Samantha spent \( 1 \frac{1}{2} \) hours, \( 3 \frac{3}{4} \) hours, and \( 3 \frac{3}{8} \) hours, respectively, in the last three days, studying for an exam. How much time did she spend studying, over the last three days?

Let's convert each mixed number to an improper fraction first for easier addition. 1. \( 1 \frac{1}{2} = \frac{3}{2} \) 2. \( 3 \frac{3}{4} = \frac{15}{4} \) 3. \( 3 \frac{3}{8} = \frac{27}{8} \) Now we need to add these fractions. To do this, we'll find a common denominator, which in this case is 8. Rewriting each fraction with 8 as the denominator: - \( \frac{3}{2} = \frac{3 \times 4}{2 \times 4} = \frac{12}{8} \) - \( \frac{15}{4} = \frac{15 \times 2}{4 \times 2} = \frac{30}{8} \) - \( \frac{27}{8} = \frac{27}{8} \) Now, add these fractions together: \[ \frac{12}{8} + \frac{30}{8} + \frac{27}{8} = \frac{12 + 30 + 27}{8} = \frac{69}{8} \] To convert \( \frac{69}{8} \) back to a mixed number, we divide 69 by 8. 69 divided by 8 is 8 with a remainder of 5. So, \[ \frac{69}{8} = 8 \frac{5}{8} \] Therefore, Samantha spent \( 8 \frac{5}{8} \) hours studying over the last three days.