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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.


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