Question

Question 127.
Write a pair of fractions whose sum is $\frac{7}{11}$ and difference is $\frac{2}{{11}^{\cdot }}$

Answer 1

Let a and b be the pair of fractions whose sum is $\frac{7}{11}$ and difference is $\frac{2}{11}$, then
a + b = $\frac{7}{11}$ $\cdots \left(i\right)$
and a - b = $\frac{2}{11}$ $\cdots \left(ii\right)$
On adding Eqs. (i) and (ii), we get
(a + b) + (a - b) =$\frac{7}{11}+\frac{2}{11}\Rightarrow a+b+a-b=\frac{7+2}{11}$

$\Rightarrow$ 2a = $\frac{9}{11}\Rightarrow a=\frac{9}{11\times 2}=\frac{9}{22}$
On substituting the value of a in Eq. (i), we get
$\frac{9}{22}+b=\frac{7}{11}\Rightarrow b=\frac{7}{11}-\frac{9}{22}$
$\Rightarrow$ b = $\frac{7\times 2}{11\times 2}-\frac{9}{22}$ $\left[\begin{array}{c}\because \text{LCM of 11 and 22 is 22, so we convert}\\ \text{each of the given fraction to an equivalent}\\ \text{fraction with denominator 22.}\end{array}\right]$
$\Rightarrow$ b = $\frac{14}{22}-\frac{9}{22}$
$\Rightarrow$ b = $\frac{14-9}{22}=\frac{5}{22}$
So, $\frac{9}{22}$ and $\frac{5}{22}$ is a pair of fractions, whose sum is $\frac{7}{11}$ and difference is $\frac{2}{11}$.