Pre-Algebra & Elementary Algebra Summary

ACT Math · Axiom Academy

SUMMARY Pre-Algebra & Elementary Algebra Summary You just covered ten topic areas — number properties, fractions/decimals/percentages, ratios and rates, exponents and roots, variables and equations, linear equations and inequalities, absolute value, probability, statistics, and real-world finance. Here's the full arc in one place. Order of operations (PEMDAS) and the sign rules for negatives — negative × negative = positive , negative × positive = negative — are the two most common silent error sources in this unit, not the hardest concepts to learn. Fractions, decimals, and percentages are the same number in three costumes: percentage is always , and converting cleanly (rather than re-deriving each time) is what makes these fast. Ratios, proportions, and rates are one relationship read four ways — set up the proportion with matching units in matching positions on both sides, then cross-multiply. Solving any linear equation or inequality is the same balance-preserving move repeated until x is alone — except multiplying or dividing an inequality by a negative flips the inequality sign , the one asymmetry between the two. Mean, median, mode, and basic probability all answer "what's typical / how likely" — the ACT expects you to know which measure or count method a question is actually asking for, not just how to compute each one. Core Concept Number Properties & Operations

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