Question: Homework 4.3: Dividing Fractions
Score: 6/8
Answered: 6/8
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Question 7
0/1 pt
100
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Divide. Write your answer in lowest terms.
- 9/20 ÷ ( -21/5 )
Graph shape: a purple-highlighted rectangular equation box containing the fraction -9/20 divided by the parenthesized fraction -21/5, located at bottom-left.
1. **Problem:** Divide $-\frac{9}{20} \div \left(-\frac{21}{5}\right)$ and write the answer in lowest terms.
2. **Use the rule for dividing fractions:**
$$a \div \frac{b}{c} = a \times \frac{c}{b}$$
When dividing by a fraction, multiply by its reciprocal.
3. **Rewrite the division as multiplication by the reciprocal:**
$$-\frac{9}{20} \div \left(-\frac{21}{5}\right) = -\frac{9}{20} \times \left(-\frac{5}{21}\right)$$
4. **Multiply the fractions:**
$$-\frac{9}{20} \times \left(-\frac{5}{21}\right) = \frac{45}{420}$$
A negative times a negative is positive.
5. **Simplify the fraction using cancellation:**
$$\frac{\cancel{45}}{\cancel{420}} = \frac{3}{28}$$
Or, more clearly:
$$\frac{45}{420} = \frac{45 \div 15}{420 \div 15} = \frac{3}{28}$$
6. **Final answer:**
$$\frac{3}{28}$$