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# 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