Multiply Mixed Numbers: 3 2/5 × 1 1/6 Step-by-Step Solution

To solve the problem of multiplying $3 \frac{2}{5}$ by $1 \frac{1}{6}$, follow these steps:

• Step 1: Convert Mixed Numbers to Improper Fractions.
  - For $3 \frac{2}{5}$, convert by multiplying 3 (the whole number) by 5 (the denominator) and adding 2 (the numerator):
  $(3 \times 5) + 2 = 15 + 2 = 17$. Thus, $3 \frac{2}{5} = \frac{17}{5}$.
  - For $1 \frac{1}{6}$, convert by multiplying 1 (the whole number) by 6 (the denominator) and adding 1 (the numerator):
  $(1 \times 6) + 1 = 6 + 1 = 7$. Thus, $1 \frac{1}{6} = \frac{7}{6}$.
• Step 2: Multiply the Improper Fractions.
  Multiply $\frac{17}{5}$ by $\frac{7}{6}$:
  $\frac{17}{5} \times \frac{7}{6} = \frac{17 \times 7}{5 \times 6} = \frac{119}{30}$.
• Step 3: Convert the Result to a Mixed Number.
  Divide 119 by 30. The quotient is 3 with a remainder of 29, so the mixed number is $3 \frac{29}{30}$.

Conclusion: $3 \frac{2}{5} \times 1 \frac{1}{6} = 3 \frac{29}{30}$.

The correct choice from the options provided is Choice 4: $3 \frac{29}{30}$.