11. Suzy spent \( 6 \frac{7}{8} \) days working on her English paper, \( 3 \frac{1}{6} \) days doing her science project, and \( 1 \frac{1}{2} \) days studying for her math test. How many more days did Suzy spend on her English paper and math test combined than on her science project?

To determine how many more days Suzy spent on her English paper and math test combined than on her science project, we'll follow these steps: 1. **Convert Mixed Numbers to Improper Fractions** 2. **Calculate the Total Days for English Paper and Math Test** 3. **Calculate the Days Spent on Science Project** 4. **Find the Difference** Let's go through each step in detail. --- ### 1. Convert Mixed Numbers to Improper Fractions First, convert all mixed numbers to improper fractions for easier calculations. - **English Paper:** \(6 \frac{7}{8}\) \[ 6 \frac{7}{8} = \frac{6 \times 8 + 7}{8} = \frac{48 + 7}{8} = \frac{55}{8} \] - **Science Project:** \(3 \frac{1}{6}\) \[ 3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6} \] - **Math Test:** \(1 \frac{1}{2}\) \[ 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \] --- ### 2. Calculate the Total Days for English Paper and Math Test Add the days spent on the English paper and the math test: \[ \frac{55}{8} + \frac{3}{2} \] To add these fractions, they need a common denominator. The least common denominator (LCD) of 8 and 2 is 8. Convert \(\frac{3}{2}\) to have a denominator of 8: \[ \frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8} \] Now, add the fractions: \[ \frac{55}{8} + \frac{12}{8} = \frac{55 + 12}{8} = \frac{67}{8} \] Convert \(\frac{67}{8}\) back to a mixed number: \[ \frac{67}{8} = 8 \frac{3}{8} \text{ days} \] --- ### 3. Calculate the Days Spent on Science Project Suzy spent: \[ \frac{19}{6} \text{ days on her science project} \] --- ### 4. Find the Difference Subtract the days spent on the science project from the combined days for the English paper and math test: \[ \frac{67}{8} - \frac{19}{6} \] Find a common denominator for 8 and 6, which is 24. Convert both fractions: \[ \frac{67}{8} = \frac{67 \times 3}{8 \times 3} = \frac{201}{24} \] \[ \frac{19}{6} = \frac{19 \times 4}{6 \times 4} = \frac{76}{24} \] Subtract the fractions: \[ \frac{201}{24} - \frac{76}{24} = \frac{125}{24} \] Convert \(\frac{125}{24}\) to a mixed number: \[ \frac{125}{24} = 5 \frac{5}{24} \text{ days} \] --- ### **Conclusion** Suzy spent **\(5 \frac{5}{24}\) days** more on her English paper and math test combined than on her science project.