① Integer Operations
🧠 SAME signs → ADD, keep sign | DIFFERENT signs → SUBTRACT, take the BIGGER sign
⚡ Memory Keywords
SAME → SUM | DIFF → DISTANCE | Neg × Neg = Pos | Neg × Pos = Neg
| Signs | Operation | Example | Result |
|---|
| (+)(+) | Add, keep + | 3 + 5 | 8 |
| (−)(−) | Add, keep − | −3 + (−5) | −8 |
| (+)(−) | Subtract, bigger wins | 7 + (−3) | 4 |
| (−)(+) | Subtract, bigger wins | −7 + 3 | −4 |
✏️ Example
−8 − (−3) → change to addition:
−8 + 3 = −5
−4 × (−6) = +24 (neg × neg = POSITIVE!)
② Rational Number Operations
⚡ Memory Keywords
ADD/SUB fractions: "SAME BOTTOM first!" → LCD (Least Common Denominator)
MULTIPLY: "Top × Top, Bottom × Bottom" → straight across
DIVIDE: "Keep · Change · Flip" (KCF) → multiply by reciprocal
Adding/Subtracting: get LCD first, then add numerators
Multiplying: multiply straight across, then simplify
Dividing: flip the second fraction (reciprocal), then multiply
✏️ Example – KCF (Keep·Change·Flip)
34
÷
25
=
34
×
52
=
158
③ Distributive Property
📐 a(b + c) = ab + ac · a(b − c) = ab − ac
Think: the outside number VISITS each term inside
⚡ Memory Keywords
DISTRIBUTE = DELIVER – the factor knocks on every door inside the parentheses
✏️ Examples
3(x + 4) = 3x + 12
−2(a − 5) = −2a + 10 ← watch the sign!
x(2x + 3y − 1) = 2x² + 3xy − x
④ Factoring (Reverse Distribute)
🔍 Factoring = UN-distribute · Find the GCF (Greatest Common Factor) first!
⚡ Memory Keywords
FACTOR = FIND the common piece → PULL IT OUT
GCF out front, leftover terms inside ( )
✏️ Examples
6x + 9 = 3(2x + 3) GCF = 3
4a² − 8a = 4a(a − 2) GCF = 4a
15xy + 10x = 5x(3y + 2) GCF = 5x
✦ ✦ ✦
⚠️ Common Traps to Watch!
Subtracting a negative: −(−x) = +x "double negative = positive"
Distributing a negative: −3(x−2) = −3x +6, NOT −3x−6
Zero rules: 0 × anything = 0 | anything ÷ 0 = UNDEFINED
Fraction ÷ Fraction: Always KCF – never divide tops/bottoms separately
Factoring check: always verify by distributing back!
Choose the correct answer. Answers revealed after each question!
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