Multiply Mixed Numbers: 4 10/12 × 2 2/10 Step-by-Step Solution

To solve this problem, we'll convert the mixed numbers into improper fractions and perform the multiplication.

• Convert $4\frac{10}{12}$ into an improper fraction:
  Multiply the whole number 4 by the denominator 12, then add the numerator 10: $4 \times 12 + 10 = 58$.
  The improper fraction is $\frac{58}{12}$.
• Convert $2\frac{2}{10}$ into an improper fraction:
  Multiply the whole number 2 by the denominator 10, then add the numerator 2: $2 \times 10 + 2 = 22$.
  The improper fraction is $\frac{22}{10}$.
• Multiply the two improper fractions:
  $\frac{58}{12} \times \frac{22}{10} = \frac{58 \times 22}{12 \times 10} = \frac{1276}{120}$.
• Simplify the result:
  First, find the greatest common divisor (GCD) of 1276 and 120, which is 4.
  Divide both numerator and denominator by 4 to simplify:
  $\frac{1276 \div 4}{120 \div 4} = \frac{319}{30}$.
• Convert $\frac{319}{30}$ into a mixed number:
  Divide 319 by 30: the quotient is 10 and the remainder is 19.
  Thus, $\frac{319}{30} = 10\frac{19}{30}$.

Therefore, the solution to the problem is $10\frac{19}{30}$, which corresponds to choice 3.