Question

$\frac{2}{5}$ of the students of a class likes to play chess while $\frac{1}{8}$ likes to play Volleyball. What fraction of the students like to play both volleyball and chess?

• A. $\frac{21}{40}$
• B. $\frac{40}{21}$
• C. $\frac{3}{5}$
• D. $\frac{3}{8}$

Answer 1

The correct option is A $\frac{21}{40}$

Fraction of students playing chess $=\frac{2}{5}$

Fraction of students playing volleyball $=\frac{1}{8}$

Fraction of students playing fchess and volleyball $=\frac{2}{5}+\frac{1}{8}$

Make the denominator same for both the fraction.

Multiplying with 8 in the fraction $\frac{2}{5}$, we get:
$\frac{2}{5}=\frac{2\times 8}{5\times 8}=\frac{16}{40}$

$(\because \text{multiplying with the denominator 8 of the second fraction})$

Multiplying with 5 in the fraction $\frac{1}{8}$, we get:
$\frac{1}{8}=\frac{1\times 5}{8\times 5}=\frac{5}{40}$

$(\because \text{multiplying with the denominator 5 of the first fraction})$

Fraction of students playing chess and volleyball $=\frac{2}{5}+\frac{1}{8}$
$=\frac{16}{40}+\frac{5}{40}$

$=\frac{16+5}{40}$

$=\frac{21}{40}$

Hence, $\frac{21}{40}$ of students likes to play chess and volleyball.