Question

If each of the following pairs represents a pair of equivalent rational numbers, find the values of x:
(i) $\frac{2}{3}\mathrm{and}\frac{5}{x}$
(ii) $\frac{-3}{7}\mathrm{and}\frac{x}{4}$
(iii) $\frac{3}{5}\mathrm{and}\frac{x}{-25}$
(iv) $\frac{13}{6}\mathrm{and}\frac{-65}{x}$

Answer 1

(i) $\frac{2}{3}=\frac{5}{x},\mathrm{then}x=5\times \frac{3}{2}=\frac{15}{2}$
(ii) $\frac{-3}{7}=\frac{x}{4},\mathrm{then}x=\frac{-3}{7}\times 4=\frac{-12}{7}$
(iii) $\frac{3}{5}=\frac{x}{-25},\mathrm{then}x=\frac{3}{5}\times (-25)=\frac{-75}{5}=-15$
(iv) $\frac{13}{6}=\frac{-65}{x},\mathrm{then}x=\frac{6}{13}\times (-65)=6\times (-5)=-30$