Question

Fill in the blanks:
(i) $\frac{-5}{7}=\frac{\dots }{35}=\frac{\dots }{49}$
(ii) $\frac{-4}{-9}=\frac{\dots }{18}=\frac{12}{\dots }$
(iii) $\frac{6}{-13}=\frac{-12}{\dots }=\frac{24}{\dots }$
(iv) $\frac{-6}{\dots }=\frac{3}{11}=\frac{\dots }{-55}$

Answer 1

$$\begin{gathered} \text{(i)} \\ \mathrm{Here},\frac{-5\times 5}{7\times 5}=\frac{-25}{35} \\ \text{A}\mathrm{lso},\frac{-5\times 7}{7\times 7}=\frac{-35}{49}. \\ \mathrm{Therefore},\frac{-5}{7}=\frac{-25}{35}=\frac{-35}{49} \\ \left(\mathrm{ii}\right)\mathrm{Here},\frac{-4\times -2}{-9\times -2}=\frac{8}{18} \\ \text{A}\mathrm{lso},\frac{-4\times -3}{-9\times -3}=\frac{12}{27} \\ \mathrm{Therefore},\frac{-4}{-9}=\frac{8}{18}=\frac{12}{27} \\ \left(\mathrm{iii}\right)\mathrm{Here},\frac{6\times -2}{-13\times -2}=\frac{-12}{26} \\ \mathrm{Also},\frac{6\times 4}{-13\times 4}=\frac{24}{-52} \\ \mathrm{Therefore},\frac{6}{-13}=\frac{-12}{26}=\frac{24}{-52} \\ \left(\mathrm{iv}\right)\mathrm{Here},\frac{-6/-2}{-22/-2}=\frac{3}{11} \\ \mathrm{Also},\frac{-6}{-22}=\frac{3\times -5}{11\times -5}=\frac{-15}{-55} \\ \mathrm{Therefore},\frac{-6}{-22}=\frac{3}{11}=\frac{-15}{-55} \end{gathered}$$