Lesson 3: Integer Operations
Integers include all whole numbers and their negatives: ...-3, -2, -1, 0, 1, 2, 3... Operations with negative numbers follow specific rules that are essential for algebra.
Key Concepts
Number Line
Positive numbers are to the right of zero. Negative numbers are to the left. The further left, the smaller. -5 < -2 < 0 < 3 < 7. The absolute value |x| is the distance from zero — always positive.
Adding & Subtracting
Same signs: add the numbers, keep the sign. (-3) + (-4) = -7. Different signs: subtract, take the sign of the larger absolute value. (-8) + 5 = -3. Subtracting a negative: 4 - (-3) = 4 + 3 = 7.
Multiplying & Dividing
Same signs → positive. Different signs → negative. (+)×(+)=+ (-)×(-)=+ (+)×(-)=- (-)×(+)=-. Same rules for division. (-12) ÷ 3 = -4. (-6) × (-5) = +30.
Order of Operations
PEMDAS: Parentheses → Exponents → Multiplication & Division (left to right) → Addition & Subtraction (left to right). 3 + 4 × 2 = 3 + 8 = 11 (NOT 14).
🔬 Interactive Lab: Integer Operations Lab
✅ Check Your Understanding
1. What is (-7) + 3?
2. What is (-5) × (-4)?
3. Evaluate: 3 + 4 × 2