SAT Ratios, Rates, and Units Questions
Scaling quantities and converting units. Most of the difficulty is setting the proportion up the right way round.
In short
- Ratios, Rates, and Units is part of Problem-Solving and Data Analysis, about 15% of the scored Math questions: 5 to 7 on every test.
- Math questions from all four areas are mixed in each module and arranged from easiest to hardest.
- Scale proportion is the trap Rivie's practice tests set most often in Ratios, Rates, and Units questions.
Common traps
Most common first, from Rivie's ten practice tests.
Scale proportion
Map / model / similar-figure scaling: the wrong choice scales by the wrong dimension, e.g. uses linear scale when the question asks for area (which scales by the square).
The usual mistake: You scale 'something' by the given ratio without checking whether the quantity is a length, an area, or a volume.
Unit rate
Convert a ratio to a per-unit form to compare or solve; the wrong choice uses the inverted rate (e.g. seconds per meter when you needed meters per second).
The usual mistake: You set up the proportion correctly but invert numerator and denominator at the last step.
Try a question
From Rivie's practice tests. Pick an answer to see why it is right or wrong.
A recipe calls for 2/3 cup of sugar to make 12 cookies. How many cups of sugar would be needed to make 30 cookies at the same rate?
Video lessons
Free on YouTube, picked for this topic.