How to Determine the Unit Rate in Math

A unit rate is essentially a ratio used to compare a quantity (unit) to the way it is being measured. What makes a unit rate unique from other types of ratios is that the two numbers being compared aren't of the same type. In other words, they are in different units. For example, a car's speed is measured as a unit rate--miles per hour is a ratio based on how far a car travels over time. It's not that hard to determine the unit rate in math, as a long as you have all the variables from which to work.

Difficulty:

Moderate

Instructions

1. Determine whether the variables you are expressing speak of two different types that relate to each other. Common unit rates include: miles per hour, price per item or dollars per hour.

2. Identity whether you have a multiple unit rate or a single unit rate. For instance, if you want to know how much money Jim makes per hour and you know that he gets paid $1,000 per 40 hours of work, then $1,000 is a multiple unit rate. He gets paid $1,000 for every 40 hours worth of work. Notice the two rates correlate but are not expressed in the same type of unit.

3. Translate multiple unit rates into single unit rates by using a simple ratio or proportion. In the payday example, the ratio is 1000:40 because that's how much Jim gets paid and how often.

4. Divide the ratio to determine the single unit rate, remembering what it was you were trying to determine. In this case, when you divide the ratio you discover that Jim makes $25 per hour--his single unit rate (1000/40= 25).

5. Extrapolate the single unit rate to solve other math problems. Here, you can use the single unit rate to answer the question "If Jim make $1,000 for 40 hours of work, how much will he be paid for 70 hours of work?" Knowing that the single unit rate is $25 per hour, it's easy to multiply $25 by 70 hours and discover that Jim will make $1,750 (25 * 70 = 1750).

Tips & Warnings

• Whenever your math problem uses the word "per," it's a hint that you are dealing with a unit rate.