Question

Shubham painted $\frac{2}{3}$ of the wall space in his room. His sister Madhavi helped and painted $\frac{1}{4}$ of the wall space. How much fraction of the wall did they paint together?

• A. 1
• B. $\frac{10}{12}$
• C. $\frac{1}{2}$
• D. $\frac{11}{12}$

Answer 1

The correct option is D $\frac{11}{12}$

As per the question, fraction of wall painted by Shubham = $\frac{2}{3}$ and fraction of wall painted by Madhavi = $\frac{1}{4}$
Fraction of wall painted by both of them = $\frac{2}{3}+\frac{1}{4}$

$\frac{2}{3}$ and $\frac{1}{4}$ are unlike fractions, so let us convert them into like fractions and then add the fractions.
LCM of denominators of $\frac{2}{3}+\frac{1}{4}$ , i.e., LCM of 3 and 4 is 12.
So, $\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$ and $\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}$

$\therefore$ Fraction of wall painted by both of them $=\frac{8}{12}+\frac{3}{12}=\frac{8+3}{12}=\frac{11}{12}$
Therefore, they both painted $\frac{11}{12}$ of the whole wall.