To find out how much closer James is to the post office than to the library, we need to compare the distances he lives from each location.
James lives:
- 4 miles from the library
- \(2 \frac{5}{6}\) miles from the post office
First, we convert \(2 \frac{5}{6}\) into an improper fraction:
\[ 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \text{ miles} \]
Now, we need to find the difference in distance between the library and the post office:
\[ \text{Distance to the library} - \text{Distance to the post office} = 4 - \frac{17}{6} \]
To perform this subtraction, we first convert 4 into a fraction with a denominator of 6:
\[ 4 = \frac{4 \times 6}{6} = \frac{24}{6} \]
Now we can subtract:
\[ \frac{24}{6} - \frac{17}{6} = \frac{24 - 17}{6} = \frac{7}{6} \]
Thus, James is \(\frac{7}{6}\) miles closer to the post office than to the library. This can also be expressed as:
\[ \frac{7}{6} \text{ miles} \approx 1 \frac{1}{6} \text{ miles} \]
Therefore, James is \(\frac{7}{6}\) miles (or approximately 1.17 miles) closer to the post office than to the library.
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