Question

The product of two rational numbers is $\dfrac{-9}{16}$. If one of the numbers is$\dfrac{-4}{3}$, then the other number is:
(A). $\dfrac{36}{48}$
(B). $\dfrac{25}{64}$
(C). $\dfrac{27}{49}$
(D). $\dfrac{27}{64}$

Answer 1

This question is based on the simple concept of multiplication of rational numbers, in this question the product of two rational numbers is given and one of the rational numbers is given, so if we divide the product with a given rational number, we will get another number.

Complete step-by-step answer:

In the question, we are given that the product of two rational numbers is $\dfrac{-9}{16}$ . So, let the two rational numbers be x and y. So, according to the question, their product is equal to $\dfrac{-9}{16}$ .
$\Rightarrow xy=\dfrac{-9}{16}..........(i)$ .
It is also given that one of the rational numbers is $\dfrac{-4}{3}$ . So, let $x=\dfrac{-4}{3}$ . We will substitute this value of x in equation (i). On substituting the value of x, i.e. $x=\dfrac{-4}{3}$ in equation (i), we get:
$\dfrac{-4}{3}\times y=\dfrac{-9}{16}$
Now, on the left-hand side, the two terms have a multiplication sign in between them. If we shift one of the terms to the right-hand side, the sign will change to a division sign. We will shift $\dfrac{-4}{3}$ from the left-hand side of the equation to the right-hand side of the equation. So, we get:
$\dfrac{-4}{3}\times y=\dfrac{-9}{16}$
$\Rightarrow y=\dfrac{-9}{16}\div \dfrac{-4}{3}$
$\Rightarrow y=\dfrac{-9}{16}\times \dfrac{3}{-4}$
$\Rightarrow y=\dfrac{27}{64}$
Hence, the value of the other rational number is $\dfrac{27}{64}$ . Hence, option D is the correct option.

Note: If we multiply or divide two rational numbers then the resulting number will also be a rational number, which can be verified from the above question. Also, while shifting the terms from left-hand side to the right-hand side of the equation, or vice-versa, then take care of the change in sign. Plus becomes minus, multiply becomes divide and vice-versa. Make sure to change the sign on shifting the terms, failing which will result in a wrong answer.