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

Hint: We will start the solution by assuming the other number to be $ x $ . We already have one number and the product. So, we will multiply both numbers and put them equal to the given product and simplify the obtained equation to find the value of $ x $ which is the other number.

Complete step by step answer:
We have been given that the product of two rational numbers is $ \dfrac{-9}{16} $ and one of the numbers is $ \dfrac{-4}{3} $ .
We have to find the other number.
Let us assume the other number is $ x $.
Now, the product of two numbers is given, so we have
 $ \Rightarrow x\times \dfrac{-4}{3}=\dfrac{-9}{16} $
Now, shifting the terms from LHS to RHS and solving further, we get
 $ \begin{align}
  & \Rightarrow x=\dfrac{-9}{16}\div \dfrac{-4}{3} \\
 & \Rightarrow x=\dfrac{-9}{16}\times \dfrac{-3}{4} \\
 & \Rightarrow x=\dfrac{27}{64} \\
\end{align} $
Hence the other number is $ \dfrac{27}{64} $ .

Option D is the correct answer.

Note:
 While shifting terms from LHS to RHS or vice-versa, make sure to change the sign. Multiply becomes divide and the plus sign becomes minus, else it will result in a wrong answer. Also, we can check the answer by multiplying both the numbers to whether we will get the same product or not.
For this question we get the other number as $ \dfrac{27}{64} $ and the given number is $ \dfrac{-4}{3} $ .
So, the product of this two numbers will be $ \begin{align}
  & \dfrac{27}{64}\times \dfrac{-4}{3}=\dfrac{-9}{16} \\
 & \\
\end{align} $ which is equal to the given product.