Question

Peter bought various colored shirts from a shop. He gave $\frac{1}{2}$ the number of the green shirts to his friend and $\frac{1}{2}$ of his black shirts to his brother. If the pie chart represents all the shirts he bought, what fraction of the total shirts are left?

• A. $\frac{10}{22}$
• B. $\frac{12}{24}$
• C. $\frac{16}{20}$
• D. $\frac{18}{10}$

Answer 1

The correct option is C $\frac{16}{20}$

Total number of divisions representing all shirts in the pie chart $=20$

Number of divisions representing green shirts $=6$

Fraction representing green shirts $=\frac{6}{20}$

Fraction of the green shirts he gave to his friend $=\frac{1}{2}$

Number of green shirts given to his friend
$=\frac{1}{2}$ of fractions representing the total number of green shirts

$=\frac{1}{2}\times \frac{6}{20}=\frac{6}{40}=\frac{3}{20}$

Number of divisions representing black shirts $=2$

Fraction representing black shirts$=\frac{2}{20}$

Fraction of the black shirts he gave to his brother $=\frac{1}{2}$

Number of black shirts he gave to his brother

$=\frac{1}{2}$ of fractions representing the total number of black shirts

$=\frac{1}{2}\times \frac{2}{20}=\frac{2}{40}=\frac{1}{20}$

Total number of shirts he gave altogether $=\frac{3}{2}+\frac{1}{20}=\frac{4}{20}$

Therefore, number of shirts left = total
− number of shirts Peter gave altogether

$=\frac{20}{20}-\frac{4}{20}=\frac{16}{20}$

Fraction of shirts available $=\frac{16}{20}$