1. Ratios

2. What is a ratio?
A ratio is comparison of two quantities. You may carefully use the word “numbers” to replace the word quantities, as it does not always have to be numbers.
A ratio can be written in 3 different ways.

3. Example:
Suppose you have a box. Inside this box, there are 5 blouses and there are 3 skirts. What is the ratio of blouses to skirts?
First, understand that the ratio must always follow order. In other words, the order of my answer must be correct. You cannot give me an answer that is skirts to blouses. Your ratio must be blouses to skirts.
The answer is: 5 blouses to 3 skirts.

4. Ways to write a ratio
In the previous example, we saw that there were 5 blouses to 3 skirts. We can write this ratio in one of three different ways:
1. 5 to 3 (or 5 blouses to 3 skirts)
2. 5 : 3
(remember, this is not a fraction, just a ratio in fraction form)

5. Lets look at an example to make sure that we got it.
In this example, what is the ratio of Green triangles to Blue Circles?

6. Continued Yes, the answer here is 9 to 6.
However, when the two number have a GCF that is greater than 1, we need to simplify the ratio. So in this example, although it is 9 to 6, both 9 and 6 have a greatest common factor of 3. By dividing out a 3 from both numbers, you should get a simplified ratio of: 3:2. If you had difficulty understanding GCF, you need to revisit Unit 1, GCF.
Yes, ratio are that simple. However, ratios always seem to be somewhat tricky for 6th graders to understand.

7. Equivalent ratios
Equivalent ratios means just what is sounds like- EQUAL ratios. That is, two different ratios that still have the same comparison. In the below example, remember that the equals sign, or =, means that one ratio is equal to another.
2 3 = This means that 2 to 3 and 4 to 6 have the same ratio. Yes, the numbers look to be bigger, but in truth, that’s ok. We aren’t worried if one is bigger or smaller, we want to know, does the ratio remain the same in both sets of numbers? To determine this, we should follow one simple rule:

8. The rule of equivalent ratios
In order to keep the same ratio, the top number of the first ratio and the bottom number of the second ratio must be multiplied or divided by the same number.
Huh? What does that mean? Well, just like when we simplified, what we actually did was we divided both numbers by the GCF. Since the top and bottom numbers were divided by the same number, then the new ratio created will be equivalent.
2 3 = Here, we multiply 2 by 2 to get 4. Then, we multiply 3 by 2 to get 6. So, the ratios must be equivalent.

9. So you are saying that I just multiply or divide both numbers to get a new ratio?
Yes!
In cooking, you may be given a recipe for just 2 people (2 servings). However, if you want to cook for 4 people, then you need to double the recipe, right?
Suppose that a pie recipe needs 4 carrots and 2 potatoes for 2 servings. If 6 people are at the party, then I must multiply my recipe by 3, this way, everyone get a serving. So that my pie doesn’t taste weird, I better make sure that the ratio remains the same as I increase the recipe ingredient amounts. So, I have to multiply my carrots needs by 3 and my potatoes needs by 3 to be sure that everyone gets the same amount.
So, my new ratio is 12:6