To find out how many miles farther it is from the school to the library than from the library to Town Hall, we first need to convert the mixed numbers into improper fractions.
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Convert the distance from the school to the library, which is \(3 \frac{1}{2}\) miles: \[ 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \text{ miles} \]
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Convert the distance from the library to Town Hall, which is \(1 \frac{1}{4}\) miles: \[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \text{ miles} \]
Now we can find the difference in distances.
- Subtract the distance from the library to Town Hall from the distance from the school to the library: \[ \frac{7}{2} - \frac{5}{4} \]
To perform this subtraction, we need a common denominator. The least common multiple of 2 and 4 is 4.
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Convert \(\frac{7}{2}\) to a fraction with a denominator of 4: \[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]
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Now we can proceed with the subtraction: \[ \frac{14}{4} - \frac{5}{4} = \frac{14 - 5}{4} = \frac{9}{4} \]
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Convert \(\frac{9}{4}\) back to a mixed number: \[ \frac{9}{4} = 2 \frac{1}{4} \text{ miles} \]
Thus, the distance from the school to the library is \(2 \frac{1}{4}\) miles farther than the distance from the library to Town Hall.
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