Question

A runner ran 2/3
mile in the morning and 3/4
mile in the evening. How far did the runner run in total?

Answer 1

To find the total distance the runner ran, you need to add the two distances together: \(\frac{2}{3}\) mile and \(\frac{3}{4}\) mile.

First, find a common denominator for the fractions. The denominators are 3 and 4. The least common denominator (LCD) is 12.

Now, convert each fraction:

1. Convert \(\frac{2}{3}\) to a fraction with a denominator of 12:
\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]

2. Convert \(\frac{3}{4}\) to a fraction with a denominator of 12:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

Now, add the two fractions:
\[
\frac{8}{12} + \frac{9}{12} = \frac{8 + 9}{12} = \frac{17}{12}
\]

The total distance the runner ran is \(\frac{17}{12}\) miles.

To express this in a mixed number:
\[
\frac{17}{12} = 1 \text{ mile } \frac{5}{12} \text{ mile}
\]

Therefore, the runner ran a total of \(1 \frac{5}{12}\) miles.