Math · Ratios & measurement
Rates, Unit Rates, and Rate of Change
Estimated time includes reading and one quiz. Take the time you need.
Start here: key ideas
- A rate compares quantities with different units.
- A unit rate has a denominator of one unit.
- Common units are required before rates can be compared.
- Rate of change is vertical change divided by horizontal change.
What you’ll be able to do
- Compute and interpret unit rates with units.
- Compare rates after converting them to common units.
- Find and interpret rate of change from a table or graph.
A rate compares quantities with different units. A unit rate has a denominator of one unit.
Optional review
If you’d like to review the basics, visit Ratios and Proportions. You can start this lesson without completing those first.
Divide to find “per one”
A rate compares different units, such as dollars per pound. A unit rate has 1 in the denominator. If 6 notebooks cost $15, divide both quantities by 6: $15 ÷ 6 = $2.50 per notebook. Keep the units attached; 2.50 alone does not say what was measured.
Worked example 1: A car travels 156 miles in 3 hours. 156 miles ÷ 3 hours = 52 miles per hour. Multiplying 52 by 3 returns 156, which checks the result.
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