Question

Simplify:
(i) $\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}$
(ii) $\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}$
(iii) $\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}$
(iv) $\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\frac{-3}{2}+\frac{5}{4}-\frac{7}{4}=\frac{-3\times 2}{2\times 2}+\frac{5}{4}-\frac{7}{4}=\frac{-6+5-7}{4}=\frac{-8}{4}=-2 \\ \left(\mathrm{ii}\right)\frac{5}{3}-\frac{7}{6}+\frac{-2}{3}=\frac{5\times 2}{3\times 2}-\frac{7}{6}+\frac{-2\times 2}{3\times 2}=\frac{10-7-4}{6}=\frac{-1}{6} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=\frac{5\times 3}{4\times 3}-\frac{7\times 2}{6\times 2}-\frac{-2\times 4}{3\times 4}=\frac{15-14+8}{12}=\frac{9}{12}=\frac{3}{4} \\ \left(\mathrm{iv}\right)\frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7}=\frac{-2\times 14}{5\times 14}-\frac{-3\times 7}{10\times 7}-\frac{-4\times 10}{7\times 10}=\frac{-28+21+40}{70}=\frac{33}{70} \end{gathered}$$