Question

Write a pair of fractions whose sum is $\frac{8}{11}$ and difference is $\frac{2}{11}$.

Answer 1

Let the first fraction is $=\text{x}$

So the second fraction $=\frac{8}{11}$$-\text{x}$ (because sum is $\frac{8}{11}$)

Now according to the question difference is $=\frac{2}{11}$

$$\begin{gathered} \frac{8}{11}-\text{x-x=}\frac{2}{11} \\ \frac{8}{11}\text{-2x=}\frac{2}{11} \\ -2\text{x=}\frac{2}{11}\text{-}\frac{8}{11}\text{(transfering}\frac{8}{11}\text{on R.H.S)} \\ \text{-2x=}\frac{2-8}{11}\text{=}\frac{-6}{11} \\ \text{2x=}\frac{6}{11} \\ \text{x=}\frac{6}{11}\text{×}\frac{1}{2}\text{=}\frac{3}{11}\text{(dividing both sides by 2)} \\ \text{x=}\frac{3}{11} \end{gathered}$$

So the first fraction is $\frac{3}{11}$

and the second fraction is $=\frac{8}{11}-\frac{3}{11}=\frac{8-3}{11}=\frac{5}{11}$

Hence pair of fractions are $\frac{5}{11},\frac{3}{11}$.