Question

The difference of two rational numbers is $\frac{-6}{25}$. If the greater number is $\frac{-4}{9}$, find the smaller number.

Answer 1

Let the difference of two rational numbers $\frac{-4}{9}$and $x$ is $\frac{-6}{25}$

Here $\frac{-4}{9}$ is the greater number and $x$ is the smaller number

$$\begin{gathered} \Rightarrow \frac{-4}{9}-x=\frac{-6}{25} \\ \Rightarrow -x=\frac{-6}{25}+\frac{4}{9} \\ -x=\frac{-6\times 9}{25\times 9}+\frac{4\times 25}{9\times 25}=\frac{-54}{225}+\frac{100}{225} \\ -x=\frac{-54+100}{225}=\frac{46}{225} \\ x=\frac{-46}{225} \end{gathered}$$

Hence, the smaller number is $\frac{-46}{225}.$