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Here we will learn about converting mixed numbers to improper fractions.

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.

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

An example of a proper fraction is \frac{8}{11} \

An **improper fraction** has a numerator that is bigger than the denominator of the fraction. Sometimes referred to as ‘top heavy’ fractions.

An example of an improper fraction is \frac{25}{7} \

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

An example of a mixed number is 3 \frac{3}{4} \times 2 \frac{5}{8}

**See also:** Improper fraction to mixed number

Converting a **mixed number to an improper fraction **is an important skill. When calculating with mixed numbers, it can be much easier to perform the arithmetic required if the mixed numbers are converted to improper fractions.

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

An **improper fraction** has a numerator that is bigger than the denominator of the fraction. Sometimes referred to as ‘top heavy’ fractions.

For example,

If we needed to calculate 1 \frac{2}{3} \times 4 \frac{3}{5}, one way would be to use a grid method.

This can be a very long process involving lots of other fraction arithmetic. Converting the mixed numbers to improper fractions before multiplying is a way of** simplifying the process**.

To convert the mixed numbers to improper fractions we change the **whole number** to a** fraction with the same denominator**. We then **add the numerators **together and get a new numerator **over the original denominator**.

For example,

To convert a mixed number to an improper fraction quickly we can **multiply the whole number **by the **denominator**,** add the numerato**r and then write that **over the original denominator**.

For example,

This will make the process of adding, subtracting, multiplying and dividing fractions simpler.

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

**Multiply the whole number by the denominator.****Add on the numerator.****Write the improper fraction by using the calculated value as the numerator over the original denominator.**

Get your free converting mixed numbers to improper fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free converting mixed numbers to improper fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEWrite the following mixed number as an improper fraction, 2\frac{4}{5}.

**Multiply the whole number by the denominator.**

The whole number part of the mixed number is 2 and the denominator is 5, \ 2 \times 5 = 10.

2**Add on the numerator.**

The numerator is 4, \ 10 + 4 = 14.

The new numerator for the improper fraction is 14.

3**Write the improper fraction by using the calculated value as the numerator over the original denominator.**

Write the following mixed number as a improper fraction, 3\frac{1}{6}.

**Multiply the whole number by the denominator.**

The whole number part of the mixed number is 3 and the denominator is 6, \ 3 \times 6 = 18.

**Add on the numerator.**

The numerator is 1, \ 18 + 1 = 19.

The new numerator for the improper fraction is 19.

3\frac{1}{6}=\frac{19}{6}

Write the following mixed number as a improper fraction, 4\frac{3}{7}.

**Multiply the whole number by the denominator.**

The whole number part of the mixed number is 4 and the denominator is 7, \ 4 \times 7 = 28.

**Add on the numerator.**

The numerator is 3, \ 28 + 3 = 31.

The new numerator for the improper fraction is 31.

4\frac{3}{7}=\frac{31}{7}

**Adding the whole number to the denominator instead of multiplying**

A common error can occur when adding the whole number to the denominator instead of multiplying.

**Confusing mixed numbers and improper fractions**

Mixed numbers are written with a whole number and a fractional part.

For example, 4 \frac{5}{6}.

Improper fractions are not written with a whole number part, but the numerator is always bigger than the denominator.

For example, \frac{29}{6}.

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 mixed number as an improper fraction, 2\frac{3}{5}.

3\frac{2}{5}

\frac{13}{5}

\frac{23}{5}

2\frac{1}{5}

2\frac{3}{5}=\frac{2\times5+3}{5}=\frac{10+3}{5}=\frac{13}{5}

2. Write the following mixed number as an improper fraction, 5\frac{2}{7}.

\frac{37}{7}

\frac{52}{7}

\frac{25}{7}

\frac{34}{7}

5\frac{2}{7}=\frac{5\times7+2}{7}=\frac{35+2}{7}=\frac{37}{7}

3. Write the following mixed number as an improper fraction, 8\frac{1}{4}.

\frac{81}{4}

\frac{33}{8}

\frac{35}{4}

\frac{33}{4}

8\frac{1}{4}=\frac{8\times4+1}{4}=\frac{32+1}{4}=\frac{33}{4}

4. Write the following mixed number as an improper fraction, 5\frac{3}{11}.

\frac{16}{11}

\frac{55}{11}

\frac{58}{11}

\frac{58}{3}

5\frac{3}{11}=\frac{5\times11+3}{11}=\frac{55+3}{11}=\frac{58}{11}

5. Write the following mixed number as an improper fraction, 4\frac{2}{13}.

\frac{21}{13}

\frac{54}{13}

\frac{19}{13}

\frac{52}{13}

4\frac{2}{13}=\frac{4\times13+2}{13}=\frac{52+2}{13}=\frac{54}{13}

6. Write the following mixed number as an improper fraction, 2\frac{8}{9}.

\frac{26}{9}

\frac{25}{9}

\frac{19}{9}

\frac{16}{9}

2\frac{8}{9}=\frac{2\times9+8}{9}=\frac{18+8}{9}=\frac{26}{9}

1. Choose the fraction which is the same as 5 \frac{3}{7}?

\frac{22}{7} \hspace{1cm} \frac{38}{7} \hspace{1cm} \frac{15}{7} \hspace{1cm} \frac{35}{7}

**(1 mark)**

Show answer

\frac{38}{7}

**(1)**

2. (a) Write 3.2 as an improper fraction in its simplest form.

(b) Work out 3\frac{1}{4}-1\frac{1}{3}.

**(5 marks)**

Show answer

(a)

For any correct mixed number. For example, 3\frac{2}{10}.

**(1)**

**(1)**

(b)

Converting one of the fractions to an improper fraction. For example, \frac{13}{4} or \frac{4}{3}.

**(1)**

Write both fractions with a common denominator. For example, \frac{39}{12}, \frac{16}{12}.

**(1)**

\frac{23}{12} or 1 \frac{11}{12}.

**(1)**

3. Work out 4 \frac{1}{2} \div 3\frac{2}{3}.

**(3 marks)**

Show answer

Converting one of the fractions to an improper fraction. For example, \frac{9}{2} or \frac{11}{3}.

**(1)**

Correct process to divide used. For example, finding common denominator for multiplying by the reciprocal.

**(1)**

\frac{27}{22} or 1 \frac{5}{22}.

**(1)**

You have now learned how to:

- Convert a mixed number to an improper fraction

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