Question

Mark the correct alternative in each of the following:

The rational number equal to $\frac{2}{-3}$ is

(a) $\frac{14}{-18}$ (b) $\frac{-6}{9}$ (c) $\frac{-8}{-12}$ (d) $\frac{3}{-2}$

Answer 1

We know that two rational numbers are equal if they have the same standard form.

$\frac{2}{-3}=\frac{2\times \left(-1\right)}{-3\times \left(-1\right)}=\frac{-2}{3}$

The standard form of $\frac{2}{-3}$ is $\frac{-2}{3}$.

Consider the rational number $\frac{-6}{9}$.

HCF of 6 and 9 = 3

Dividing the numerator and denominator of $\frac{-6}{9}$ by 3, we have

$\frac{-6}{9}=\frac{-6÷3}{9÷3}=\frac{-2}{3}$

Thus, the standard form of $\frac{-6}{9}$ is $\frac{-2}{3}$.

So, the rational number $\frac{-6}{9}$ is equal to $\frac{2}{-3}$.

It can be checked that

Standard form of $\frac{14}{-18}$ = $\frac{-7}{9}$

Standard form of $\frac{-8}{-12}$ = $\frac{2}{3}$

Standard form of $\frac{3}{-2}$ = $\frac{-3}{2}$

Hence, the correct answer is option (b).