Francis ran 2 1/5 miles in 7/12 of an hour. How many miles can Francis run in one hour
A. 3 27/35
B. 18 6/7
C. 35/132
D. 3 16/35
To find how many miles Francis can run in one hour, we divide the distance he ran by the fraction of an hour he ran for: \[
\begin{array}{c|c}
\text{Miles} & \text{Hours} \\
\hline
2 \frac{1}{5} & \frac{7}{12}
\end{array}
\] When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction: \[
2 \frac{1}{5} \div \frac{7}{12} = 2 \frac{1}{5} \cdot \frac{12}{7}
\] Simplifying the fraction gives \[
2 \frac{1}{5} \cdot \frac{12}{7} = \frac{11}{5} \cdot \frac{12}{7} = \frac{11 \cdot 12}{5 \cdot 7} = \frac{132}{35}
\] This fraction simplifies to 3 $\frac{17}{35}$. Answer: $\boxed{\textbf{(A) } 3 \frac{27}{35}}$.
To find out how many miles Francis can run in one hour, we need to divide the distance he ran by the time it took.
The distance Francis ran is 2 1/5 miles, which can be written as a mixed number: 2 + 1/5 = 11/5 miles.
The time Francis took to run is 7/12 of an hour.
To divide 11/5 miles by 7/12 hours, we need to multiply the distance by the reciprocal of the time:
(11/5) * (12/7) = 132/35 = 3 12/35
Therefore, Francis can run 3 12/35 miles in one hour.
The answer is not listed exactly like this, but we can convert it into one of the given answer choices.
3 12/35 = 3 + 12/35 = 105/35 + 12/35 = 117/35
So, Francis can run 117/35 miles in one hour.
Therefore, the correct answer is D. 3 16/35.
To find out how many miles Francis can run in one hour, we need to divide the distance Francis ran by the time it took.
First, let's convert the mixed number "2 1/5" to an improper fraction. The whole number 2 can be written as 2/1. So, 2 1/5 can be written as (2/1) + (1/5) = 11/5.
Next, we divide the distance (11/5 miles) by the time (7/12 hours). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, (11/5) ÷ (7/12) = (11/5) * (12/7).
To multiply fractions, we simply multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
(11/5) * (12/7) = (11 * 12) / (5 * 7) = 132/35 = 3 27/35.
Therefore, Francis can run 3 27/35 miles in one hour.
So, the correct option is A. 3 27/35.