Question

joey walked east for 15 2/3 meaters from home. then he walked west for 21 3/4 meters. how far was joey from home? write answer an a mixed number only.

Answer 1

joey walked east for 15 2/3 meaters from home. then he walked west for 21 3/4 meters. how far was joey from home? write answer an a mixed number only.




- 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. Convert these fractions to a common denominator to make it easier to compute:
- The least common multiple of 3 and 4 is 12.

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

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

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

The negative sign indicates that Joey is west of his starting point.

4. Convert \( \frac{73}{12} \) to a mixed number:
- \(\frac{73}{12}\) can be calculated as:
- \(73\) divided by \(12\) is \(6\) with a remainder of \(1\).
- Therefore, \( \frac{73}{12} = 6 \frac{1}{12} \).

Joey is \( 6 \frac{1}{12} \) meters away from home, in the west direction. Thus, the answer is:

\[
\text{Joey is } 6 \frac{1}{12} \text{ meters from home.}
\]

answe it in a number correctly

Answer 2

To find out how far Joey is from home, we need to calculate his total movement to the east and west.

1. Convert the mixed numbers to improper fractions:
- For \( 15 \frac{2}{3} \):
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]

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

2. Convert these fractions to a common denominator to make it easier to compute:
- The least common multiple of 3 and 4 is 12.

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

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

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

The negative sign indicates that Joey is west of his starting point.

4. Convert \( \frac{73}{12} \) to a mixed number:
- \(\frac{73}{12}\) can be calculated as:
- \(73\) divided by \(12\) is \(6\) with a remainder of \(1\).
- Therefore, \( \frac{73}{12} = 6 \frac{1}{12} \).

Joey is \( 6 \frac{1}{12} \) meters away from home, in the west direction. Thus, the answer is:

\[
\text{Joey is } 6 \frac{1}{12} \text{ meters from home.}
\]

Answer 3

To find how far Joey is from home, we can follow these steps:

1. Joey walked east for \(15 \frac{2}{3}\) meters. To convert this to an improper fraction:
\[
15 \frac{2}{3} = \frac{15 \times 3 + 2}{3} = \frac{45 + 2}{3} = \frac{47}{3}
\]

2. Joey then walked west for \(21 \frac{3}{4}\) meters. Converting this to an improper fraction:
\[
21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4}
\]

3. Convert these fractions to a common denominator. The least common multiple of 3 and 4 is 12.

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

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

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

The negative sign indicates that Joey is west of his starting point.

5. Convert \(\frac{73}{12}\) to a mixed number:
- \(73\) divided by \(12\) is \(6\) with a remainder of \(1\).
- Therefore,
\[
\frac{73}{12} = 6 \frac{1}{12}
\]

Thus, the distance from home, expressed as a mixed number, is:

\[
\text{Joey is } 6 \frac{1}{12} \text{ meters from home.}
\]

So, if the format is just the mixed number, the answer is:

**6 \( \frac{1}{12} \)**