Rates and Unit Rates
A rate compares different units; a unit rate has a denominator of 1.
About this topic
A rate compares two quantities with different units, such as 120 km in 2 hours or $6 for 3 apples. A unit rate reduces the comparison to one unit of the second quantity, like 60 km per hour or $2 per apple.
Unit rates make fair comparisons possible, for instance finding which store sells a product more cheaply or which runner is faster. Dividing the first quantity by the second gives the unit rate, and it is the same as the slope of a line through the origin on a graph. A rate with a constant value describes a proportional relationship.
Consider two cereal boxes: 500 grams for 3.00 dollars and 750 grams for 4.20 dollars. The first costs 0.6 cents per gram and the second 0.56 cents per gram, so the larger one is the better buy. Speed is a rate, such as 90 km in 1.5 hours, which is 60 km per hour. Typing speed, pay per hour, fuel economy and heart rate are all rates.
A common mistake is dividing in the wrong order, which gives hours per kilometre instead of kilometres per hour. Both can be right, but they answer different questions, so check that the units match what is asked. Also, when comparing, make sure the units are the same, such as converting minutes to hours first.
Key ideas
- Speed is distance per time
- Divide to find the amount per one unit
- Constant rate gives a straight line
Quick check
Use cases: where Rates and Unit Rates helps
- Homework: review the key idea behind Rates and Unit Rates before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Rates and Unit Rates without notes.
- Visual learning: play with the interactive lab to see how Rates and Unit Rates changes when you adjust its inputs.
- Teaching a friend: explain Rates and Unit Rates in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Rates and Unit Rates?
A rate compares different units; a unit rate has a denominator of 1.
What will I learn in Rates and Unit Rates?
Speed is distance per time. Divide to find the amount per one unit. Constant rate gives a straight line.
Is Rates and Unit Rates part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Rates and Unit Rates lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Rates and Unit Rates?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.