Question

By what numbers should we multiply $\frac{-15}{20}$ so that the product may be $\frac{-5}{7}$ ?

Answer 1

Given

Product of two rational number $=\frac{-5}{7}$

and One number $=\frac{-15}{20}$

Find out

We have to determine the other number

Let us assume the other number be $x$.

According to given details, we have

$\begin{array}{rcl}x\times \left(\frac{-15}{20}\right)& =& \frac{-5}{7}\\ & \Rightarrow & x=\frac{{\displaystyle \frac{-5}{7}}}{{\displaystyle \frac{-15}{20}}}\\ & \Rightarrow & x=\frac{-5}{7}\times \frac{-20}{15}\\ & \Rightarrow & x=\frac{-1}{7}\times \frac{-20}{3}\\ & \Rightarrow & x=\frac{-20}{21}\end{array}$

So, the other number is $\frac{-20}{21}$.