As a mixed number, \( 3 \frac{6}{7} \times 2 \frac{2}{3} \)

To multiply the mixed numbers \( 3 \frac{6}{7} \) and \( 2 \frac{2}{3} \) and express the result as a mixed number, follow these steps: 1. **Convert Mixed Numbers to Improper Fractions:** - \( 3 \frac{6}{7} = \frac{(3 \times 7) + 6}{7} = \frac{21 + 6}{7} = \frac{27}{7} \) - \( 2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \) 2. **Multiply the Improper Fractions:** \[ \frac{27}{7} \times \frac{8}{3} = \frac{27 \times 8}{7 \times 3} = \frac{216}{21} \] 3. **Simplify the Fraction:** - Divide both the numerator and the denominator by 3: \[ \frac{216 ÷ 3}{21 ÷ 3} = \frac{72}{7} \] 4. **Convert Back to a Mixed Number:** - Divide 72 by 7: \[ 72 ÷ 7 = 10 \text{ with a remainder of } 2 \] - So, \( \frac{72}{7} = 10 \frac{2}{7} \) **Final Answer:** \[ 3 \frac{6}{7} \times 2 \frac{2}{3} = 10 \frac{2}{7} \]