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 homework for both subjects, we first need to convert the mixed number \( 1 \frac{3}{4} \) hours into an improper fraction. \[ 1 \frac{3}{4} = \frac{4 \cdot 1 + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \] Now, we can add \( \frac{5}{6} \) and \( \frac{7}{4} \). To add these fractions, we need a common denominator. The least common multiple of \( 6 \) and \( 4 \) is \( 12 \). Convert both fractions: \[ \frac{5}{6} = \frac{5 \cdot 2}{6 \cdot 2} = \frac{10}{12} \] \[ \frac{7}{4} = \frac{7 \cdot 3}{4 \cdot 3} = \frac{21}{12} \] Now we can add: \[ \frac{10}{12} + \frac{21}{12} = \frac{10 + 21}{12} = \frac{31}{12} \] Converting this improper fraction back into a mixed number: \[ \frac{31}{12} = 2 \frac{7}{12} \] Thus, Lin spent a total of \( 2 \frac{7}{12} \) hours on homework for both subjects.