A rate has a denominator of 1 unit when the numerator and denominator represent different units of measurement but there is a constant proportion between them. For example suppose you are interested in the rate of change of speed as distance traveled changes. The rate would be expressed as speed divided by distance or miles per hour. In this case the 1 unit in the denominator cancels out the units of measurement in the numerator leaving only the rate itself. This is how rates are usually expressed in mathematical and scientific contexts.
When the numerator and denominator of a rate are both expressed in the same units the rate is said to be a unitless quantity. This is often the case when the quantity being measured is a pure number such as in the case of a batting average. The units cancel out and all that remains is the ratio itself. In general rates that are unitless are easier to work with since they can be directly compared without having to worry about converting units.
One final note on rates: when the denominator of a rate is something other than 1 it is called a derivative. Derivatives are beyond the scope of this blog post but they are important in calculus and other advanced mathematical disciplines.
What is a unit rate?
A rate that has a denominator of 1 unit.
What is an example of a unit rate?
60 miles per hour
How do you find a unit rate?
By dividing the numerator and denominator by the same value
What is the unit rate of 30 miles in 2 hours?
15
What is the unit rate of 15 miles in 1 hour?
15
What is the unit rate of 60 miles in 3 hours?
20
What is the unit rate of 75 miles in 5 hours?
15
What is the unit rate of 2 minutes in 1 hour?
1/30
What is the unit rate of 10 minutes in 1 hour?
1/6
What is the unit rate of 4 minutes in 1 hour?
1/15
What is the unit rate of 5 hours in 1 day?
1/5
What is the unit rate of 10 hours in 2 days?
1/5
What is the unit rate of 48 hours in 4 days?
1/2
What is the unit rate of 72 hours in 6 days?
1/4
What is the unit rate of 24 hours in 1 day?
1
