Pre-Algebra · Self Study

Master the Math
Before It Masters You.

Integers, rationals, variables, the distributive property, and factoring — the tricky parts explained clearly, then tested smartly.

⚡ Quick Memory Points

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Cheat Sheet — Say it out loud!

Same sign → ADD, keep sign Different sign → SUBTRACT, bigger wins negative × negative = positive negative ÷ positive = negative a(b + c) = ab + ac ab + ac = a(b + c) LCD before adding fractions! ÷ fraction = × its reciprocal combine LIKE terms only GCF first when factoring

📖 Worked Examples

Example 1 — Integer Operations (the tricky signs!)

Simplify: −3 + (−8)

Memory cue Same sign \to ADD the numbers, KEEP the sign

Step Both are negative \to add 3 + 8 = 11, keep the (-) Answer: -11

Now try: −5 − (−9)

Key rule Subtracting a negative = ADDING a positive - (-9) \to +9 So: -5 + 9 = +4

Example 2 — Distributive Property & Factoring

Expand: −2(3x − 5)

Rule: a(b + c) = ab + ac -2 \times 3x = -6x -2 \times (-5) = +10 \leftarrow negative \times negative! Result: -6x + 10

Factor: 12x − 8

Find GCF (Greatest Common Factor) GCF of 12 and 8 = 4 12x \div 4 = 3x 8 \div 4 = 2 Result: 4(3x - 2)

Example 3 — Rational Number Arithmetic

Calculate: −¾ + ⅝

LCD = 8 -¾ = -6/8 -6/8 + 5/8 = -1/8 (different signs \to subtract, bigger absolute wins)

Calculate: −⅔ ÷ ¼

Dividing = Multiply by reciprocal -⅔ \times 4/1 = -8/3 = -2⅔

Master the MathBefore It Masters You.

All Done! 🎉

Master the Math
Before It Masters You.