*Contributor: Marlene Vogel. Lesson ID: 10259*

What if I said one out of every ten students understands ratios? Are you one of the 10? Using a video, worksheets, an online quiz, and Fruit Loops, learn about ratios and why you would use them!

categories

subject

Math

learning style

Auditory, Visual

personality style

Lion, Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Dear Joleen,

It's too bad you weren't in town for Rebecca's 12^{th} birthday party. It was really great, except that there wasn't enough pizza. *There were only 2 slices for each kid*. She had an angel food cake topped by *2 candles for each year of her age*.

The guest list favored girls: *3 out of every 5 guests were girls*. Rebecca asked for jeans and got what she wanted: *out of every 7 presents, 4 were jeans*.

I hope you can make it to Rebecca's party next year!

Your friend,

Stephanie

What can you say about the *italicized* statements in this letter?

They are all ratios!

Believe it or not, we all use ratios (not "radios") every day!

For example, doctors and pharmacists use ratios to prescribe and mix medications. Chefs and bakers use ratios when mixing ingredients. Teachers use ratios for grading, bankers and accountants use ratios when working with money, and even artists use ratios when mixing colors for painting.

The big question is, what is a *ratio*? Very simply, ratios are a *comparison* of two quantities.

In the opening exercise of this lesson, Joleen is comparing several quantities at Rebecca’s birthday party. Joleen talks about how many boys, compared to girls, attended. She also discussed the amount of presents that were jeans compared to the total number of gifts. She even compared the amount of candles on the cake to Rebecca’s age.

In this lesson, you will learn how to write a ratio.

There are three different ways to write a ratio. Read the following example to see each way to express the ratio:

- Write or say a ratio comparing the number of cats and dogs that can be adopted at the animal shelter as shown in this picture:

The pictures shows that the shelter has 2 cats and 7 dogs. Write the ration of cats and dogs using the items found in the problem as a model.

Cats to dogs = 2 to 7

1. The first way to express a ratio in writing is simply to replace the words of the quantities with the numbers that show the amount. In this example, the label "cats" was replaced with the number 2, and the label "dogs" was replaced with the number 7.

2. The second way is to replace the word “to” with a colon (:) within the ratio expression. The colon represents the comparison between the two amounts:

- 2:7

3. The third way to write a ratio is in the form of a *fraction*. The numerator is always going to be the number on the left and the denominator is going to be on the right:

^{2}⁄_{7}

If you choose to write a ratio in the form of a fraction, just remember that, like every fraction, you can write it in its lowest term. Below is an example illustrating this point:

- Six out of every 10 bicycle accidents happen when riders forget to obey the traffic laws.

Looking at the problem, you can see that you are comparing 6 bike accidents to 10 bike accidents. Write that as your model:

- 6 out of 10

Now, write it as a fraction:

^{6}⁄_{10}

Looking at the fraction that you just wrote, can the fraction be simplified?

Yes, it can! Remember, when simplifying a fraction, you need to figure out if there is one number that you can divide both the numerator and denominator by and come up with lower numbers. In this case, you can divide both 6 and 10 by 2; 6 divided by 2 equals 3, and 10 divided by 2 equals 5. Rewrite your fraction in its lowest terms:

^{3}⁄_{5}

There! You now know the three different ways to write a ratio: (2 to 7), (2:7), (^{2}⁄_{7}). Below is a KHAN Academy video lesson called *Introduction to ratios | Ratios, proportions, units, and rates | Pre-Algebra | Kahn Academy*:

Now that you are getting comfortable with ratios, move on to the *Got It?* section to work on some problems on your own!

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