Multiply Mixed Numbers: 3 4/6 × 2 2/4 Step-by-Step Solution

To solve the problem of multiplying these mixed fractions, we will proceed through the following steps:

• Step 1: Convert each mixed number into an improper fraction.
  $3\frac{4}{6}$ must first be simplified to $3\frac{2}{3}$.
  To convert $3\frac{2}{3}$ to an improper fraction: $3 \times 3 + 2 = 11$, so we have $\frac{11}{3}$.
  For $2\frac{2}{4}$, simplify $\frac{2}{4}$ to $\frac{1}{2}$ making the fraction $2\frac{1}{2}$.
  Convert $2\frac{1}{2}$ to an improper fraction: $2 \times 2 + 1 = 5$, so we have $\frac{5}{2}$.
• Step 2: Multiply the two improper fractions:
  The calculation is $\frac{11}{3} \times \frac{5}{2} = \frac{11 \times 5}{3 \times 2} = \frac{55}{6}$.
• Step 3: Simplify $\frac{55}{6}$ by converting it back to a mixed number.
  Divide 55 by 6 which gives 9 as the quotient and 1 as the remainder. Therefore, $\frac{55}{6} = 9\frac{1}{6}$.

Therefore, the result of the multiplication is $9\frac{1}{6}$.