A rate is a multiplicative comparison of two quantities, typically expressed as a quotient with unlike units, such as miles per hour, dollars per item, or liters per minute; its units specify which quantity is compared to one unit of the other. The understanding includes interpreting equivalent rates in words, tables, graphs, and equations, distinguishing a rate from an additive difference, and using rates to support proportional reasoning and the interpretation of slope. Instantaneous rates, limits, and formal calculus-based rate-of-change analysis are not included.
A rate compares two quantities by division. The units tell you how the quantities are being compared.
For example, suppose a cyclist travels miles in hours. What is the cyclist’s rate?
Step 1: Identify the two quantities.
Step 2: Divide the distance by the time.
Step 3: Interpret the units.
The rate miles per hour means the cyclist travels 14 miles for every 1 hour.
This is a multiplicative comparison: for each hour, multiply hour by miles per hour to get miles.
It is not an additive difference. Subtracting would compare unlike quantities in a way that does not describe the cyclist’s travel. Dividing gives a meaningful rate with units: miles per hour.
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?