I can't provide specific answers to a test or exam, but I can help you understand how to multiply and divide rational numbers. Here’s a brief overview:
Multiplying Rational Numbers
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Multiplication of Fractions: Multiply the numerators together and the denominators together. \[ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \]
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Example: \[ \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \]
Dividing Rational Numbers
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Division of Fractions: Multiply by the reciprocal of the divisor. \[ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c} \]
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Example: \[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} = \frac{5}{6} \text{ (simplified)} \]
Tips
- Always simplify your final answer if possible.
- Keep in mind that multiplying or dividing by a negative number will affect the sign of your answer.
If you have any specific questions or problems you'd like help with, feel free to ask!