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*Contributor: Marlene Vogel. Lesson ID: 12668*

1200 out of 12,000 students agree this is a great lesson on equivalent ratios. Or is it 12 out of 120? Or 1 out of 10? Actually, it's every student, but learn why equivalent ratios are so important!

categories

subject

Math

learning style

Kinesthetic, Visual

personality style

Lion, Beaver

Grade Level

Intermediate (3-5), Middle School (6-8)

Lesson Type

Skill Sharpener

**Did you know?**

A successful marketing strategy, used by advertising agencies for decades, is based on equal ratios. *Equal ratios* are used to demonstrate how many out of a given number of people choose to use their product or service over another. Think about how many times you've heard a commercial with a line similar to this, "Nine out of 10 dentists recommend Minty Mouth to their patients!"

This lesson will help you refresh your math skill of equivalent ratios.

One way to find a ratio that is equivalent to a given ratio is to multiply each quantity in each ratio by the same number. For example, when given the ratio 4:5, and asked to find a ratio that is equivalent to this ratio, simply multiply the 4 and the 5 by the same number. For this example, use the number 3. The given ratio is 4:5. Multiply each quantity in this ratio by 3 (see below):

4 x 3 : 5 x 3

Following the multiplication of each quantity by 3, you now have a new ratio, 12:15. You now have equivalent ratios! 4:5 is equivalent to 12:15. Great job!

**Refresh your memory**

Sometimes, you need to find two equivalent ratios without having a starting ratio. There is a simple way to do this as well. Below is an exercise you can use to help you create equivalent ratios.

Take a look at the following example, then complete the activity to see how well you understand how to find an equivalent ratio for a given ratio, and how to create two equivalent ratios.

Suppose your parent or teacher asks you to show an example of two equivalent ratios. A good way to complete this task is with a hands-on activity that can be done with a pair of scissors and some paper. Choose two different quantities of paper, making sure that each quantity is a different color from the other quantity (see below):

As you can see, for this example, three pieces of blue paper and five pieces of pink paper were chosen. You can use these quantities as your first ratio. You can say that your first ratio is 3 to 5 or 3:5. The next step is to use the same papers to find a ratio equivalent to 3:5. Take your scissors and cut each of the blue papers in half, then cut each of the pink papers in half:

After cutting each piece of paper in half, you now have six pieces of blue paper and 10 pieces of pink paper:

You now have two sets of equivalent ratios! Your first ratio represents the original quantity of each of the colors of paper (3:5). Your second ratio — and the ratio that is equivalent to the first one — is the ratio that you developed by cutting each quantity of paper in half (6:10). You can continue making equivalent ratios by cutting each piece of paper in half again!

**Remember** Just like you can *multiply* the quantities of a given ratio by any number to make an equivalent ratio, you can also *divide* the quantities of a larger ratio by the same number to get a smaller, equivalent ratio. For example, suppose you're given the ratio 15:20. You can state this given ratio in its lowest form by dividing it by the number 5 (Hint: when putting a ratio into its lowest form, you will need to review your multiplication facts.):

15 ÷ 5 : 20 ÷ 5

Once you complete the division, you are left with 3:4. You now have an equivalent ratio to 15:20. Also remember that a ratio can be written in three forms. Using this latest example, the three ways you can represent the ratio are 15 to 20 or 15:20 or ^{15}⁄_{20}.

Below is an exercise for you to complete.

- Now that you know how to find equivalent ratios, can you think of some scenarios where this skill might be useful in your everyday life?

In the *Got It? *section of this lesson, you will have the opportunity to continue to practice this skill and demonstrate your understanding of how to apply this skill in real-world situations.