Multiply Mixed Numbers: 1⁴/₆ × 1²/₈ Step-by-Step Solution

$1\frac{4}{6}\times1\frac{2}{8}=$

To solve this problem, we'll convert the given mixed numbers to improper fractions, multiply them, and simplify the result. Let's proceed step by step:

• Step 1: Convert the mixed numbers to improper fractions.
  For $1\frac{4}{6}$: Multiply the whole number by the denominator and add the numerator: $1\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6}$.
  For $1\frac{2}{8}$: Similarly, multiply the whole number by the denominator and add the numerator: $1\frac{2}{8} = \frac{1 \times 8 + 2}{8} = \frac{10}{8}$.
• Step 2: Multiply the improper fractions.
  $\frac{10}{6} \times \frac{10}{8} = \frac{10 \times 10}{6 \times 8} = \frac{100}{48}$.
• Step 3: Simplify the resulting fraction.
  Find the GCD of 100 and 48, which is 4. Divide both the numerator and the denominator by 4:
  $\frac{100}{48} = \frac{100 \div 4}{48 \div 4} = \frac{25}{12}$.
• Step 4: Convert the simplified improper fraction back to a mixed number.
  Divide 25 by 12: 25 divided by 12 is 2 with a remainder of 1. So, $\frac{25}{12} = 2\frac{1}{12}$.

Therefore, the solution to the problem is $2\frac{1}{12}$. This matches the correct answer choice 2.