Here's a quick guide on how to multiply and divide rational numbers:
Multiplying Rational Numbers
- Multiply the Numerators: Multiply the top numbers (numerators) together.
- Multiply the Denominators: Multiply the bottom numbers (denominators) together.
- Simplify if Necessary: If the resulting fraction can be simplified, do so.
Example: \[ \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \]
Dividing Rational Numbers
- Multiply by the Reciprocal: Instead of dividing by a fraction, multiply by its reciprocal (flip the second fraction).
- Follow Multiplication Steps: Then use the multiplication steps (multiply numerators and denominators).
- Simplify if Necessary: If the resulting fraction can be simplified, do so.
Example: \[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} = \frac{5}{6} \text{ (simplified)} \]
Quick Tips
- Simplify Early: If you can simplify fractions before multiplying/dividing, it can make calculations easier.
- Negative Signs: Remember that a negative times a negative is a positive, and a negative times a positive (or vice versa) is a negative.
- Always ensure your final answer is in its simplest form.
If you have specific problems or examples you want help with, feel free to provide them!
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