Question

Write a pair of fractions whose sum is $\frac{7}{11}$ and difference is $\frac{2}{11}$.

Answer 1

Let the pair fraction $F_1$ and $F_2$

$\therefore$ According to the question

$F_1+F_2=\frac{7}{11}......\left(i\right)$

$F_1-F_2=\frac{2}{11}......\left(ii\right)$

Adding the equation (i) and (ii) we get that

$2F_1=\frac{7}{11}+\frac{2}{11}=\frac{7+2}{11}=\frac{9}{11}$

$\Rightarrow F_1=\frac{9}{11}\times \frac{1}{2}=\frac{9}{22}$

Put the value of $F_1$ in equation (i) we get that

$\Rightarrow \frac{9}{11}+F_2=\frac{7}{11}$

$\Rightarrow F_2=\frac{7}{11}-\frac{9}{22}=\frac{7}{11}\times \frac{2}{2}-\frac{9}{22}=\frac{14}{22}-\frac{9}{22}=\frac{14-9}{22}$

$\Rightarrow F_2=\frac{5}{22}$