A runner completes \frac{2}{5} of a mile as a warm-up and then runs another \frac{1}{3} of… — Armed Services Vocational Aptitude Battery (ASVAB)

A runner completes $\frac{2}{5}$ of a mile as a warm-up and then runs another $\frac{1}{3}$ of a mile. What is the total distance, in miles, the runner covered?

$\frac{11}{15}$ Answer
B
$\frac{3}{8}$
C
$\frac{2}{15}$
D
$\frac{1}{5}$

Answer

\frac{11}{15}

To find the total distance, the fractions must be added. Since they have unlike denominators (5 and 3), the lowest common denominator (15) must be found. Converting the fractions yields

\frac{6}{15}

and

\frac{5}{15}

. Adding the numerators provides the final total of

\frac{11}{15}

Step-by-Step Solution

Identify the operation needed.

Addition:

\frac{2}{5} + \frac{1}{3}

The question asks for the total distance covered, requiring the sum of the two distinct parts of the run.

Find a common denominator for 5 and 3.

The lowest common multiple of 5 and 3 is 15.

Fractions must have a common denominator before they can be added together.

Convert both fractions to have a denominator of 15.

\frac{2}{5} = \frac{6}{15}

and

\frac{1}{3} = \frac{5}{15}

To maintain the same value, multiply the numerator and denominator of the first fraction by 3, and the second fraction by 5.

Add the numerators and keep the common denominator.

\frac{6}{15} + \frac{5}{15} = \frac{11}{15}

Once denominators are the same, only the numerators are added to find the total.

Key Concept

Adding Fractions with Unlike Denominators

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