Question

Joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was Joey from home? Write your answer as a mixed number only.(1 point)
Joey was meters from home

Answer 1

To find out how far Joey is from home, we need to calculate the total distance he walked in each direction and determine his final position relative to home.

1. First, let's convert the mixed numbers into improper fractions.

For \( 15 \frac{2}{3} \):
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]

For \( 21 \frac{3}{4} \):
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]

2. Now, we convert the distances he walked east and west to have a common denominator so we can subtract them easily. The least common multiple of 3 and 4 is 12.

Convert \( \frac{47}{3} \) to a denominator of 12:
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]

Convert \( \frac{87}{4} \) to a denominator of 12:
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]

3. Now, subtract the distance walked west from the distance walked east:
\[
\frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12}
\]

The negative sign indicates that Joey walked more west than east. Thus, we take the absolute value:
\[
\left| \frac{-73}{12} \right| = \frac{73}{12}
\]

4. Now, convert \( \frac{73}{12} \) back to a mixed number:
- Divide 73 by 12.
- The whole number part is \( 6 \) (since \( 12 \times 6 = 72 \)).
- The remainder is \( 1 \) (since \( 73 - 72 = 1 \)).
- Thus, \( \frac{73}{12} = 6 \frac{1}{12} \).

So, Joey was \( 6 \frac{1}{12} \) meters from home.

Final answer:
Joey was \( 6 \frac{1}{12} \) meters from home.