Question

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

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Answer 1

Let one of the fractions be $x$ and the other be $❲ \frac{7}{11}- x ❳$

Now,.

$x - ❲ \frac{7}{11} - x❳= \frac{2}{11}$

$\implies x - \frac{7}{11} + x = \frac{2}{11}$

$\implies2x = \frac{2}{11} + \frac{7}{11}$

$\implies2x = \frac{9}{11}$

$\implies x = \frac{9}{22}$

∴ Other fractions is

$\frac{7 }{11} - \frac{9}{22} = \frac{14 - 9}{22} = \frac{5}{22}$

Hence, the fractions are $\frac{9}{22}$ and $\frac{5}{22}$