Which of the
following are pairs of equivalent rational numbers?
(i) $$\dfrac{-4}{13},
\dfrac{60}{-195}$$
(ii) $$\dfrac{7}{-15},
\dfrac{-35}{-75}$$
(iii) $$\dfrac{16}{-20},
\dfrac{-56}{70}$$
(i) $$\dfrac{-4}{13},
\dfrac{60}{-195}$$
$$\dfrac{60}{-195}=\dfrac{4}{-13}=\dfrac{4(-1)}{-13(-1)}=\dfrac{-4}{13}$$
$$\therefore
\dfrac{-4}{13}$$ and $$\dfrac{60}{-195}$$ are equivalent.
(ii) $$\dfrac{7}{-15},
\dfrac{-35}{-75}$$
$$\dfrac{-35}{-75}=\dfrac{-7}{-15}=\dfrac{7}{15}$$
$$\therefore
\dfrac{7}{-15}$$ and $$\dfrac{-35}{-75}$$ are not equivalent.
(iii) $$\dfrac{16}{-20},
\dfrac{-56}{70}$$
$$ \dfrac{-16}{20}=\dfrac{-16
\div 4}{20+4}=\dfrac{-4}{5} $$
$$\dfrac{-56}{70}=\dfrac{-56
\div 14}{70 \div 14}=\dfrac{-4}{5} $$
$$\therefore
\dfrac{-16}{20}$$ and $$\dfrac{-56}{70}$$ are equivalent
$$\therefore(i)$$
and $$(i i i)$$ are equivalent rationals.