In one week, Shannon's family drank \( 1 / 3 \) of a carton of regular milk and \( 33 / 5 \) cartons of soy milk. How much milk did they drink in all? Write your answer as a fraction or as a whole or mixed number. cartons

To solve the problem, we first need to find a common denominator for the fractions of milk consumed. Shannon's family drank \( \frac{1}{3} \) of a carton of regular milk and \( \frac{33}{5} \) cartons of soy milk. To add these fractions together, we convert \( \frac{1}{3} \) to a fraction that has a denominator of 15 (the least common multiple of 3 and 5): \[ \frac{1}{3} = \frac{5}{15} \] And for \( \frac{33}{5} \): \[ \frac{33}{5} = \frac{99}{15} \] Now we can add the two amounts of milk: \[ \frac{5}{15} + \frac{99}{15} = \frac{104}{15} \] Now, we can convert \( \frac{104}{15} \) to a mixed number: \[ 104 \div 15 = 6 \quad \text{(remainder } 14\text{)} \] So, \( \frac{104}{15} = 6 \frac{14}{15} \). In total, Shannon's family drank \( 6 \frac{14}{15} \) cartons of milk.