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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.

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 change 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.

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

COMING SOONWrite 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}.

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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#### GCSE Maths Papers - November 2022 Topics

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Practice paper packs based on the November advanced information for Edexcel 2022 Foundation and Higher exams.

Designed to help your GCSE students revise some of the topics that are likely to come up in November exams.