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

$$ F_1 + F_2 = \dfrac {7}{11}......(i) $$

$$ F_1 - F_2 = \dfrac {2}{11}......(ii) $$

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

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

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

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

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

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

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