Math & Desmos

SAT Ratio and Unit Problems: label every number with its unit

Ratio and rate mistakes are almost never arithmetic: they are dropped units. Label every number with its unit, write the units into the equation, and check that the final unit matches the question. Three original SAT-style practice questions with the traps explained.

Read the form before reaching for a tool.
y = (x − 2)² + 1vertex (2, 1)

Reader question: I know how to do SAT rate and ratio problems, but I keep picking the wrong answer. How do I stop?

Here is the short answer: your arithmetic is not the problem; your units are. "Ratios, rates, proportional relationships, and units" is a named skill inside College Board's Problem-Solving and Data Analysis domain. The test cannot make the math harder than middle school, so it makes the units confusing instead. The fix is a mechanical habit: label every number with its unit, write the units into your equation, and cancel them like algebra.

The unit-label method

  1. Write the units next to every number before you compute anything: 240 widgets/hour, 20 minutes.
  2. When you multiply or divide, multiply or divide the units too, and cancel what cancels. Your final unit must match the unit the question asks for.
  3. If your final unit is wrong, the number is wrong, no matter how clean the arithmetic looked.

Three rules this catches: mismatched units (minutes vs hours), inverted ratios (flour to sugar is not sugar to flour), and answering the rate instead of the question (computing miles per gallon and stopping, when the question asked for gallons).

SAT-style practice

Each question below is original SAT-style practice, not an official College Board item.

Question 1. A machine produces 240 widgets per hour. How many widgets does it produce in 20 minutes?

A) 4,800 B) 80 C) 12 D) 720

Answer: B. Label: 240 widgets/hour, 20 minutes. The units fight: you cannot multiply widgets per hour by minutes. Convert first: 20 minutes is one third of an hour, so (240 widgets/hour) x (1/3 hour) = 80 widgets, and the hours cancel. The tempting wrong answer is A. It is the result of 240 x 20 with no conversion, and it survives if you never write the units down. Labeling forces the conversion.

Question 2. In a recipe, the ratio of flour to sugar is 3 to 2. If the baker uses 15 cups of flour, how many cups of sugar are needed?

A) 10 B) 22.5 C) 7.5 D) 13

Answer: A. Write the ratio as a fraction with labels: flour/sugar = 3/2. Then 15 cups flour / s cups sugar = 3/2, so s = 15 x 2/3 = 10 cups of sugar. The tempting wrong answer is B. It comes from multiplying 15 by 3/2 instead of 2/3, which is the ratio flipped upside down. The written labels (flour on top, sugar on bottom) make the flip visible before you compute.

Question 3. A car travels 180 miles on 6 gallons of gas. At this rate, how many gallons are needed for a 450-mile trip?

A) 15 B) 30 C) 180 D) 2,700

Answer: A. First find the rate: 180 miles / 6 gallons = 30 miles per gallon. Then divide the trip by the rate: 450 miles / (30 miles per gallon) = 15 gallons, and the miles cancel. The tempting wrong answer is B. It is the correct rate, but the question did not ask for the rate; it asked for gallons. Students who skip the final "does my unit match the question" check hand in their scratch work instead of their answer.

Drill it

Pull five Problem-Solving and Data Analysis ratio and unit questions from College Board's free student question bank and solve each one twice: once fast, and once with full unit labels. Whenever the two attempts disagree, trust the labeled one and find exactly where the fast version dropped a unit.

Sources & Updates

Updated October 21, 2026. Our editorial approach

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