Write a pair of fractions whose sum is 7 11 and difference is 2 1… - Vidyadip

Question

Write a pair of fractions whose sum is $\frac{7}{11}$ and difference is $\frac2{11}.$

✓

Answer

Let $a$ and $b$ be the pair of fraction whose sum is $\frac{7}{11}$ and difference is $\frac{2}{11},$
then $\text{a}+\text{b}=\frac{7}{11}\ ...\text{(i)}$
and $\text{a}-\text{b}=\frac{2}{11}\ ...\text{(ii)}$
On adding $Eqs. (i)$ and $(ii),$ we get
$(\text{a}+\text{b})+(\text{a}-\text{b})=\frac{7}{11}+\frac{2}{11}$
$\Rightarrow\text{a}+\text{b}+\text{a}-\text{b}=\frac{7+2}{11}$
$\Rightarrow\text{2a}=\frac{9}{11}$
$\Rightarrow\text{a}=\frac{9}{11\times2}=\frac9{22}$
On substituting value of a in $Eq. (i),$ we get
$\frac{9}{22}+\text{b}=\frac{7}{11}$
$\Rightarrow\text{b}=\frac{7}{11}-\frac{9}{22}$
$\Rightarrow\text{b}=\frac{7\times2}{11\times2}-\frac{9}{22} [ \because LCM$ of $11$ and $22$ is $22$ so convert each fraction to an equivalent fraction with denominator $22.]$
$\Rightarrow\text{b}=\frac{14}{22}-\frac{9}{22}$
$\Rightarrow\text{b}\frac{14-9}{22}=\frac{5}{22}$
So, $\frac{9}{22}$ and $\frac{5}{22}$ is a pair of fraction,
whose sum is $\frac{7}{11}$ and defferences is $\frac{2}{11}.$

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