\frac{2\times3+1}{3}=2\frac{1}{3}$

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

$\frac{7}{3}=2\frac{1}{3}$

### Example 2:  change an improper fraction to a mixed number

Write the following improper fraction as a mixed number:

$\frac{17}{5}$

The denominator of the fraction is 5 and the numerator of the fraction is 17.

5 divides into 17 three times. This gives the whole number 3.

The remainder is 2. This gives the numerator for the fractional part.
The denominator stays the same.

$\frac{17}{5}=\frac{3\times5+2}{5}=3\frac{2}{5}$

$\frac{17}{5}=3\frac{2}{5}$

### Example 3: change an improper fraction to a mixed number

Write the following improper fraction as a mixed number:

$\frac{17}{7}$

The denominator of the fraction is 7 and the numerator of the fraction is 17.

7 divides into 17 three times. This gives the whole number 2.

The remainder is 3. This gives the numerator for the fractional part. The denominator stays the same.

$\frac{7}{3}=\frac{2\times7+3}{7}=2\frac{3}{7}$

$\frac{17}{7}=2\frac{3}{7}$

### Common misconceptions

• 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:

### Practice improper fraction and mixed number questions

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}

### Converting improper fractions to mixed numbers GCSE questions

1.  Write this improper fraction as a mixed number

\frac{25}{8}

(1 mark)

\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}

(1 mark)

\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

(2 marks)

\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)

## Learning checklist

You have now learned how to:

• Convert an improper fraction to a mixed number

## Still stuck?

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#### FREE GCSE Maths Practice Papers - 2022 Topics

Practice paper packs based on the advanced information for the Summer 2022 exam series from Edexcel, AQA and OCR.

Designed to help your GCSE students revise some of the topics that will come up in the Summer exams.