Question

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 determine how far Joey is from home after walking east and then west, we can set up the problem as follows:

1. **Convert mixed numbers to improper fractions:**

- **15 2/3 meters:**
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]

- **21 3/4 meters:**
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]

2. **Convert both fractions to a common denominator.**

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. **Calculate Joey's total distance walked from home.**

Since he first walked east and then west, we subtract the two distances:
\[
\text{Distance from home} = \text{East distance} - \text{West distance}
\]
\[
= \frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12}
\]

The negative value indicates that Joey walked 73/12 meters to the west past his starting position (home).

4. **Convert \(\frac{73}{12}\) back to a mixed number:**

Divide 73 by 12:
\[
73 \div 12 = 6 \quad \text{(whole number)}
\]
\[
73 - (12 \times 6) = 73 - 72 = 1 \quad \text{(remainder)}
\]
Thus,
\[
\frac{73}{12} = 6 \frac{1}{12}
\]

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

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