Higher Order Thinking Kayla walked $$ 1 \frac{1}{4} $$ miles from home to school. Then, she walked $$ 1 \frac{3}{4} $$ miles from school to the store and $$ 2 \frac{1}{2} $$ miles from the store to the library. How many miles did Kayla walk from school to the library?

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To find out how many miles Kayla walked from school to the library, we need to add the distances she walked from home to school and from school to the store, and then subtract that total from the distance she walked from home to the library.

1. **Convert mixed numbers to improper fractions:**
   - For $$ 1 \frac{1}{4} $$:
     $$
     1 \frac{1}{4} = \frac{5}{4}
     $$
   - For $$ 1 \frac{3}{4} $$:
     $$
     1 \frac{3}{4} = \frac{7}{4}
     $$
   - For $$ 2 \frac{1}{2} $$:
     $$
     2 \frac{1}{2} = \frac{5}{2}
     $$

2. **Calculate the total distance from home to the library:**
   - The total distance from home to the library is the sum of the distances from home to school, school to store, and store to library:
   $$
   \text{Total distance} = \frac{5}{4} + \frac{7}{4} + \frac{5}{2}
   $$

3. **Convert $$ \frac{5}{2} $$ to have a common denominator with the other fractions:**
   - The common denominator for $$ 4 $$ and $$ 2 $$ is $$ 4 $$:
   $$
   \frac{5}{2} = \frac{10}{4}
   $$

4. **Now add the fractions:**
   $$
   \text{Total distance} = \frac{5}{4} + \frac{7}{4} + \frac{10}{4} = \frac{5 + 7 + 10}{4} = \frac{22}{4} = \frac{11}{2}
   $$

5. **Now, we need to find the distance from school to library:**
   - The distance from school to library is the total distance from home to library minus the distance from home to school and from school to store:
   $$
   \text{Distance from school to library} = \text{Total distance} - \text{Distance from home to school} - \text{Distance from school to store}
   $$
   $$
   = \frac{11}{2} - \frac{5}{4} - \frac{7}{4}
   $$

6. **Combine the distances from home to school and school to store:**
   $$
   \frac{5}{4} + \frac{7}{4} = \frac{12}{4} = 3
   $$

7. **Now subtract this from the total distance:**
   $$
   \text{Distance from school to library} = \frac{11}{2} - 3
   $$
   - Convert $$ 3 $$ to a fraction with a denominator of $$ 2 $$:
   $$
   3 = \frac{6}{2}
   $$
   $$
   = \frac{11}{2} - \frac{6}{2} = \frac{5}{2}
   $$

Thus, the distance Kayla walked from school to the library is $$ 2 \frac{1}{2} $$ miles.
Kayla walked $$ 2 \frac{1}{2} $$ miles from school to the library.

Higher Order Thinking Kayla walked \( 1 \frac{1}{4} \) miles from home to school. Then, she walked \( 1 \frac{3}{4} \) miles from school to the store and \( 2 \frac{1}{2} \) miles from the store to the library. How many miles did Kayla walk from school to the library?

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