I don’t have access to specific test materials from Connexus or any other educational platform, but I can help you understand how to multiply and divide rational numbers. Here are some general principles and examples to assist you in studying for your Unit 3 test:
Multiplying Rational Numbers
To multiply rational numbers:
- Multiply the numerators: \( a/b \times c/d = (a \times c)/(b \times d) \)
- Simplify if necessary.
Example: \[ \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \]
Dividing Rational Numbers
To divide rational numbers:
- Multiply by the reciprocal: Dividing by a fraction is the same as multiplying by its reciprocal. \[ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \]
- Simplify if necessary.
Example: \[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} = \frac{5}{6} \quad \text{(after simplification)} \]
Additional Tips
- When multiplying or dividing, always look for opportunities to simplify before completing the operation.
- Remember to keep track of signs: a positive times a positive is positive; a negative times a negative is positive; a positive times a negative is negative.
Practice Problems
- Multiply: \( \frac{3}{4} \times \frac{2}{5} \)
- Divide: \( \frac{5}{6} \div \frac{1}{2} \)
- Multiply: \( -\frac{2}{3} \times \frac{3}{4} \)
- Divide: \( -\frac{7}{8} \div -\frac{2}{3} \)
Answers
- \( \frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10} \)
- \( \frac{5}{6} \div \frac{1}{2} = \frac{5}{6} \times \frac{2}{1} = \frac{10}{6} = \frac{5}{3} \)
- \( -\frac{2}{3} \times \frac{3}{4} = -\frac{6}{12} = -\frac{1}{2} \)
- \( -\frac{7}{8} \div -\frac{2}{3} = -\frac{7}{8} \times -\frac{3}{2} = \frac{21}{16} \)
Feel free to ask more questions if you need further clarification or additional practice!
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