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

Question

146×128= 1\frac{4}{6}\times1\frac{2}{8}=

Video Solution

Step-by-Step Solution

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 1461\frac{4}{6}: Multiply the whole number by the denominator and add the numerator: 146=1×6+46=1061\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6}.
    For 1281\frac{2}{8}: Similarly, multiply the whole number by the denominator and add the numerator: 128=1×8+28=1081\frac{2}{8} = \frac{1 \times 8 + 2}{8} = \frac{10}{8}.
  • Step 2: Multiply the improper fractions.
    106×108=10×106×8=10048 \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:
    10048=100÷448÷4=2512 \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, 2512=2112\frac{25}{12} = 2\frac{1}{12}.

Therefore, the solution to the problem is 2112 2\frac{1}{12} . This matches the correct answer choice 2.

Answer

2112 2\frac{1}{12}