Onsego Math GED Program

Finding Unit Rates & Unit Prices

Finding Unit Rates

Unit rates compare quantities to 1 unit of the measure. Often, you’ll see the speed of objects traveling expressed in terms of unit rates.

For instance, when we want to describe the speed of a guy riding his bike—and we have the measurement of his distance traveled in \(2\) hours in miles-we would probably express his speed by giving the distance he traveled in 1 hour.

Now, this is what we call a unit rate. This tells us the distance traveled in 1 hour. So a unit rate’s denominator will be 1, always.

Another example. Consider a car that traveled, in \(5\) hours\(,300\) miles. If we want to find the unit rate here, we have to look for the number of miles this car traveled in 1 hour.

We usually write this unit rate as: [latex]60\) miles per hour.

Finding Unit Prices

Unit prices are unit rates that describe the prices of things. Unit prices describe the prices of single units, always. This helps us to compare prices easily.

Perhaps you have noticed that in groceries, the shelves mark both unit prices and the total prices of products. Well, unit prices make it a lot easier for shoppers when comparing prices of various brands and varying package sizes.

Now, how do we find unit prices?

Here’s an example. Suppose a shopper wants to work with unit prices when comparing a \(3-pack\, of\, tissue\) that costs \(\$4.98\) to one single box of tissue that costs \(\$1.60\). Now, which offer is the best deal?

Well, then we’ll have to find our unit price of the \(3-pack:\frac{\$4.98}{3\,boxes}\).

Because the given price applies to for \(3\) boxes, we’ll have to divide here both our denominator and our numerator by \(3\) if we want to determine the price of \(one\) box, our unit price. So our unit price here is \(\$1.66\) per box.

So we found that the unit price in our example of the \(3-pack\) tissue is \(\$1.66\) per single box. When we compare this to a single box a/price, \(\$1.60\), we see that, surprisingly, the \(3-pack\) tissue box comes at a higher unit price! So buying a single box gives us a better value.

Like unit rates, we often describe unit prices with the expression “per.”

Sometimes, we use a slanted line / to express “per.” Then, the price of our tissue box can be written as \(\frac{\$1.60}{box }\). This is read as \(“\$1.60\: per\: box.”\)