A shipment of sugar fills 9 containers. If each container holds \( 3 \frac{5}{6} \) tons of sugar, what is the amount of sugar in the entire shipment? Write your answer as a mixed number in simplest form.

To find the total amount of sugar in the shipment, we first need to calculate the total weight of sugar in the 9 containers. Each container holds \( 3 \frac{5}{6} \) tons of sugar. We convert the mixed number into an improper fraction: \[ 3 \frac{5}{6} = \frac{3 \times 6 + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6} \] Now, we multiply the amount of sugar per container by the number of containers: \[ \text{Total sugar} = 9 \times \frac{23}{6} \] To multiply the whole number by the fraction, we can express 9 as a fraction: \[ 9 = \frac{9}{1} \] Now we multiply the two fractions: \[ \text{Total sugar} = \frac{9}{1} \times \frac{23}{6} = \frac{9 \times 23}{1 \times 6} = \frac{207}{6} \] Next, we convert the improper fraction \( \frac{207}{6} \) into a mixed number. We divide 207 by 6: \[ 207 \div 6 = 34 \quad \text{(remainder 3)} \] Thus, we can express it as: \[ \frac{207}{6} = 34 \frac{3}{6} \] Finally, simplify \( \frac{3}{6} \): \[ 34 \frac{3}{6} = 34 \frac{1}{2} \] So, the total amount of sugar in the entire shipment is \[ \boxed{34 \frac{1}{2}} \] tons.