Unit Rate Calculator
Last updated: August 31, 2022
This Unit Rate Calculator will help you find the unit rate or unit price. The rate is the ratio between two terms are in different units. If the denominator of the ratio is one, then this ratio is called a unit rate. Any ratio that is not a unit rate can be turned into one.
Unit Rate Formula
{unit\:rate = \dfrac{quantity\:1}{quantity\:2}}
What is the ratio?
Let’s say we bought 15 candies for $5.53, 4lb of sugar for $3.24 and a 24-pack of 20-ounce soda for $9.48. Let’s write the data to the table:
| # | Item | Cost | Rate |
|---|---|---|---|
| 1 | 15 candies | $5.53 | $5.53 / 15 candies |
| 2 | 4lb of sugar | $3.24 | $3.24 / 4lb of sugar |
| 3 | 24-pack of 20-ounce soda | $9.48 | $9.48 / 24-pack of 20-ounce soda |
In the last column we got the ratios.
A ratio is a comparison of two numbers that indicates their sizes in relation to each other.
What is the Unit Rate?
Let’s go back to the previous example. We bought 24 20-ounce soda packs for $9.48. Our ratio looks like this $9.48 / 24-pack of 20-ounce soda. To get a unit rate, it is necessary that there is a unit in the denominator of the fraction. To do this, divide the numerator and denominator of the fraction by 24 – the denominator of the fraction. We will get a unit rate.
{\dfrac{\$9.48}{24{–}pack\:of\:20{–}ounce\:soda} = \dfrac{\$9.48 ÷ 24}{24{–}pack\:of\:20{–}ounce\:soda ÷ 24} = \dfrac{\$0.395}{1 {–}pack\:of\:20{–}ounce\:soda} = \$0.395\:per\:1\:pack\:of\:20{–}ounce\:soda}
How to find Unit Rate?
Another example – a car travels 540 miles in 5 hours, find the unit rate.
Solution:
Let ‘s make up the ratio:
{\dfrac{540\:miles}{5\:hours}}
Let’s make a unit in the denominator by dividing the numerator and the denominator by 5:
{\dfrac{540\:miles ÷ 5}{5\:hours ÷ 5}}
We get a unit rate:
{\dfrac{540\:miles ÷ 5}{5\:hours ÷ 5} = \dfrac{108\:miles}{1\:hour} = 108\:miles\:per\:hour\:(mph)}
The result is easy to check on the calculator check
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