Question

The sum of two rational numbers is $\frac{-4}{7}$. If one of them is $\frac{6}{13}$, find the other.

Answer 1

Given : Sum $=\frac{-4}{7}$, one number $=\frac{6}{13}$

Let the other number be $\mathrm{X}$,

So according to given condition,

$$\begin{gathered} \mathrm{X}+\frac{6}{13}=\frac{-4}{7} \\ \Rightarrow \mathrm{X}=\frac{-4}{7}-\frac{6}{13} \end{gathered}$$

Take LCM of $7$ and $13$ is $91$.

Now convert both the fractions into equivalent fractions with denominator $91$,

$$\begin{gathered} \mathrm{X}=\frac{-4\times 13}{7\times 13}-\frac{6\times 7}{13\times 7} \\ \mathrm{X}=-\frac{52}{91}-\frac{42}{91} \\ \mathrm{X}=\frac{-52-42}{91} \\ \mathrm{X}=\frac{-94}{91} \end{gathered}$$

Hence, other number is $\frac{-94}{91}$.