Jackie studies for \( 3 \frac{1}{2} \) hours, runs for \( 2 \frac{1}{4} \) hours and washed the dishes for \( \frac{1}{2} \) an hour. The total time she spent on these tasks is:

To find the total time Jackie spent on her tasks, we need to add the three time durations together. 1. Convert the mixed numbers to improper fractions: - For \( 3 \frac{1}{2} \): \[ 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \] - For \( 2 \frac{1}{4} \): \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \] - For \( \frac{1}{2} \), it is already in proper form. 2. Now, we need to add these fractions together: \[ \text{Total time} = \frac{7}{2} + \frac{9}{4} + \frac{1}{2} \] 3. To add these fractions, we need a common denominator. The least common multiple of 2 and 4 is 4. We will convert all fractions to have a denominator of 4: - Convert \( \frac{7}{2} \): \[ \frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4} \] - Convert \( \frac{1}{2} \): \[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] 4. Now we can add the fractions: \[ \text{Total time} = \frac{14}{4} + \frac{9}{4} + \frac{2}{4} = \frac{14 + 9 + 2}{4} = \frac{25}{4} \] 5. Convert \( \frac{25}{4} \) back to a mixed number: \[ \frac{25}{4} = 6 \frac{1}{4} \] Thus, the total time Jackie spent on these tasks is \( 6 \frac{1}{4} \) hours.