Unit Rate Calculator

Enter two different quantities and two different units to calculate the ratio between them as a unit rate.

What is a unit rate?

To understand a unit rate, you must first understand what a rate is. A rate is known as a ratio of two numbers. This ratio is some unit x per unit y typically displayed as x/y. A unit rate is a conversion of a normal rate, to a rate with the per unit, otherwise known as a denominator, of 1.

For example, let’s say you have a ratio of apples to oranges. You have 8 apples and 2 oranges. This rate could be displayed as 8/2 or 8 apples per two oranges. The unit rate for this would be 4/1. So, 4 apples for every 1 orange. It is equivalent to the first rate, but the denominator is 1. Below we will explore the formula for calculating a unit rate.

Unit Rate Formula

The following formula can be used to convert a rate into a unit rate.

X/Y = (a/b / (b/b)

  • Where X/Y is the unit rate
  • a is the original numerator
  • b is the original denominator

To analyze this a little further, we know that the unit rate is equivalent to the normal rate, therefore, we can only multiply or divide the rate by 1. In this case, we divide by 1, which is b/b. Dividing both the numerator and the denominator by the denominator yields the unit rate.

How to calculate a unit rate?

The following example is a step by step guide on how to calculate the unit rate.

  1. For this example we will assume we are comparing apples to oranges again. We will say that we have 20 apples and 10 oranges. This yields a ratio of 20/10.
  2. Next, we must divide the ratio by a unit of 1. In this case, that would be 10/10.
  3. Finally, we find the resulting unit ratio to be 2/1 after we divided both sides of the ratio by 10.
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