Question

$\frac{1}{4}$ of the students of a class likes to play football while $\frac{1}{3}$ likes to play tennis. What fraction of the students like to play both Football and Tennis?

• A. $\frac{7}{12}$
• B. $\frac{2}{3}$
• C. $\frac{2}{4}$

Answer 1

The correct option is A $\frac{7}{12}$

Fraction of students playing football $=\frac{1}{4}$

Fraction of students playing tennis $=\frac{1}{3}$

Fraction of students playing football and tennis $=\frac{1}{4}+\frac{1}{3}$

Make the denominator same for both the fraction.

Multiplying with 3 in the fraction $\frac{1}{4}$, we get:
$\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}$

Multiplying with 4 in the fraction $\frac{1}{3}$, we get:
$\frac{1}{3}=\frac{1\times 4}{3\times 4}=\frac{4}{12}$

Fraction of students playing football and tennis $=\frac{1}{4}+\frac{1}{3}$
$=\frac{3}{12}+\frac{4}{12}$

$=\frac{3+4}{12}$

$=\frac{7}{12}$

Hence, $\frac{7}{12}$ of students likes to play football and tennis.