During a physical education class, a student ran \frac{1}{4} of a mile and walked \frac{3}… — ACT

During a physical education class, a student ran $\frac{1}{4}$ of a mile and walked $\frac{3}{5}$ of a mile. What total distance, in miles, did the student cover by running and walking?

A
$\frac{4}{9}$
B
$\frac{13}{20}$
C
$\frac{23}{40}$
$\frac{17}{20}$ Answer
E
$\frac{7}{10}$

Answer

The correct answer is

\frac{17}{20}

miles, which represents the sum of the distances covered by running and walking.

The correct answer is found by finding a common denominator for the two fractions representing the distances. The least common multiple of

4

and

5

20

. Converting the fractions gives

\frac{5}{20}

and

\frac{12}{20}

. Adding these values yields a total of

\frac{17}{20}

miles.

Step-by-Step Solution

Set up the addition expression for the two distances.

\frac{1}{4} + \frac{3}{5}

To find the total distance, the distance run and the distance walked must be added together.

Find the least common denominator (LCD) for the fractions.

The LCD for

4

and

5

20

Fractions can only be added when they share a common denominator.

Convert each fraction to an equivalent fraction with the denominator of

20

\frac{1 \times 5}{4 \times 5} = \frac{5}{20}

and

\frac{3 \times 4}{5 \times 4} = \frac{12}{20}

This scales the fractions correctly so they can be combined.

Add the numerators together while keeping the denominator the same.

\frac{5 + 12}{20} = \frac{17}{20}

Adding the numerators of fractions with like denominators gives the total fractional quantity.

Key Concept

Adding fractions with unlike denominators by finding a common denominator.

Alternative Method

Convert the fractions to decimals before adding.

\frac{1}{4}

is equivalent to

0.25

, and

\frac{3}{5}

is equivalent to

0.60

. Adding these decimals yields

0.25 + 0.60 = 0.85

. Converting the decimal back to a fraction results in

\frac{85}{100} = \frac{17}{20}

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Topics

More questions from this topic