Adding and Subtracting Fractions

To add and subtract fractions that do not have the same denominator, we convert them into equivalent fractions with the same denominators and then proceed as above.

For example: Add \dfrac{1}{2} and  & \dfrac{1}{5}.

\dfrac{1}{2} = \dfrac{{1 \times 5}}{{2 \times 5}} = \dfrac{5}{{10}}                 [See LCM (2, 5) =10]

\dfrac{1}{5} = \dfrac{{1 \times 2}}{{5 \times 2}} = \dfrac{2}{{10}}

So, \dfrac{1}{2} + \dfrac{1}{5} = \dfrac{5}{{10}} + \dfrac{2}{{10}} = \dfrac{{5 + 2}}{{10}} = \dfrac{7}{{10}}

Again, subtract  & \dfrac{1}{5} and \dfrac{1}{2}.

\dfrac{1}{2} - \dfrac{1}{5} = \dfrac{5}{{10}} - \dfrac{2}{{10}} = \dfrac{{5 - 2}}{{10}} = \dfrac{3}{{10}}.

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