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 after walking, we need to perform the operations step by step.

1. First, let's convert the mixed numbers to improper fractions.
- For 15 2/3:
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]
- For 21 3/4:
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]

2. Next, find out how far Joey traveled in total:
- Joey walked east (positive direction) for \( \frac{47}{3} \) meters and then walked west (negative direction) for \( \frac{87}{4} \) meters. Thus, the total distance he is from home (east - west) is:
\[
\text{Distance from home} = \frac{47}{3} - \frac{87}{4}
\]

3. To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.
- Convert \( \frac{47}{3} \) to have a denominator of 12:
\[
\frac{47}{3} = \frac{47 \times 4}{3 \times 4} = \frac{188}{12}
\]
- Convert \( \frac{87}{4} \) to have a denominator of 12:
\[
\frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12}
\]

4. Now subtract these two fractions:
\[
\frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12}
\]

5. The negative sign indicates that Joey is 73/12 meters west of home. To express this as a mixed number:
- Divide 73 by 12:
\[
73 \div 12 = 6 \quad \text{remainder} \quad 1
\]
- This can be expressed as:
\[
6 \frac{1}{12}
\]

Thus, Joey is \( 6 \frac{1}{12} \) meters from home.

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