To find out how much farther Terrell and his best friend have to walk to school after stopping at his best friend's house, we need to calculate the distance from the best friend's house to the school.
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Convert the distances into improper fractions:
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Terrell's distance to his best friend's house: \[ 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \text{ blocks} \]
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Terrell's distance to school: \[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \text{ blocks} \]
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Now, we need to find the distance from the best friend's house to the school. This can be done by subtracting the distance to the best friend's house from the distance to the school:
\( \text{Distance from best friend's house to school} = \text{Distance to school} - \text{Distance to best friend's house} \)
First, we need a common denominator to subtract these fractions. The least common multiple of 6 and 3 is 6.
- Convert \( \frac{13}{3} \) to have a denominator of 6: \[ \frac{13}{3} = \frac{13 \times 2}{3 \times 2} = \frac{26}{6} \]
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Now, perform the subtraction: \[ \frac{26}{6} - \frac{17}{6} = \frac{26 - 17}{6} = \frac{9}{6} \]
- Simplifying \( \frac{9}{6} \): \[ \frac{9}{6} = \frac{3}{2} = 1 \frac{1}{2} \text{ blocks} \]
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Conclusion: After stopping at his best friend's house, Terrell and his friend have to walk \( 1 \frac{1}{2} \) blocks farther to reach school.