Lin spent \( \frac{5}{6} \) hour on math homework and \( 1 \frac{3}{4} \) hours on science homework. How many hours in all did she spend on homework for both) subjects?

To find the total time Lin spent on both math and science homework, we'll add the time spent on each subject together. Here's a step-by-step breakdown: 1. **Convert Mixed Numbers to Improper Fractions (if necessary):** - **Math Homework:** \( \frac{5}{6} \) hour (already a simple fraction). - **Science Homework:** \( 1 \frac{3}{4} \) hours. Convert \( 1 \frac{3}{4} \) to an improper fraction: \[ 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4} \] 2. **Add the Two Fractions:** \[ \frac{5}{6} + \frac{7}{4} \] To add these fractions, they need a common denominator. The least common denominator (LCD) for 6 and 4 is 12. 3. **Convert Each Fraction to Have the Common Denominator:** - **Math Homework:** \[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \] - **Science Homework:** \[ \frac{7}{4} = \frac{7 \times 3}{4 \times 3} = \frac{21}{12} \] 4. **Add the Converted Fractions:** \[ \frac{10}{12} + \frac{21}{12} = \frac{31}{12} \] This improper fraction can be converted back to a mixed number: \[ \frac{31}{12} = 2 \frac{7}{12} \] 5. **Conclusion:** Lin spent a total of \( 2 \frac{7}{12} \) hours on homework for both math and science. **Answer:** Lin spent a total of \( 2 \frac{7}{12} \) hours on homework for both subjects.