# Fractions

### Addition and subtraction of fractions

- To add or subtract fractions they need to have the same denominator.
- Remember that fractions should always be left in lowest form.
- When adding or subtracting mixed numbers (whole number with a fraction), convert to improper fractions, add or subtract using the rules for addition and subtraction of fractions and then convert your answer back to mixed numbers.

For example:

\[1\frac{2}{5} + \frac{3}{8}\]

Firstly, convert the mixed number to an improper fraction:

\[ 1 \frac{2}{5} = \frac{7}{5}\]

Secondly, find the common denominator: \(5\times 8=40\)

\begin{eqnarray*}

&&1\frac{2}{5} + \frac{3}{8} \\

&=& \frac{7}{5} + \frac{3}{8} \\

&=& \frac{7\times 8}{5\times 8}+ \frac{3\times 5}{8\times 5} \\

&=& \frac{56}{40} + \frac{15}{40} \\

&=& \frac{56+15}{40} \\

&=& \frac{71}{40} \\

&=& 1\frac{31}{40}

\end{eqnarray*}

Remember to check if it is in simplest form. Yes it is.

#### To do

- Fractions 2 (Addition and Subtraction worksheet (sigma Mathematics and Statistics Support Coventry University)
- Add fractions with unlike denominators activity
- Subtracting fractions with unlike denominators activity