Question

The product of two rational numbers is $24$. If one of them is $\frac{-36}{11}$, find the other.

Answer 1

Step 1: Using the concept of multiplication of rational numbers
Let, the required number be $x$.
According to the given question,
product of $x$ and $\frac{-36}{11}=24$
$x\times \frac{-36}{11}=24-------\left(i\right)$
Step 2: Simplify the given equation to get required unknown.
From (i), $x=24/\left(\frac{-36}{11}\right)$
$x=24\times \frac{-11}{36}$
$[-\frac{11}{36}]$ is the multiplicative inverse of $-\frac{36}{11}$.
$x=-24\times \frac{11}{36}$

$=-\frac{24}{1}\times \frac{11}{36}=-\frac{24\times 11}{1\times 36}$
$=-\frac{22}{3}$
$=-7\frac{1}{3}$

Hence, the other number is $-7\frac{1}{3}$.