Question

Verify whether the given statement is true or false:
(i) $\frac{13}{5}÷\frac{26}{10}=\frac{26}{10}÷\frac{13}{5}$
(ii) $-9÷\frac{3}{4}=\frac{3}{4}÷\left(-9\right)$
(iii) $\frac{-8}{9}÷\frac{-4}{3}=\frac{-4}{3}÷\frac{-8}{9}$
(iv) $\frac{-7}{24}÷\frac{3}{-16}=\frac{3}{-16}÷\frac{-7}{24}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \frac{13}{5}÷\frac{26}{10}=\frac{26}{10}÷\frac{13}{5} \\ \text{LHS} \\ \frac{13}{5}÷\frac{26}{10} \\ =\frac{13}{5}\times \frac{10}{26} \\ =\frac{130}{130} \\ =1 \\ \text{RHS} \\ \frac{26}{10}÷\frac{13}{5} \\ =\frac{26}{10}\times \frac{5}{13} \\ =\frac{130}{130} \\ =1 \\ \text{TRUE} \\ (\mathrm{ii})-9÷\frac{3}{4}=\frac{3}{4}÷(-9)\text{LHS}-9÷\frac{3}{4}=-9\times \frac{4}{3}=\frac{-36}{3}=-12\text{RHS}\frac{3}{4}\text{÷(-9)}\text{=}\frac{3}{4}\text{×}\frac{1}{-9}\text{=}\frac{3}{-36}\text{=}\frac{-1}{12}\mathrm{FALSE}\mathrm{iii})\frac{-8}{9}÷\frac{-4}{3}=\frac{-4}{3}÷\frac{-8}{9}\mathrm{LHS}\frac{-8}{9}÷\frac{-4}{3}=\frac{-8}{9}\times \frac{3}{-4}=\frac{24}{36}=\frac{2}{3}\mathrm{RHS}\frac{-4}{3}÷\frac{-8}{9}=\frac{-4}{3}\times \frac{9}{-8}=\frac{36}{24}=\frac{3}{2}\mathrm{FALSE}(\mathrm{iv})\frac{-7}{24}÷\frac{3}{-16}=\frac{3}{-16}÷\frac{-7}{24}\mathrm{LHS}\frac{-7}{24}\times \frac{-16}{3}=\frac{112}{72}\mathrm{RHS}\frac{3}{-16}÷\frac{-7}{24}=\frac{3}{-16}\times \frac{24}{-7}=\frac{72}{112}\mathrm{FALSE} \end{gathered}$$