Question

Multiply 49%0D%0A4%0D%0A9%0D%0A by −3%0D%0A−%0D%0A3%0D%0A. Write the answer as a mixed number in simplest form.(1 point)

Answer 1

To multiply \( 49 \frac{4}{9} \) by \( -3 \frac{3}{1} \), we need to first convert both mixed numbers into improper fractions.

1. **Convert \( 49 \frac{4}{9} \) to an improper fraction**:
\[
49 \frac{4}{9} = 49 + \frac{4}{9} = \frac{49 \times 9 + 4}{9} = \frac{441 + 4}{9} = \frac{445}{9}
\]

2. **Convert \( -3 \frac{3}{1} \) to an improper fraction**:
\[
-3 \frac{3}{1} = -3 - 3 = -6 \quad \text{(as improper fraction: } -6 = \frac{-6}{1} \text{)}
\]

3. **Now multiply the two fractions**:
\[
\frac{445}{9} \times \frac{-6}{1} = \frac{445 \times -6}{9 \times 1} = \frac{-2670}{9}
\]

4. **Now convert \( \frac{-2670}{9} \) into a mixed number**:
- Divide \( 2670 \) by \( 9 \):
\[
2670 \div 9 = 296 \quad \text{ R } 6
\]
- This means \( \frac{2670}{9} = 296 \frac{6}{9} \).
- Simplify \( \frac{6}{9} \) to \( \frac{2}{3} \):
\[
\frac{2670}{9} = 296 \frac{2}{3}
\]

5. **Putting the negative back**:
\[
\frac{-2670}{9} = -296 \frac{2}{3}
\]

Thus, the final answer expressed as a mixed number in simplest form is:
\[
\boxed{-296 \frac{2}{3}}
\]