Question

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

Answer 1

To find out how far Joey is from home after walking east and then west, we first need to convert the mixed numbers into improper fractions for easier calculation.

1. Convert 15 2/3 to an improper fraction:
\[
15 2/3 = 15 + \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]

2. Convert 21 3/4 to an improper fraction:
\[
21 3/4 = 21 + \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]

3. Joey walked east, which is positive, and then west, which is negative:
- The total distance Joey is from home can be calculated as:
\[
\text{Distance from home} = \left(\text{Distance East}\right) - \left(\text{Distance West}\right)
\]
This translates to:
\[
\text{Distance from home} = \frac{47}{3} - \frac{87}{4}
\]

4. To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.

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

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

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

Since distance cannot be negative, we take the absolute value:
\[
\text{Distance from home} = \frac{73}{12}
\]

6. Convert \(\frac{73}{12}\) to a mixed number:
- Divide 73 by 12:
\[
73 \div 12 = 6 \quad \text{(whole number part)}
\]
- The remainder is:
\[
73 - (12 \times 6) = 73 - 72 = 1
\]

Thus, we can write:
\[
\frac{73}{12} = 6 \frac{1}{12}
\]

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