Ratios and Proportions — SAT Math Explained
A ratio is a comparison of two quantities by division. A proportion is a statement that two ratios are equal, written as a/b = c/d.
The Core Idea
Proportional reasoning is the ability to recognize when two quantities scale together. If one doubles, the other doubles. Proportions solve for unknown quantities in these scaled relationships.
Key Vocabulary
A comparison of two quantities: 3:5 or 3/5
Two equal ratios: a/b = c/d
If a/b = c/d, then ad = bc — the tool to solve proportions
Ratios that simplify to the same value: 2/4 = 1/2
The multiplier used to convert one ratio to an equivalent one
Solving Proportions
Set up the proportion with the unknown as x
Cross-multiply: multiply diagonally across the equals sign
Solve the resulting equation for x
Check by verifying the two ratios are equal
Real World Applications
Map scales: if 1 inch = 50 miles, how many inches = 200 miles?
Recipe scaling: if 2 cups makes 12 cookies, how many cups for 30 cookies?
Similar figures in geometry: if two triangles are similar, their side ratios are equal
Currency conversion, fuel efficiency calculations
Common Errors to Avoid
Setting up the proportion with inconsistent units (miles/hour vs. hours/mile)
Cross-multiplying incorrectly (multiplying wrong diagonals)
Not simplifying ratios before comparing
Practice: Ratios and Proportions
5 SAT-style questions. Select your answer and get an instant explanation.
If the ratio of red to blue marbles is 3:5, and there are 15 red marbles, how many blue marbles are there?
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