1 1/7 • 3 1/16

To multiply the mixed numbers \( 1 \frac{1}{7} \) and \( 3 \frac{1}{16} \), we first need to convert them into improper fractions.

1. Convert \( 1 \frac{1}{7} \) to an improper fraction: \[ 1 \frac{1}{7} = \frac{(1 \times 7) + 1}{7} = \frac{7 + 1}{7} = \frac{8}{7} \]

2. Convert \( 3 \frac{1}{16} \) to an improper fraction: \[ 3 \frac{1}{16} = \frac{(3 \times 16) + 1}{16} = \frac{48 + 1}{16} = \frac{49}{16} \]

3. Now, multiply the two improper fractions: \[ \frac{8}{7} \times \frac{49}{16} = \frac{8 \times 49}{7 \times 16} \]

4. Calculate the numerator and the denominator: \[ 8 \times 49 = 392 \] \[ 7 \times 16 = 112 \] So, the multiplication gives us: \[ \frac{392}{112} \]

5. Now, simplify \( \frac{392}{112} \): To simplify, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 56: \[ \frac{392 \div 56}{112 \div 56} = \frac{7}{2} \]

6. Convert \( \frac{7}{2} \) back to a mixed number (if necessary): \[ \frac{7}{2} = 3 \frac{1}{2} \]

Therefore, \( 1 \frac{1}{7} \cdot 3 \frac{1}{16} = \frac{7}{2} = 3 \frac{1}{2} \).