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 to improper fractions.
-
The distance from the school to the library is \(3 \frac{1}{2}\) miles. This can be converted to an improper fraction: \[ 3 \frac{1}{2} = \frac{7}{2} \text{ miles} \]
-
The distance from the library to town hall is \(1 \frac{1}{4}\) miles. This can be converted to an improper fraction: \[ 1 \frac{1}{4} = \frac{5}{4} \text{ miles} \]
Next, we calculate how much farther the distance from the school to the library is compared to the distance from the library to town hall by subtracting the two distances:
\[ \text{Difference} = \text{Distance from school to library} - \text{Distance from library to town hall} \] \[ = \frac{7}{2} - \frac{5}{4} \]
To perform this subtraction, we first need a common denominator. The least common denominator of 2 and 4 is 4. We can convert \(\frac{7}{2}\) to have a denominator of 4:
\[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \]
Now we can perform the subtraction:
\[ \frac{14}{4} - \frac{5}{4} = \frac{14 - 5}{4} = \frac{9}{4} \]
Finally, we can 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.
1 answer