Q.6 Which of the following pairs represent the same rational number?
(i) $$\frac{-7}{21}$$ and $$\frac{3}{9}$$
(ii) $$\frac{-16}{20}$$ and $$\frac{20}{-25}$$
(iii)$$\frac{-2}{-3}$$ and $$\frac{2}{3}$$
(iv) $$\frac{-3}{5}$$ and $$\frac{-12}{20}$$
(v) $$\frac{8}{-5}$$ and $$\frac{-24}{15}$$
(vi) $$\frac{1}{3}$$ and $$\frac{-1}{9}$$
(vii) $$\frac{-5}{-9}$$ and $$\frac{5}{-9}$$

(i) $$\frac{-7}{21}$$ and $$\frac{3}{9}$$
Or, $$\frac{-7×3}{21×3}$$ and $$\frac{3×7}{9×7}$$
Or, $$\frac{-21}{63}$$ and $$\frac{21}{63}$$
Since -21$$\neq$$ 21 so $$\frac{-7}{21}$$ and $$\frac{3}{9}$$do not represent the same rational number
(ii) $$\frac{-16}{20}$$ and $$\frac{20}{-25}$$
Or, $$\frac{-16×5}{20×5}$$ and $$\frac{20×4}{25×4}$$
Or, $$\frac{-80}{100}$$ and $$\frac{80}{100}$$
Since -80$$\neq$$ 80 so $$\frac{-16}{20}$$ and $$\frac{20}{-25}$$do not represent the same rational number
(iii) $$\frac{-2}{-3}$$ and $$\frac{2}{3}$$
Or, $$\frac{2}{3}$$ and $$\frac{2}{3}$$
so$$\frac{2}{3}$$ and $$\frac{2}{3}$$ represent the same rational number
(iv) $$\frac{-3}{5}$$ and $$\frac{-12}{20}$$
Or, $$\frac{-3×4}{5×4}$$ and $$\frac{-12×1}{20×1}$$
Or, $$\frac{-12}{20}$$ and $$\frac{-12}{20}$$
Since $$\frac{-12}{20}$$ = $$\frac{-12}{20}$$
so $$\frac{-3}{5}$$ and $$\frac{-12}{20}$$ represent the same rational number