Hobbs Rojas
02/19/2023 · High School
\begin{tabular}{|l|l|}\hline 3) \( -\frac{9}{11}\left(-\frac{22}{15}\right) \) & 4) \( -4 \frac{3}{8}\left(2 \frac{4}{7}\right) \) \\ \hline\end{tabular}
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Let's solve each problem step by step.
### Problem 3: \( -\frac{9}{11}\left(-\frac{22}{15}\right) \)
1. **Multiply the numerators:** \( -9 \times -22 = 198 \)
2. **Multiply the denominators:** \( 11 \times 15 = 165 \)
3. **Simplify the fraction:** \( \frac{198}{165} \)
4. **Find the greatest common divisor (GCD) of 198 and 165:** The GCD is 33.
5. **Divide both the numerator and the denominator by the GCD:** \( \frac{198 \div 33}{165 \div 33} = \frac{6}{5} \)
So, the answer to problem 3 is \( \frac{6}{5} \).
### Problem 4: \( -4 \frac{3}{8}\left(2 \frac{4}{7}\right) \)
1. **Convert mixed numbers to improper fractions:**
- \( -4 \frac{3}{8} = -\frac{4 \times 8 + 3}{8} = -\frac{35}{8} \)
- \( 2 \frac{4}{7} = \frac{2 \times 7 + 4}{7} = \frac{18}{7} \)
2. **Multiply the fractions:** \( -\frac{35}{8} \times \frac{18}{7} \)
3. **Multiply the numerators:** \( -35 \times 18 = -630 \)
4. **Multiply the denominators:** \( 8 \times 7 = 56 \)
5. **Simplify the fraction:** \( \frac{-630}{56} \)
6. **Find the GCD of 630 and 56:** The GCD is 2.
7. **Divide both the numerator and the denominator by the GCD:** \( \frac{-630 \div 2}{56 \div 2} = \frac{-315}{28} \)
So, the answer to problem 4 is \( -\frac{315}{28} \).
In summary:
- Problem 3: \( \frac{6}{5} \)
- Problem 4: \( -\frac{315}{28} \)
Quick Answer
Problem 3: \( \frac{6}{5} \)
Problem 4: \( -\frac{315}{28} \)
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