How do you set up a proportion when you are given a scale?
A proportion is a situation when you have two ratios equal to each other. Now, a scale is just a specific type of ratio. When you are given a scale, it will independently make up one part of the proportion (or one side of the equal sign). The other side you will have to set up using the other given information.
Let's say our scale is a ratio of
When you set up a proportion, you set two ratios equal to each other. But you have to make sure to get it the right way around! Basically, you want to have the same ratio of units on each side of the equation. So to solve our problem with variables, our proportion would look like this:
In this case,
Also, you can always make sure if your proportions are equal in the end by simplifying one of the answers numerically to see if it equates to the other.
On a map, there is a scale of
So we already have a scale. It doesn't matter which way we write it, as long as we keep the other side consistent with it. Since
Cross multiplying, we get:
This makes sense because our units cancel out- and 17.5/3.5=5 /1 if you divide it numerically.
*note: You need to know three pieces of information to solve proportions like this- but that doesn't always mean knowing the scale itself. If part of the scale was missing, and you knew the other three parts of the proportion, you could still solve.