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

$1\frac{2}{8}\times1\frac{7}{14}=$

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

• Step 1: Convert the Mixed Numbers to Improper Fractions
  For $1\frac{2}{8}$, the improper fraction is calculated as:
  $1\frac{2}{8} = 1 + \frac{2}{8} = \frac{8}{8} + \frac{2}{8} = \frac{10}{8}$
• For $1\frac{7}{14}$, simplify $\frac{7}{14} = \frac{1}{2}$, hence: $1\frac{7}{14} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}$
• Step 2: Multiply the Improper Fractions
  Multiply the fractions $\frac{10}{8}$ and $\frac{3}{2}$:
  $\frac{10}{8} \times \frac{3}{2} = \frac{10 \times 3}{8 \times 2} = \frac{30}{16}$
• Step 3: Simplify the Resulting Fraction
  Simplify $\frac{30}{16}$ by finding the greatest common divisor (GCD) of 30 and 16, which is 2:
  $\frac{30}{16} = \frac{30 \div 2}{16 \div 2} = \frac{15}{8}$
• Step 4: Convert Back to a Mixed Number
  Convert $\frac{15}{8}$ to a mixed number:
  $\frac{15}{8} = 1\frac{7}{8}$

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