Question

What should be added to $-\frac{3}{16}$ to get $\frac{11}{24}$?

Answer 1

Step 1: Finding equations by using given conditions
Let, the required rational number be 𝑥.
Given sum of the rational number is $\frac{11}{24}$ and, one of the numbers $=-\frac{3}{16}$
$\therefore x+(-\frac{3}{16})=\frac{11}{24}$
$\Rightarrow x-\frac{3}{16}=\frac{11}{24}...\left(i\right)$

Step 2: Solving equation to get required number
From (i),
$x=\frac{11}{24}+\frac{3}{16}$
$x=\frac{11\times 2}{24\times 2}+\frac{3\times 3}{16\times 3}$
$[\because$ LCM of 16 and 24 = 48]
$x=\frac{22}{48}+\frac{9}{48}$
$=\frac{22+9}{48}$
$=\frac{31}{48}$
Hence, $\frac{31}{48}$ should be added to $-\frac{3}{16}$ to get $\frac{11}{24}$.