Ratios, Rates, Proportions, Units
Unit 3 · Problem-Solving & Data Analysis
What the SAT asks here
A ratio compares two quantities; a rate is a ratio with different units; a proportion sets two ratios equal. The Digital SAT uses these for pricing, speed, and variation problems. Expect 1–2 problems per test.
Cross-multiplication
Direct vs. inverse variation
Direct (y doubles when x doubles)
Inverse (y halves when x doubles)
SAT Tip: When chaining unit conversions, write the fractions so the unwanted unit cancels diagonally. If your result has the wrong unit, you flipped a fraction.
Caution: Keep matching units on top of both ratios in a proportion. 'Oranges over dollars' on one side, 'oranges over dollars' on the other.
Type 1
Solve a proportion
Set up a proportion that aligns the units, then cross-multiply.
Example 1
If 5 oranges cost $3.00, how much do 8 oranges cost at the same rate?
Practice more of this type— AI-generated · always-new problems
Generate Problems →Type 2
Unit conversion
Multiply by carefully chosen conversion factors so unwanted units cancel diagonally.
Example 2
A car travels at 90 kilometers per hour. How many meters does it travel per second? (1 km = 1000 m)
Practice more of this type— AI-generated · always-new problems
Generate Problems →Type 3
Direct or inverse variation
Identify the constant k from one data point, then apply the variation rule at the requested input.
Example 3
y varies inversely with x. When x = 4, y = 9. Find y when x = 12.
Practice more of this type— AI-generated · always-new problems
Generate Problems →