Question

Replace $\boxed{}$ by the correct number:
(i) $\boxed{}-\frac{5}{8}=\frac{1}{4}$
(ii) $\boxed{}-\frac{1}{5}=\frac{1}{2}$
(iii) $\frac{1}{2}-\boxed{}=\frac{1}{6}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\square -\frac{5}{8}=\frac{1}{4} \\ \square =\frac{1}{4}+\frac{5}{8} \\ \square =\frac{1\times 2}{4\times 2}+\frac{5\times 1}{8\times 1}(\mathrm{Because}\mathrm{LCM}\mathrm{of}4\&8\mathrm{is}8) \\ \square =\frac{2}{8}+\frac{5}{8}=\frac{2+5}{8}=\frac{7}{8} \\ \square =\frac{7}{8} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{ii}\right)\square -\frac{1}{5}=\frac{1}{2} \\ \square =\frac{1}{2}+\frac{1}{5} \\ \square =\frac{1\times 5}{2\times 5}+\frac{1\times 2}{5\times 2}=\frac{5}{10}+\frac{2}{10}=\frac{5+2}{10} \\ \square =\frac{7}{10} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)\frac{1}{2}-\square =\frac{1}{6} \\ \square =\frac{1}{2}-\frac{1}{6} \\ \square =\frac{1\times 3}{2\times 3}-\frac{1\times 1}{6\times 1}(\mathrm{Because}\mathrm{LCM}\mathrm{of}2\&6\mathrm{is}6) \\ \square =\frac{3}{6}-\frac{1}{6}=\frac{2÷2}{6÷2}(\mathrm{HCF}\mathrm{of}\mathrm{the}\mathrm{numerator}\&\mathrm{denominator}\mathrm{is}2) \\ \square =\frac{1}{3} \end{gathered}$$