Find the product of `- 2 (3)/(4) and 5 (6)/(7)`.

Answer

To find the product of \(-2 \frac{3}{4}\) and \(5 \frac{6}{7}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \(-2 \frac{3}{4}\):
\[ -2 \frac{3}{4} = -\left(2 \times 4 + 3\right)/4 = -\left(8 + 3\right)/4 = -\frac{11}{4} \]

For \(5 \frac{6}{7}\):
\[ 5 \frac{6}{7} = \left(5 \times 7 + 6\right)/7 = \left(35 + 6\right)/7 = \frac{41}{7} \]

### Step 2: Multiply the Improper Fractions
Now we will multiply the two improper fractions:
\[ -\frac{11}{4} \times \frac{41}{7} \]

### Step 3: Multiply the Numerators and Denominators
We multiply the numerators together and the denominators together:
\[ \text{Numerator: } -11 \times 41 = -451 \]
\[ \text{Denominator: } 4 \times 7 = 28 \]

### Step 4: Write the Result as a Fraction
Putting it all together, we get:
\[ -\frac{451}{28} \]

### Final Answer
Thus, the product of \(-2 \frac{3}{4}\) and \(5 \frac{6}{7}\) is:
\[ -\frac{451}{28} \]

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