Question

Which of the
following pairs of rational numbers are equal?

(i) $$\dfrac{-3}{-7}$$
and $$\dfrac{15}{35}$$

(ii) $$\dfrac{-6}{8}$$
and $$\dfrac{10}{-15}$$

(iii) $$\dfrac{6}{-10}$$
and $$\dfrac{-12}{20}$$

Answer 1

(i) $$\dfrac{-3}{-7}$$
and $$\dfrac{15}{35} \Rightarrow \dfrac{15}{35}=\dfrac{3}{7}$$

$$\therefore
\dfrac{-3}{-7}=\dfrac{15}{35}$$

(ii) $$\dfrac{-6}{8}$$
and $$\dfrac{10}{-15}$$ if $$-6 \times(-15)=10 \times 8$$

$$\Rightarrow
90=80$$ which is not true.

$$\therefore
\dfrac{-6}{8} \neq \dfrac{10}{-15}$$

(iii) $$\dfrac{6}{-10}$$
and $$\dfrac{-12}{20}$$ if $$6 \times 20=-12 \times(-10)$$

$$\Rightarrow
120=120$$ which is true.

$$\therefore
\dfrac{6}{-10}=\dfrac{-12}{20}$$