📋 Pre Algebra Basics

Part 1 of 7 — Number Properties

Integers, primes, factors, multiples — these form the foundation of ACT Math.

Even × odd = even; odd × odd = odd; even + odd = odd.

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Key Insight: Prime factorization helps with GCF and LCM.

ACT Tip: Divisibility rules: by 2 (even), by 3 (digit sum divisible by 3), by 5 (ends in 0 or 5).

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Fractions & Decimals

Part 2 of 7 — Fractions & Decimals

Convert between fractions, decimals, and percents fluently.

To add/subtract fractions: find a common denominator.

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Key Insight: Multiply fractions: multiply across (numerator × numerator, denominator × denominator).

ACT Tip: Divide fractions: multiply by the reciprocal (flip and multiply).

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Ratios & Proportions

Part 3 of 7 — Ratios & Proportions

Ratio a:b means for every a of one thing, there are b of another.

Proportion: a/b = c/d — cross multiply to solve.

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Key Insight: Scale factors: if a model is 1:50, multiply model measurements by 50.

ACT Tip: Unit rates: simplify to "per one" (e.g., miles per hour, cost per item).

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Percentages

Part 4 of 7 — Percentages

Percent = part/whole × 100.

Percent of a number: (percent/100) × number.

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Key Insight: Percent increase = (new - old)/old × 100.

ACT Tip: Discount then tax: calculate discount first, then apply tax to the reduced price.

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Order of Operations

Part 5 of 7 — Order of Operations

PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Multiplication and division have equal priority — go left to right.

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Key Insight: Same for addition and subtraction — left to right.

ACT Tip: Nested parentheses: work from the innermost out.

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Problem-Solving Workshop

Part 6 of 7 — Problem-Solving Workshop

PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Multiplication and division have equal priority — go left to right.

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Key Insight: Same for addition and subtraction — left to right.

ACT Tip: Nested parentheses: work from the innermost out.

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Review & Applications

Part 7 of 7 — Review & Applications

PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Multiplication and division have equal priority — go left to right.

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Key Insight: Same for addition and subtraction — left to right.

ACT Tip: Nested parentheses: work from the innermost out.

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Match the Concepts 🔍