-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: \[ -\frac{1144}{77} \quad \text{or} \quad -14 \frac{66}{77} \]