What’s a "unit rate" as opposed to a rate?

We often use the word “unit” to mean something related to the number one.  A “unit circle” has a radius of one. A “unit fraction” has a 1 in the numerator.

And a unit rate is a rate with a “1” in the denominator.

If you have a dragonfly that goes 50 feet in 2 seconds, you can express its speed by dividing the distance by the time:

This makes perfect sense: the dragonfly goes 50 feet in 2 seconds, and you can use that speed to perform any calculation. But we traditionally don’t leave the result that way. We perform the division to figure out how far the dragonfly goes in one second—that is, we get a “1” in the denominator:

Then, since 25/1 is just 25, we typically omit the one—but keep the “second”—and move the units into a fraction of their own. We then further change the expression by writing the fraction with feet and seconds using the word “per.” And then we often abbreviate it:

Any of these are a “unit rate,” and students can get confused if they don’t understand that these expressions are all the same.

To make matters worse, we call these unit rates (having a 1 in the denominator), and at the same time worry about keeping the units (the feet and seconds) straight. Imagine you’re an English Learner. Just try to distinguish “unit rate” and “units straight.” They’re related, but different.

 

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