Overview
This lesson covers how to multiply and divide real numbers, focusing on rules for handling positive and negative values and tips for adding decimals.
Types of Negative Fractions
- Negative fractions can have the negative sign out front, with the numerator, or with the denominator; all mean the same.
- Example: -1/5, (-1)/5, and 1/(-5) are equivalent.
- It's important to recognize these forms to handle negatives properly in calculations.
Rules for Multiplying Real Numbers
- Positive × Positive = Positive.
- Negative × Positive or Positive × Negative = Negative (different signs, negative result).
- Negative × Negative = Positive (same signs, positive result).
- Order does not affect the sign outcome.
Practice with Multiplying Integers
- Example: -2 × 6 = -12 (different signs).
- Example: -2 × -6 = 12 (same signs).
- Example: 4 × 5 = 20 (same signs).
- Example: -4 × 5 = -20 (different signs).
- Always compare the signs to determine the result.
Multiplying Multiple Numbers
- Multiply two numbers at a time, checking the sign after each step.
- Any even number of negative factors results in a positive product; odd number results in negative.
Coefficients and Parentheses
- A negative in front of parentheses acts as multiplying by -1.
- Example: -1 × 4 = -4.
- Two negatives multiplied together result in a positive.
Adding Decimals Efficiently
- When adding decimals, if the digits after the decimal sum to 10 or more, add 1 to the whole number sum.
- Example: 2.6 + 16.4 → 2 + 16 = 18, .6 + .4 = 1, total is 19.
- Example: 7.2 + 5.8 → 7 + 5 = 12, .2 + .8 = 1, total is 13.
- Example: 4.3 + 12.7 → 4 + 12 = 16, .3 + .7 = 1, total is 17.
Key Terms & Definitions
- Numerator — the top number in a fraction.
- Denominator — the bottom number in a fraction.
- Coefficient — a number multiplying a variable or group, often outside parentheses.
Action Items / Next Steps
- Memorize the rules for multiplying positive and negative numbers.
- Practice recognizing and rewriting negative fractions in all their forms.
- Complete lesson 10 homework, especially problems involving decimals and negative numbers.