In this lesson we're going to learn about ratios. Ratios are used a lot of different ways in math to solve many different types of problems. But first, let's learn what a ratio is. A ratio is used to compare two values by showing their relationship. And there are three main types of ratios. We can compare the total amount of one thing to the total amount of another thing, or we can compare part of something to the total amount of that thing, or we can compare part of something to another part of that same thing. Let's look at some examples. So first we have the total to total ratio, and here we're going to compare two different types of values. Here we have stars and circles. So if we were asked what is the ratio of stars to circles, first we need to count the number of each type of item. We have four stars and seven circles. And then to write a ratio to represent this, we do need to pay attention to the order that it's worded in the question. So it's asking for the ratio of stars to circles. So when we write the ratio, we'll put the number of stars first and then the number of circles. So we can write it as simply as four to seven to represent four stars to seven circles. Another type of ratio is a part to total ratio, where we compare a part of something to the total amount of that item. So here we have a rectangle that has a bunch of squares in it. And if we were asked what is the ratio of orange squares to the total number of squares, we would first have to count the orange squares and count the total number of squares. So we have three orange squares, and ten for the total number of squares. When we write the ratio, we want to put the number of orange squares first and then the total number of the squares. So we can write it as three to ten to represent the three orange squares to the ten total squares. Another type of ratio is part to part where we compare a part of something to another part of it. So for this one, we'll look at the same rectangle that's made up of the smaller squares. But this time we'll compare just a part of the rectangle to another part of the rectangle. So our question is what is the ratio of orange squares to blue squares? We have three orange and five blue squares, so we can set up our ratio paying attention to the order. Put orange squares first and then the number of blue squares second. So we can say it's three orange squares to five blue squares, or just put three to five. Now we can represent ratios in different ways, and the examples that we just saw replace the word “to” in between the numbers. So that's the first way, just using the word “to.” So we could have four to seven, or we could say, four stars to seven circles or whatever type of items we're working with. But we can also use a colon instead of the word “to.” We could write it as four colon, seven or four stars, colon, seven circles. And we could also represent ratios using fractions. And we'll see this as one of the more common ways to represent ratios in math because fractions are useful when we're solving different mathematical problems. When we set it up, we'll put the first number as the numerator at the top of the fraction and the second number at the bottom as the denominator. So for this example, we'll have four over seven or four stars over seven circles. And remember that the order does matter. So make sure that you pay attention to the wording of the problem that you're working with and whatever way they have it phrased in the problem, you want to keep the same order in your ratio.