Question

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:
(i) 9
(ii) −7
(iii) $\frac{12}{5}$
(iv) $\frac{-7}{9}$
(v) $\frac{-3}{-5}$
(vi) $\frac{2}{3}\times \frac{9}{4}$
(vii) $\frac{-5}{8}\times \frac{16}{15}$
(viii) $-2\times \frac{-3}{5}$
(ix) −1
(x) $\frac{0}{3}$
(xi) 1

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}9=\frac{1}{9} \\ (\mathrm{ii})\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}-7=\frac{-1}{7} \\ \left(\mathrm{iii}\right)\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}\frac{12}{5}=\frac{5}{12} \\ (\mathrm{iv})\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}\frac{-7}{9}=\frac{-9}{7} \\ \left(\mathrm{v}\right)\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}\frac{-3}{-5}=\frac{-5}{-3}or\frac{5}{3} \\ (\mathrm{vi})\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}\frac{2}{3}\times \frac{9}{4}=\frac{3}{2}\times \frac{4}{9}=\frac{2}{3} \\ \left(\mathrm{vii}\right)\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}\frac{-5}{8}\times \frac{16}{15}=\frac{8}{-5}\times \frac{15}{16}=\frac{-3}{2} \\ (\mathrm{viii})\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}-2\times \frac{-3}{5}=\frac{1}{-2}\times \frac{5}{-3}=\frac{5}{6} \\ \left(\mathrm{ix}\right)\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}-1=\frac{1}{-1}=-1 \\ (\mathrm{x})\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}\frac{0}{3}=\frac{3}{0}=\mathrm{undefined} \\ \left(\mathrm{ix}\right)\mathrm{Multiplicative}\mathrm{inverse}(\mathrm{reciprocal)}\mathrm{of}1=\frac{1}{1}=1 \end{gathered}$$