Question

Joey walked east for 15 2/3 meters from home then he walked west for 21 3/4 how far away joey is from home

Answer 1

To determine how far away Joey is from home, we need to calculate the total distance he walked in each direction and then find the net distance from home.

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

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

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

2. **Calculate the total distance Joey walked:**
- Joey walked 15 2/3 meters east: \( \frac{47}{3} \) meters.
- Joey walked 21 3/4 meters west: \( \frac{87}{4} \) meters.

3. **To find his net distance from home, subtract the distance east from the distance west:**
\[
\text{Net distance} = \text{Distance west} - \text{Distance east} = \frac{87}{4} - \frac{47}{3}
\]

4. **Find a common denominator:**
- The least common multiple of 4 and 3 is 12.

- Convert \( \frac{87}{4} \) to twelve:
\[
\frac{87}{4} \times \frac{3}{3} = \frac{261}{12}
\]

- Convert \( \frac{47}{3} \) to twelve:
\[
\frac{47}{3} \times \frac{4}{4} = \frac{188}{12}
\]

5. **Now combine the fractions:**
\[
\text{Net distance} = \frac{261}{12} - \frac{188}{12} = \frac{261 - 188}{12} = \frac{73}{12}
\]

6. **Convert this back to a mixed number:**
- \( \frac{73}{12} \) can be converted as follows:
- 73 divided by 12 is 6 with a remainder of 1.
- Thus, \( \frac{73}{12} = 6 \frac{1}{12} \).

Therefore, Joey is \( 6 \frac{1}{12} \) meters away from home, to the west.