Question

In a school, the fraction of students that chose chess as their favorite game is $\frac{2}{5}$ and the fraction of students that chose volleyball is $\frac{1}{8}$. If there are $1200$ students in the school, find the total number of students who chose chess and volleyball.

• A. 650
• B. 630
• C. 600

Answer 1

The correct option is B 630

Fraction of students that chose chess $=\frac{2}{5}$
Fraction of students that chose volleyball $=\frac{1}{8}$
Sum of the fraction of students that chose chess and volleyball $=\frac{2}{5}+\frac{1}{8}$

We need to make the denominators the same for both fractions.
Multiplying the fraction $\frac{2}{5}$ by $8$, we get:
$\frac{2}{5}=\frac{2\times 8}{5\times 8}=\frac{16}{40}$
$\frac{1}{8}$ by $5$, we get:
$\frac{1}{8}=\frac{1\times 5}{8\times 5}=\frac{5}{40}$
Sum of the fraction of students that chose chess and volleyball $=\frac{16}{40}+\frac{5}{40}=\frac{21}{40}$
Hence, total fraction of students that chose chess and volleyball $=\frac{21}{40}$
Total number of students $=1200$

Number of students that chose chess and volleyball = sum of the fraction of students that chose chess and volleyball × total number of students $=\frac{21}{40}\times 1200$
$=21\times 30=630$