The SAT and ACT keep asking the same ratio, proportion, and percentage questions — and students keep losing points on them, not because the math is hard, but because nobody showed them a clean, repeatable method.

**TLDR: Ratios, Proportions, and Percentages** is a focused 15-page primer that covers exactly what the tests ask. You'll learn how to set up and scale ratios, build proportions that solve themselves with one cross-multiply, and attack any percent word problem using a single three-part equation. The book also breaks down percent change, markup, and discount — including the reverse-percent trap that catches students who haven't seen it before. The final section maps the recurring problem archetypes on both the SAT and ACT and gives you time-saving tactics: when to plug in numbers, when to estimate, and which answer choices are almost always wrong.

This guide is for high school students in grades 9–12 who want a quick SAT math review before a test or a tutoring session, and for parents helping their kids make sense of ratio and proportion problems that look deceptively simple. Every concept is explained in plain language, every technique is shown with worked numbers, and nothing is padded.

If you've been dropping easy points on percent and ratio questions, this is the fix. Grab it, read it once, and walk in ready.

• Read and manipulate ratios fluently, including part-to-part vs. part-to-whole and three-term ratios
• Set up and solve proportions, including unit conversions and similar-figure problems
• Translate percent word problems into equations and handle percent change, percent of percent, and reverse-percent traps
• Recognize the standard SAT/ACT problem patterns and apply the fastest solution method under time pressure
• Avoid the most common student mistakes (mixing up part and whole, compounding percents incorrectly, misreading 'increased by' vs. 'increased to')

1. 1. Ratios: What They Mean and How to Use Them
   Defines ratios, distinguishes part-to-part from part-to-whole, and shows how to scale and split quantities using ratio reasoning.
2. 2. Proportions: Setting Up Equations That Solve Themselves
   Covers proportional reasoning, cross-multiplication, unit conversions, and similar-figure problems using a consistent setup.
3. 3. Percentages: The Three Questions and the Decimal Trick
   Builds the core percent equation, the convert-to-decimal shortcut, and the three standard percent question types.
4. 4. Percent Change, Markup, and Discount
   Handles increase/decrease problems, the multiplier method, and reverse-percent problems where you must find the original.
5. 5. SAT/ACT Test Patterns and Time-Saving Tactics
   Surveys the recurring problem archetypes on the SAT and ACT, with strategy notes on plugging in numbers, estimating, and avoiding common traps.