Question

Equalise the denominators to determine which number is bigger and which smaller.

(5) $\frac{-2}{3},\frac{-3}{4}$

Answer 1

$\frac{-2}{3},\frac{-3}{4}$
L.C.M of 3 and 4 is 12.

$$\begin{gathered} \therefore \frac{-2}{3}=\frac{-2\times 4}{3\times 4}=\frac{-8}{12} \\ \mathrm{And}\frac{-3}{4}=\frac{-3\times 3}{4\times 3}=\frac{-9}{12} \end{gathered}$$
Denominators of both the numbers are same; therefore, the rational number with the greater numerator will be greater.
$$\begin{gathered} \therefore \frac{-8}{12}>\frac{-9}{12} \\ \therefore \frac{-2}{3}>\frac{-3}{4} \end{gathered}$$