Question

Mark the correct alternative in each of the following:

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

(a) $\frac{-10}{25}$ (b) $\frac{10}{-15}$ (c) $\frac{-9}{6}$ (d) None of these

Answer 1

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

The rational number $\frac{-2}{3}$ is in its standard form.

Consider the rational number $\frac{10}{-15}$.

This rational number can be expressed in standard form as follows:

$\frac{10}{-15}=\frac{10\times \left(-1\right)}{-15\times \left(-1\right)}=\frac{-10}{15}$ (Multiplying numerator and denominator by −1 to make denominator positive)

HCF of 10 and 15 = 5

Dividing the numerator and denominator of $\frac{-10}{15}$ by 5, we have

$\frac{-10}{15}=\frac{-10÷5}{15÷5}=\frac{-2}{3}$

Thus, the standard form of $\frac{-10}{15}$ is $\frac{-2}{3}$, which is same as the given rational number.

So, the rational number equal to $\frac{-2}{3}$ is $\frac{10}{-15}$.

Let us check why options (a) and (c) are not correct.

The standard form of $\frac{-10}{25}$ is $\frac{-2}{5}$.

HCF of 10 and 25 = 5

Dividing the numerator and denominator of $\frac{-10}{25}$ by 5, we have

$\frac{-10}{25}=\frac{-10÷5}{25÷5}=\frac{-2}{5}$

The standard form of $\frac{-9}{6}$ is $\frac{-3}{2}$.

HCF of 6 and 9 = 3

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

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

Hence, the correct answer is option (b).