Percentages
Finding parts, wholes, percent change, and multi-step percentage problems
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Finding parts, wholes, percent changes, and setting up equations that involve percentages.
Why this matters
The SAT tests percentages in five ways: basic calculations, percent change, multi-step problems, algebraic reasoning with variables, and pulling the right numbers from a data table before computing.
The five patterns
Foundations
Basic percent operations — find the part, the percent, or the whole. If you know one formula, you can solve all three versions.
›Percent Change
Calculate the percent increase or decrease between two values. Or work backward from a percent change to find the original.
›Multi-Step
Two or more percentage calculations in sequence. A markup then a discount, a tax then a tip — order matters.
›Algebraic Reasoning
The values are variables, not numbers. Set up an equation using percent relationships and solve for the unknown.
›Data Extraction
The math is easy. The hard part is pulling the right numbers from a dense word problem or data table before calculating.
The biggest trap: applying a percent increase and then the same percent decrease and thinking you're back to the original. A 20% increase followed by a 20% decrease gives you 96% of the original, not 100%. The SAT loves this.