Question

The sum of two rational numbers is $\frac{9}{16}$. If one of them is $\frac{-5}{18}$, find the other.

Answer 1

Given : Sum $=\frac{9}{16}$, one number is $\frac{-5}{18}$

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

So according to given condition,

$$\begin{gathered} \mathrm{X}+\frac{-5}{18}=\frac{9}{16} \\ \Rightarrow \mathrm{X}-\frac{5}{18}=\frac{9}{16} \\ \Rightarrow \mathrm{X}=\frac{9}{16}+\frac{5}{18} \end{gathered}$$

Take LCM of $16$ and $18$ is $144$.

Now convert both the fractions into equivalent fractions with denominator $144$,

$$\begin{gathered} \Rightarrow \mathrm{X}=\frac{9\times 9}{16\times 9}+\frac{5\times 8}{18\times 8} \\ \Rightarrow \mathrm{X}=\frac{81}{144}+\frac{40}{144} \\ \Rightarrow \mathrm{X}=\frac{81+40}{144} \\ \Rightarrow \mathrm{X}=\frac{121}{144} \end{gathered}$$

Hence, other number is $\frac{121}{144}$.