Question

A runner ran 2 thirds
mile in the morning and 3 fourths
mile in the evening. How far did the runner run in total?(1 point)
Responses

1512
1 and 5 over 12

1712
1 and 7 over 12

134
1 and 3 fourths

1112

Answer 1

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

First, we need to find a common denominator for \( \frac{2}{3} \) and \( \frac{3}{4} \). The least common multiple of 3 and 4 is 12.

Now we convert each fraction:

1. \( \frac{2}{3} \) can be converted to twelfths:
\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]

2. \( \frac{3}{4} \) can be converted to twelfths:
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

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

Next, we can convert \( \frac{17}{12} \) to a mixed number. It can be expressed as:
\[
17 \div 12 = 1 \quad \text{(which is the whole number part)}
\]
With a remainder of:
\[
17 - 12 = 5 \quad \text{(which is the numerator of the fractional part)}
\]
So, \( \frac{17}{12} = 1 \frac{5}{12} \).

Therefore, the total distance the runner ran is:
**1 and 5 over 12**.

So the correct response is:
**1 and 5 over 12**.