Question

Verify the property: x × y = y × x by taking:
(i) $x=-\frac{1}{3},y=\frac{2}{7}$
(ii) $x=\frac{-3}{5},y=\frac{-11}{13}$
(iii) $x=2,y=\frac{7}{-8}$
(iv) $x=0,y=\frac{-15}{8}$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}\mathrm{to}\mathrm{verify}\mathrm{that}x\times y=y\times x. \\ \left(\mathrm{i}\right)x=\frac{-1}{3},y=\frac{2}{7} \\ x\times y=\frac{-1}{3}\times \frac{2}{7}=\frac{-2}{21} \\ y\times x=\frac{2}{7}\times \frac{-1}{3}=\frac{-2}{21} \\ \therefore \frac{-1}{3}\times \frac{2}{7}=\frac{2}{7}\times \frac{-1}{3} \\ \mathrm{Hence}\mathrm{verified}. \\ \left(\mathrm{ii}\right)x=\frac{-3}{5},y=\frac{-11}{13} \\ \mathrm{x}\times \mathrm{y}=\frac{-3}{5}\times \frac{-11}{13}=\frac{33}{65} \\ y\times x=\frac{-11}{13}\times \frac{-3}{5}=\frac{33}{65} \\ \therefore \frac{-3}{5}\times \frac{-11}{13}=\frac{-11}{13}\times \frac{-3}{5} \\ \mathrm{Hence}\mathrm{verified}. \\ \left(\mathrm{iii}\right)x=2,y=\frac{7}{-8} \\ x\times y=2\times \frac{7}{-8}=\frac{7}{-4} \\ y\times x=\frac{7}{-8}\times 2=\frac{7}{-4} \\ \therefore 2\times \frac{7}{-8}=\frac{7}{-8}\times 2 \\ \mathrm{Hence}\mathrm{verified}. \\ \left(\mathrm{iv}\right)x=0,y=\frac{-15}{8} \\ x\times y=0\times \frac{-15}{8}=0 \\ y\times x=\frac{-15}{8}\times 0=0 \\ \therefore 0\times \frac{-15}{8}=\frac{-15}{8}\times 0 \\ \mathrm{Hence}\mathrm{verified}. \end{gathered}$$