Question

A man spends $ \frac{2}{5} $ of his salary on rent, $ \frac{1}{4} $ on food, and $ \frac{1}{10} $ on transportation. What fraction of his salary is left?

• A. \( \frac{11}{20} \)
• B. \( \frac{1}{4} \)
• C. \( \frac{9}{20} \)
• D. \( \frac{13}{20} \)

Hint:

Always convert all fractions to have a common denominator when adding or subtracting. Double-check for any errors in options if your math is consistent but no choice matches.

Answer 1

The Correct Option is B

To determine the remaining fraction of salary after expenses, we will first calculate the total fraction spent and then subtract this from the whole salary (represented as 1).

The fractions of salary spent on rent, food, and transportation are \( \frac{2}{5} \), \( \frac{1}{4} \), and \( \frac{1}{10} \), respectively. The sum of these fractions represents the total expenditure:

\[ \frac{2}{5} + \frac{1}{4} + \frac{1}{10} \]

To sum these fractions, a common denominator is required. The least common multiple of 5, 4, and 10 is 20.

Each fraction is converted to an equivalent fraction with a denominator of 20:

• \( \frac{2}{5} \) becomes \( \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \)
• \( \frac{1}{4} \) becomes \( \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \)
• \( \frac{1}{10} \) becomes \( \frac{1 \times 2}{10 \times 2} = \frac{2}{20} \)

The sum of these equivalent fractions is:

\[ \frac{8}{20} + \frac{5}{20} + \frac{2}{20} = \frac{15}{20} \]

This \( \frac{15}{20} \) represents the total fraction of the salary spent. The fraction of the salary remaining is calculated by subtracting the total spent from the whole:

\[ 1 - \frac{15}{20} = \frac{20}{20} - \frac{15}{20} = \frac{5}{20} \]

To simplify \( \frac{5}{20} \), we divide both the numerator and the denominator by their greatest common divisor, which is 5:

\[ \frac{5 \div 5}{20 \div 5} = \frac{1}{4} \]

Therefore, the fraction of the salary that remains is \( \frac{1}{4} \).