Solve Mixed Number Multiplication: 3⁶/₉ × 3⁴/₂₀

To solve this problem, we will follow these steps:

• Convert the mixed numbers to improper fractions.
• Simplify the fractions when possible.
• Multiply the improper fractions.
• Convert the resulting improper fraction back to a mixed number and simplify.

Here's the step-by-step solution:

Step 1: Convert $3 \frac{6}{9}$ and $3 \frac{4}{20}$ to improper fractions.

For $3 \frac{6}{9}$, which can be simplified to $3 \frac{2}{3}$: $3 + \frac{6}{9} = 3 + \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}$.

For $3 \frac{4}{20}$, which can be simplified to $3 \frac{1}{5}$: $3 + \frac{4}{20} = 3 + \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5}$.

Step 2: Simplify fractions if possible. The fractions $\frac{11}{3}$ and $\frac{16}{5}$ are already in simplest form.

Step 3: Multiply the fractions:

$\frac{11}{3} \times \frac{16}{5} = \frac{11 \times 16}{3 \times 5} = \frac{176}{15}$.

Step 4: Convert the resulting improper fraction to a mixed number.

Divide 176 by 15: $176 \div 15 = 11$ remainder $11$. Thus, $\frac{176}{15} = 11 \frac{11}{15}$.

Therefore, the solution to the problem is $11 \frac{11}{15}$, which matches choice 3.

Therefore, the final answer is $11 \frac{11}{15}$.