Question

It is given that the sum of three rational numbers is $\frac{2}{3}$. Among the three numbers, two numbers are $\frac{5}{6}$ and $\frac{1}{4}$, find the third one.

• A. $\frac{-5}{6}$
• B. $\frac{-5}{12}$
• C. $\frac{-7}{12}$
• D. $\frac{-1}{3}$

Answer 1

The correct option is B $\frac{-5}{12}$

$\text{Let the unknown number be}x.$

$\frac{2}{3}=\frac{5}{6}+\frac{1}{4}+x\Rightarrow x=\frac{2}{3}-\frac{5}{6}-\frac{1}{4}$
Since, denominators of all three rational numbers are different, we need to take the LCM of 3, 6 and 4.
LCM of 3, 6 and 4 = 12
$\text{Taking LCM as 12, we get,}\Rightarrow x=\frac{8}{12}-\frac{10}{12}-\frac{3}{12}\Rightarrow x=\frac{8-10-3}{12}\Rightarrow x=\frac{-5}{12}$