Proportions are formed by two equal ratios. Using the examples from the previous lessons, 45 pages:30 minutes would form a proportion with 1.5 pages:1 minute because they are equivalent ratios; 10 tigers:4 lions would form a proportion with 20 tigers:8 lions. In this lesson, you will be asked to identify if two ratios form a proportion. Take a look at the ratios below:
There are two different ways we could evaluate those ratios to see if they form a proportion. The first is to simplify them both to a unit rate.
You can see from the above math that both of those ratios reduce down to the unit rate of 4:1. Therefore the two of them do form a proportion. the other way we could test this is by using a method called cross-multiplication. To do this, you multiply the top number of one side of the proportion by the bottom number of the other side of the proportion. Look at the same proportion as it is evaluated using cross-multiplication.
Again, you can see that 20 x 10 and 5 x 40 both equal 200, so those two equivalent ratios form a proportion. Here is one more example of both methods:
The final thing you’ll need to be careful of is probably the most simple. If there are units, such as the example pictured above, you need to be certain that the units on the top of both proportions is the same, and the units on the bottom of both proportions is the same, as shown above. Below is a non example of this. you’ll notice on the top of one is miles and the bottom is seconds. It is reversed on the other, and because the tops and bottoms of both are not the same thing, it does not form a proportion.
