A rate can be thought of as a type of ratio. While ratios usually compare two things of the same unit (ex: 2 blue marbles to 1 green marble), ratios compare two things with different units, one of which is usually related to time. Rates often include the word “per”, such as miles per hour, dollars per month, etc.
Like ratios and fractions, we can simply rates by dividing both parts (the numerator and denominator) by a common factor, until they can no longer be divided evenly.
Example
The unit rate is found by getting a denominator of 1 – it tells us how many units of the first term occur within one unit of the second term. Finding the unit rate can be helpful as it may make the rate more understandable to us – for example, hearing that someone drove 30 miles per hour means more to us than hearing that someone drove 60 miles per 2 hours.
To find the unit rate, divide the numerator and denominator by the denominator. This may sometimes result with a decimal in the numerator.
Example
A person can type 90 words in 2 minutes. How many words can they type in 10 minutes?
We can solve problems with rates like this in the same way we solve proportions.
The person can type 450 words in 10 minutes.
Sometimes we want to convert a rate with certain units (ex: meters per second) to a rate with a different unit (ex: kilometers per hour). We can use a process called dimensional analysis to do this in an organized way.
Using dimensional analysis, we can multiply by equivalent units of conversion until we reach our desired unit. In the process, the other units can be eliminated. This works because we are essentially multiplying by 1 each time.
Example
How many kilometers per hour is equal to 4 meters per second?
Practice Problems
Answers