Question

I spent four and 5/12th hours reading in the last week I spent one and 3/4 hours watching TV. How much longer did I read?

Answer 1

To find out how much longer you read compared to watching TV, we need to subtract the time spent watching TV from the time spent reading.

You spent:
- Reading: \( 4 \frac{5}{12} \) hours
- Watching TV: \( 1 \frac{3}{4} \) hours

First, convert both mixed numbers into improper fractions.

1. Convert \( 4 \frac{5}{12} \):
\[
4 \frac{5}{12} = \frac{4 \times 12 + 5}{12} = \frac{48 + 5}{12} = \frac{53}{12}
\]

2. Convert \( 1 \frac{3}{4} \):
\[
1 \frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\]

Next, we need to find a common denominator to subtract these fractions. The least common multiple of 12 and 4 is 12.

Now, convert \( \frac{7}{4} \) to have a denominator of 12:
\[
\frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12}
\]

Now we can subtract:
\[
\frac{53}{12} - \frac{21}{12} = \frac{53 - 21}{12} = \frac{32}{12}
\]

Now simplify \( \frac{32}{12} \):
\[
\frac{32}{12} = \frac{8}{3}
\]

Next, convert \( \frac{8}{3} \) back to a mixed number:
\[
\frac{8}{3} = 2 \frac{2}{3}
\]

Therefore, you read for \( 2 \frac{2}{3} \) hours longer than you watched TV.