Overview
This lecture explains the rules for working with integers, including how to add, subtract, multiply, and divide them.
What are Integers?
- Integers are numbers that include negatives, zero, and positives, but no fractions or decimals.
- Examples of integers: -16, -3, 0, 1, 198.
- Non-integers: 1/2, 1.1, 3.5.
Rules for Adding Integers
- Positive + Positive = Positive (e.g., 8 + 7 = 15).
- Negative + Negative = Negative (e.g., -16 + -9 = -25).
- Positive + Negative (or Negative + Positive): Subtract the absolute values and keep the sign of the larger number.
- Example: -4 + 9 = 5 (take sign of 9); 7 + -11 = -4 (take sign of -11).
Rules for Subtracting Integers (KFC Method)
- KFC: Keep the first number, Flip the subtraction sign to addition, Change the second number to its opposite.
- Then add using addition rules.
- Example: 7 - (-5) → 7 + 5 = 12.
- Example: -7 - 5 → -7 + (-5) = -12.
- Example: 7 - 5 → 7 + (-5) = 2.
- Example: -7 - (-5) → -7 + 5 = -2.
- If signs are the same, add and keep the sign; if different, subtract and take the sign of the larger number.
Rules for Multiplying & Dividing Integers
- Same signs (both positive or both negative): Answer is positive.
- Example: 3 × 3 = 9; -3 × -3 = 9.
- Example: 12 ÷ 6 = 2; -12 ÷ -6 = 2.
- Different signs (one positive, one negative): Answer is negative.
- Example: 3 × -3 = -9; -3 × 3 = -9.
- Example: 12 ÷ -6 = -2; -12 ÷ 6 = -2.
Key Terms & Definitions
- Integer — A number without fractions or decimals, includes negatives, zero, and positives.
- KFC Method — Keep, Flip, Change: A process for subtracting integers by converting to addition.
Action Items / Next Steps
- Practice adding, subtracting, multiplying, and dividing integers using sample problems.
- Review and memorize the rules for integer operations.