Ratios

1. How can we compare quantities using ratios?

Ratio: 1:2
For every 1 cat, there are 2 dogs.

Part to Part
     For every 1 cat, there are 2 dogs.
 
Part to Whole
     For every pet, 2 are dogs.
     For every pet, 1 is a cat.




2.  What is an equivalent ratio?
Ratio: 2:3
For every 2 lions, there are 3 tigers.

An equivalent ratio is a ratio that is the same as the first ratio.

For example, 2:3 is the same ratio as 4:6.

Models

Problem - For every 2 lions, there are 3 tigers. If there are 4 tigers, how many lions would there be?

Bar Model

Bar models are very useful. For this ratio, you first have to divide your bar into 5 parts, because for every 2 lions, there are 3 tigers, and 2 plus 3 is 5 total big cats. 2 of those parts would represent lions, and 3 would represent tigers. If there are 4 tigers, you would have to divide the 4 tigers into the two parts representing tigers. That would be 2 tigers per part. You have to divide the total big cats into even parts, so the other parts would all have 2 big cats. If 3 parts each had 2 tigers, that would be 6 tigers in total. There would be 4 lions and 6 tigers. Then, you can add the amount of tigers to the amount of lions to get the total number of big cats.

Double Number Line

A double number line shows how many tigers there are in comparison to how many lions there are. The top line is how many lions there are, and it counts up by 2s because there are 2 lions per 3 tigers. The bottom line is how many tigers there are, and it counts up by 3s because there are 3 tigers per 2 lions.

Ratio Table

The ratio table does the same thing as the double number line, but in table form.

3. How do unit rates help us solve problems?

Ratio - 7:21

For every 7 cakes, there are 21 pies.

Problem - If there are 7 cakes for every 21 pies, how many pies will there be if there is 2 cakes?

This problem can be hard to solve because 7 isn't a multiple of 2, so you can't just divide 7, and divide 21 by the same number for an equal ratio. There is a simple answer. You can use unit ratios. With this ratio, I divided 7 by 7 and 21 by 7 as well, that would mean one of the numbers, in this case 7, is one. That means it's a unit. I could then multiply the 1 by any number and multiply the 3 by that same number.

Dog Photo - https://www.pexels.com/search/dog/ 
Cat Photo - https://pixabay.com/en/cat-animal-pet-cats-close-up-300572/ 
Lion photo - https://pixabay.com/en/lions-zoo-animal-1660044/
Tiger photo - https://pixabay.com/en/users/Alexas_Fotos-686414/?tab=ec