Chapter 1
Integer Operations
Adding · Subtracting · Multiplying · Dividing Integers
SAME signs → ADD, keep sign
DIFFERENT signs → SUBTRACT, keep the BIGGER sign
→ Think: "Same = Sum, Different = Difference"
MULTIPLY / DIVIDE rule:
Pos × Pos = Pos | Neg × Neg = Pos
Pos × Neg = Neg | Neg × Pos = Neg
→ "SAME signs = Positive DIFFERENT = Negative"
1 (-3) + (-5) → Same sign (both −) → ADD → −8
2 (-7) + 4 → Different signs → 7−4=3, keep −'s sign → −3
3 (-4) × (-5) → Same sign → +20
4 (-18) ÷ 3 → Different sign → −6
Subtracting a negative = ADDING! 5 − (−3) = 5 + 3 = 8
Keyword: "Minus minus = Plus" (two negatives cancel!)
Chapter 2
Rational Number Operations
Fractions with positive & negative signs
ADD/SUBTRACT fractions: Get a Common Denominator first!
MULTIPLY: Numerator × Numerator, Denominator × Denominator
DIVIDE: Keep · Change · Flip (KCF)
1 (-1/2) + (3/4) → LCD = 4 → (-2/4) + (3/4) = 1/4
2 (-2/3) × (-3/5) → Same sign → +6/15 = 2/5
3 (3/4) ÷ (-3/8) → KCF → (3/4) × (-8/3) = -24/12 = -2
Chapter 3
Distributive Property
Using variables to distribute & factor
DISTRIBUTE: Expand → remove the ( )
FACTOR: Reverse → put GCF outside ( )
→ "Distribute = Spread out Factor = Pull together"
1 3(x + 4) = 3x + 12 ← distribute
2 -2(a − 5) = -2a + 10 ← careful with the sign!
3 4x + 8 = 4(x + 2) ← factor out GCF = 4
4 6a − 9b = 3(2a − 3b) ← GCF = 3
Don't forget to distribute the sign!
−3(x − 2) = −3x + 6 NOT −3x − 6 ✗
→ The minus sign distributes to every term inside!
★ QUIZ TIME
20 Practice Problems
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