Question

Last week, Andy spent 4 4/5 hours watching television. Ruth watched television for 1/2 as many hours as Andy did. How many hours did Ruth spend watching television?

Write your answer as a fraction or as a whole or mixed number.

hours

Answer 1

To find out how many hours Ruth spent watching television, we start with the amount of time Andy spent, which is \( 4 \frac{4}{5} \) hours.

First, we need to convert \( 4 \frac{4}{5} \) into an improper fraction:

1. Convert the whole number \( 4 \) into an improper fraction:
\[
4 = \frac{4 \times 5}{5} = \frac{20}{5}
\]
2. Add \( \frac{20}{5} \) to \( \frac{4}{5} \):
\[
4 \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5}
\]

Now we know that Andy watched \( \frac{24}{5} \) hours of television.

Ruth watched half as many hours as Andy did:
\[
\text{Ruth's hours} = \frac{1}{2} \times \frac{24}{5}
\]

Now we calculate this:
\[
\frac{1}{2} \times \frac{24}{5} = \frac{24 \times 1}{5 \times 2} = \frac{24}{10}
\]

Next, we simplify \( \frac{24}{10} \):
\[
\frac{24}{10} = \frac{12}{5}
\]

Now, we convert \( \frac{12}{5} \) into a mixed number:
\[
\frac{12}{5} = 2 \frac{2}{5}
\]

Thus, Ruth spent \( \boxed{2 \frac{2}{5}} \) hours watching television.