Ratios are the way to solve problems. When we have two things that are mathematically similar, most of us have seen ratios before. However, there's some tricks I'd like to show you that'll help you do them faster and more accurately.

We use ratios when we have two quantities, both of which are known for one case, one of which is known for the other. There's a number of ways to set things up. But I like to put one quantity on the top and the second quantity on the bottom, I put the known values on the left and the unknown value on the right standardizing, how you set up a ratio will make it less likely that you mess it up.

Now let's look at how to use them. Imagine that we wanna know the height of a tree, but all we have is a yard stick. Trying to measure the height of a tree with a yard stick is a non-trivial problem.  We notice that both the yard stick and the tree cash shadows, which can easily be measured, that gives us enough information to use ratios. Let's see how to do it. Our two quantities are height and shadow length. It doesn't matter which we put on the top and which we put on the bottom. We just have to pick one and stick with it. Let's put the height on the top. Now we enter the values. We know both the height and the shadow length for the yard stick. So that goes on the left. We put the shadow length for the tree on the bottom of the right ratio. Let's see how to solve it.