-3 1/7 * 4 8/11

To multiply the mixed numbers \(-3 \frac{1}{7}\) and \(4 \frac{8}{11}\), we first convert them into improper fractions. 1. Convert \(-3 \frac{1}{7}\): \[ -3 \frac{1}{7} = -\left(3 \times 7 + 1\right)/7 = -\left(21 + 1\right)/7 = -\frac{22}{7} \] 2. Convert \(4 \frac{8}{11}\): \[ 4 \frac{8}{11} = (4 \times 11 + 8)/11 = (44 + 8)/11 = \frac{52}{11} \] Now, we multiply the two improper fractions: \[ -\frac{22}{7} \times \frac{52}{11} = -\frac{22 \times 52}{7 \times 11} \] Calculating the numerator and denominator: - Numerator: \(22 \times 52 = 1144\) - Denominator: \(7 \times 11 = 77\) Thus, we have: \[ -\frac{1144}{77} \] Now, let's simplify \(-\frac{1144}{77}\). We need to check if 1144 is divisible by 77. Calculating \(1144 \div 77\): \[ 1144 \div 77 = 14.8 \quad (\text{approximately, not a whole number}) \] Since \(1144\) is not divisible by \(77\), we leave it as is. The final result is: \[ -\frac{1144}{77} \] If needed, this can be expressed as a mixed number. We compute: - When dividing, \(1144 \div 77\) gives \(14\) (since \(14 \times 77 = 1078\)), and the remainder is \(1144 - 1078 = 66\). - Thus, \(-\frac{1144}{77}\) can also be written as: \[ -14 \frac{66}{77} \] Therefore, the final answer can be stated in either form: \[ -\frac{1144}{77} \quad \text{or} \quad -14 \frac{66}{77} \]