To find out how far Joey is from home after walking, we need to perform the operations step by step.
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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: \[ 21 \frac{3}{4} = \frac{21 \times 4 + 3}{4} = \frac{84 + 3}{4} = \frac{87}{4} \]
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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: \[ \text{Distance from home} = \frac{47}{3} - \frac{87}{4} \]
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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: \[ \frac{87}{4} = \frac{87 \times 3}{4 \times 3} = \frac{261}{12} \]
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Now subtract these two fractions: \[ \frac{188}{12} - \frac{261}{12} = \frac{188 - 261}{12} = \frac{-73}{12} \]
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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.
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