Adding & Subtracting Fractions

≈ 30 min

To add or subtract fractions with different denominators, first rewrite them over a common denominator (their LCM), then add or subtract only the tops.

Worked example. $\dfrac{1}{2} + \dfrac{1}{3}$ . The LCM of $2$ and $3$ is $6$ :

\frac{1}{2} = \frac{3}{6}, \qquad \frac{1}{3} = \frac{2}{6}, \qquad \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

A fraction of a quantity uses the word "of", which means multiply. To find $\frac{3}{4}$ of R $20$ : one quarter is $20 \div 4 = 5$ , and three quarters is $3 \times 5 = 15$ , so R $15$ .

Calculate $\dfrac{1}{2} + \dfrac{1}{3}$ . Give your answer as a fraction, e.g. 5/6.

Find $\dfrac{3}{4}$ of R $20$ . Give your answer in rand (just the number).

Calculate $\dfrac{5}{6} - \dfrac{1}{3}$ . Give your answer as a fraction in lowest terms, e.g. 1/2.

Thabo writes $\dfrac{1}{4} + \dfrac{1}{2} = \dfrac{2}{6}$ . What is the correct answer?

$\dfrac{2}{6}$

$\dfrac{3}{4}$

$\dfrac{1}{6}$

$\dfrac{2}{4}$