Unit rates compare a quantity with one measure unit.

Often, we can see the speed at which objects are traveling in terms of their unit rates.

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### Video Transcription

If, for example, we want to describe the speed of a boy that rides his bike and we have the distance he travels in miles over two \((2)\) hours, we most likely would express the boy’s speed by writing the distance he traveled in \(1\) (one) hour.

Now, this is precisely a unit rate. It is giving the distance traveled per \(1\) (one) hour. The denominators of unit rates are always one.

Now take a look at this example where a car is traveling \(300 \, miles\) in \(5\) (five) hours.

To come up with the unit rate, we’ll come up with the number of miles that the car traveled in (one) hour:

\(\frac{300\,miles\,\div\,5}{5\,hours\,\div\,5}\)

\(= \frac{60\,miles}{1\,hour}\)

**How to find Unit Prices**

Unit prices are unit rates that express the price of things. A unit price will always describe the price per one \((1)\) unit so that a comparison of prices is easy.

Probably you’ll have seen that grocery shelves are marking unit prices as well as the total prices of the products. These unit prices make it easier for shoppers to compare prices of different brands or package sizes.

Now, how can we find a unit price?

Well, imagine this situation where a buyer wants to use the unit price for the comparison of a \(3-pack \,of \,tissues\) for \(\$4.98\) and a single box of tissues at \(\$1.60\). What is the best deal?

So we need to find the unit price (of a \(3-pack\): \(\$4.98\) for, or per, three \((3)\) boxes).

Since our price is for three \((3)\) boxes, we need to divide both our numerator and our denominator by three \((3)\) to end up at a price per one \((1)\) box. This is our unit price. So our unit price will be \(\$1.66\) per \(1\) box.

So our unit price of the three \((3)-pack\) is now \(\$1.66\) per box. When we compare this to the single box price at \(\$1.60\), we see that, surprisingly, the three-pack comes with a higher unit price than the single box! So buying a single box comes at a better value.

As a rate, a unit price is often described using the word “per.”

And at times, also a slanted line \(( / )\) will be used to express “per.” In our example, the price of the tissue boxes could be expressed by \(\frac{\$1.60}{box}\), which is then read as \(“\$1.60\ per\ box.”\)

*Last Updated on February 14, 2024.*