# Practice for Multiplying Rates

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Read this lesson, and you'll learn how you can find the unit rate that will help you solve any problem related to that rate. You'll also learn how you can identify unit rates in your problems.

## Rates

The mathematical definition of a rate is a ratio of two numbers with different units. For example, the speed limit given on roads is a rate because you have miles per hour, two different units. In this lesson, we'll take a look at how these rates are so very useful not just in helping us solve math problems but also in everyday life.

To begin, let's talk about rates and where you can find them. If you walk into a grocery store or simply look at a grocery ad, you'll find rates everywhere! For example, you might see bananas on sale, 6 for \$1.00. Or, you might see potatoes on sale, 20 pounds for \$5.00.

To write these rates, you write it as a fraction. The bananas would be 6 bananas / 1 dollar, and the potatoes would be 20 pounds / 5 dollars.

You can have a rate between any two units.

## The Unit Rate

When your rate has a 1 in the denominator, it becomes a special rate called the unit rate. So, the 6 bananas for \$1 is a unit rate, but the 20 pounds of potatoes for \$5 is not.

Whenever possible, you'll want to find your unit rate when working with rate problems. To do this, all you need to do is to divide the denominator by itself to get to 1. For the 20 pounds of potatoes for \$5 rate, you'll divide by 5 since the \$5 divided by 5 gives you 1. Remember, in math, whenever you divide one part of your problem by a number, you'll have to divide all the other parts of your problem by that number too. This means, you also divide your 20 pounds of potatoes by 5 too. Doing this you get this.

• 4 pounds / \$1.00

Changing your potatoes rate to its unit rate you now see that your one dollar gets you 4 pounds of potatoes.

Sometimes, your unit rate will become a decimal, and that is okay. For example, say our potatoes were 20 pounds for \$8. The unit rate in this case (dividing everything by 8) is 2.5 pounds / \$1.00. This tells you that you get 2.5 pounds for every \$1.

## Using the Unit Rate

Now that you have the unit rate, you can use it to find anything you want, related to the rate, and compare it with other rates.

Say you are a restaurant owner, and you are looking at purchasing 200 pounds of potatoes. Your restaurant happens to sell a lot of French fries, hash browns, and mashed potatoes, so you go through a lot of potatoes! You are currently shopping around for potatoes. This is what you have found so far:

 Grocery Deal 20 pounds / \$5 Abe's Foods 10 pounds / \$2 Lilly's Choice Foods 5 pounds / \$1.60

Since you are going to be buying a lot of potatoes, you want to find the best deal for your potatoes. You look at your ads, and what you have found so far, and see that you have three different rates. To compare them, you'll need to turn each of these into their respective unit rates.

For Grocery Deal, it means dividing everything by 5. For Abe's Foods, it means dividing everything by 2. For Lilly's Choice Foods, it means dividing everything by 1.60. Performing these divisions, this is what you get:

 Grocery Deal 4 pounds / \$1 Abe's Foods 5 pounds / \$1 Lilly's Choice Foods 3.125 pounds / \$1

The best deal is the one that gives you the most potatoes for your dollar. In this case, it is Abe's Foods that has 10 pounds of potatoes for \$2. It's a smaller bag than Grocery Deal, but you get more for your money with Abe's Foods.

## Example

Let's look at another example. Sally works at a hair salon and makes \$2,100 every 4 weeks. How many weeks will she need to work to earn \$3,150?

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