Calculate Mixed Number Multiplication: 1 2/8 × 1 7/14

Question

128×1714= 1\frac{2}{8}\times1\frac{7}{14}=

Video Solution

Step-by-Step Solution

To solve the problem 128×1714 1\frac{2}{8} \times 1\frac{7}{14} , follow these steps:

  • Step 1: Convert the Mixed Numbers to Improper Fractions
    For 128 1\frac{2}{8} , the improper fraction is calculated as:
    128=1+28=88+28=108 1\frac{2}{8} = 1 + \frac{2}{8} = \frac{8}{8} + \frac{2}{8} = \frac{10}{8}
  • For 1714 1\frac{7}{14} , simplify 714=12 \frac{7}{14} = \frac{1}{2} , hence: 1714=1+12=22+12=32 1\frac{7}{14} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
  • Step 2: Multiply the Improper Fractions
    Multiply the fractions 108\frac{10}{8} and 32\frac{3}{2}:
    108×32=10×38×2=3016\frac{10}{8} \times \frac{3}{2} = \frac{10 \times 3}{8 \times 2} = \frac{30}{16}
  • Step 3: Simplify the Resulting Fraction
    Simplify 3016\frac{30}{16} by finding the greatest common divisor (GCD) of 30 and 16, which is 2:
    3016=30÷216÷2=158\frac{30}{16} = \frac{30 \div 2}{16 \div 2} = \frac{15}{8}
  • Step 4: Convert Back to a Mixed Number
    Convert 158\frac{15}{8} to a mixed number:
    158=178\frac{15}{8} = 1\frac{7}{8}

Therefore, the solution to the problem is 178 1\frac{7}{8} .

Answer

178 1\frac{7}{8}