In a local park, \frac{2}{5} of the trees are maple trees and \frac{1}{3} of the trees are… — ACT

In a local park, $\frac{2}{5}$ of the trees are maple trees and $\frac{1}{3}$ of the trees are oak trees. The remaining trees are pine trees. What fraction of the trees in the park are pine trees?

A
$\frac{3}{8}$
B
$\frac{5}{8}$
$\frac{4}{15}$ Answer
D
$\frac{11}{15}$
E
$\frac{14}{15}$

Answer

\frac{4}{15}

To find the fraction of pine trees, first calculate the total fraction occupied by maple and oak trees. Finding a common denominator of

15

for

\frac{2}{5}

and

\frac{1}{3}

gives

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

. Subtracting this combined fraction from

1

(represented as

\frac{15}{15}

) yields the remaining fraction of pine trees, which is

\frac{4}{15}

Step-by-Step Solution

Find the sum of the fractions representing maple and oak trees.

\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}

Before finding the remaining fraction, we need to know the combined fraction of the park occupied by maple and oak trees.

Subtract the combined fraction of maple and oak trees from the whole.

1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}

Since the remaining trees are pine trees, subtracting the combined fraction of other trees from the total of

1

yields the fraction of pine trees.

Key Concept

To find a remaining fractional part of a whole, first sum the known fractional parts using a common denominator, and then subtract this sum from 1.

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