Question

Paul is 509/8 inches tall. Luke is 123/2 inches tall. How much taller is Paul than Luke?
1 1/2 inches
17/8 inches
3 1/2 inches
5 inches

Answer 1

To find out how much taller Paul is than Luke, we need to subtract Luke's height from Paul's height.

First, we convert both heights to improper fractions:

- Paul's height: \( 509/8 \) inches
- Luke's height: \( 123/2 \) inches

To subtract these, we need a common denominator. The denominator for \( 123/2 \) needs to be converted to match \( 8 \) (Paul's denominator). We can do this by multiplying the numerator and the denominator of \( 123/2 \) by \( 4 \):

\[
\frac{123}{2} = \frac{123 \times 4}{2 \times 4} = \frac{492}{8}
\]

Now we can subtract Luke's height from Paul's height:

\[
\text{Difference} = \frac{509}{8} - \frac{492}{8} = \frac{509 - 492}{8} = \frac{17}{8}
\]

So, Paul is \( \frac{17}{8} \) inches taller than Luke.

To convert \( \frac{17}{8} \) into a mixed number, we divide \( 17 \) by \( 8 \):

\[
17 \div 8 = 2 \quad \text{(with a remainder of } 1\text{)}
\]

Thus:

\[
\frac{17}{8} = 2 \frac{1}{8}
\]

However, since we are looking for the height difference directly given in the options, we find that:

\(\frac{17}{8}\) is indeed one of the provided options.

Therefore, the answer is \( \frac{17}{8} \) inches.