Question

the sum of two fractions is 11/16 and their difference is 5/16 what are the two fractions

Answer 1

First fraction: 1/2
Second fraction: 3/16

Answer 2

Answer:

The required fractions are

$\sf\:\dfrac{1}{2}\:\&\:\dfrac{3}{16}$

Step-by-step-explanation:

Let the greater fraction be x.

And the smaller fraction be y.

From the first condition,

$\sf\:x\:+\:y\:=\:\dfrac{11}{16}\:\:\:-\:-\:-\:(\:1\:)$

From the second condition,

$\sf\:x\:-\:y\:=\:\dfrac{5}{16}\:\:\:-\:-\:-\:(\:2\:)$

By adding both equations, we get,

$\sf\:x\:+\:\cancel{y}\:=\:\frac{11}{16}\:\:\:-\:-\:-\:(\:1\:)\\\\\sf\:x\:-\:\cancel{y}\:=\:\frac{5}{16}\:\:\:-\:-\:-\:(\:2\:)\\\\\implies\sf\:2x\:=\:\cancel{\frac{16}{16}}\\\\\implies\sf\:2x\:=\:1\\\\\implies\boxed{\red{\sf\:x\:=\:\frac{1}{2}}}$

By substituting $\sf\:x\:=\:\dfrac{1}{2}$ in equation ( 1 ), we get,

$\sf\:x\:+\:y\:=\:\frac{11}{16}\:\:\:-\:-\:-\:(\:1\:)\\\\\implies\sf\:\frac{1}{2}\:+\:y\:=\:\frac{11}{16}\\\\\implies\sf\:y\:=\:\frac{11}{16}\:-\:\frac{1}{2}\\\\\implies\sf\:y\:=\:\frac{11}{16}\:-\:\frac{8}{16}\\\\\implies\sf\:y\:=\:\dfrac{11\:-\:8}{16}\\\\\implies\boxed{\red{\sf\:y\:=\:\frac{3}{16}}}$

The required fractions are $\sf\:\dfrac{1}{2}\:\&\:\dfrac{3}{16}$