Question

multiply and divide rational numbers quick check

Answer 1

Here's a quick guide on how to multiply and divide rational numbers:

### Multiplying Rational Numbers
1. **Multiply the Numerators**: Multiply the top numbers (numerators) together.
2. **Multiply the Denominators**: Multiply the bottom numbers (denominators) together.
3. **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
1. **Multiply by the Reciprocal**: Instead of dividing by a fraction, multiply by its reciprocal (flip the second fraction).
2. **Follow Multiplication Steps**: Then use the multiplication steps (multiply numerators and denominators).
3. **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!