Percentages — SAT Math Explained
A ratio expressed as a fraction of 100, denoted with the % symbol. Percentages represent parts of a whole on a standardized scale from 0 to 100 (and beyond).
The Core Idea
Percent means 'per hundred.' It's a universal comparative language that allows you to compare proportions from different sized groups on equal footing.
Key Vocabulary
Parts per 100 — 35% = 35/100 = 0.35
The original or whole amount — what the percent is taken of
The part — the result of taking the percent of the base
The percentage increase or decrease from an original value
Key Formulas
Part = Percent × Whole (convert percent to decimal first)
Percent = (Part / Whole) × 100
Whole = Part / Percent
((New - Old) / Old) × 100
((Old - New) / Old) × 100
Percent Types
What is 30% of 80? → 0.30 × 80 = 24
20% tip on $45 → 0.20 × 45 = $9
8% tax on $150 → 0.08 × 150 = $12 → total = $162
25% off $80 → save $20, pay $60
Price went from $50 to $65 → increase of $15 → (15/50)×100 = 30%
Common Errors to Avoid
Forgetting to convert % to decimal before multiplying (using 30 instead of 0.30)
Confusing percent change (relative) with absolute change
Finding the wrong 'base' — always use the original value for percent change
Practice: Percentages
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What is 15% of 80?
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