Units, Rates, and Conversions
Key ideas for using unit reasoning to set up PSAT rate and conversion problems.
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Questions Covered in This Set
10 cards to master
What is a rate?
A comparison of two quantities with different units, written as a fraction — "per" means divide (60 miles per hour = 60 mi/1 hr).
What is "unit chasing" (dimensional analysis)?
Writing given quantities and rates as fractions so unwanted units cancel top-and-bottom, leaving only the unit the question asks for.
Is it legal to flip a rate?
Yes — 20 pages per minute can be written as 1 min/20 pages. Choose the orientation that cancels the unit you want gone.
How do you know your setup is wrong?
The leftover units are nonsense (like mile·minutes per hour). Nonsense units are your error alarm.
How many square inches are in 1 square foot?
144 in² — you must square the whole conversion (12 in/1 ft)², not just use 12.
What is a unit rate?
A rate with 1 in the denominator (e.g., dollars per ounce), which makes comparisons like "which is cheaper" easy.
How is average speed computed?
Total distance ÷ total time — never the average of two speeds.
60 mi at 30 mph then 60 mi at 60 mph: average speed?
120 miles ÷ 3 hours = 40 mph (not 45).
Set up: how far does a car at 45 mi/hr go in 20 minutes?
20 min × (1 hr/60 min) × (45 mi/1 hr) = 15 miles.
3 cups of flour per 24 cookies — cups for 60 cookies?
60 cookies × (3 cups/24 cookies) = 7.5 cups.
