In this lesson, we're going to look at operations and expressions. We'll review the operations that are used most commonly in math and we'll go over what expressions are as well as what it means to simplify an expression. There are four main operations that we use in math and you've probably probably been using them for quite some time now. They include addition, subtraction, multiplication and division. There are a few other operations, but these are the four most common ones that we will see. Next, let's talk about what an expression is. And when you hear the word expression, it might be used in a lot of different ways. For example, we can talk about someone's facial expression. Their facial expression shows or expresses how they may feel or think about something. They may smile to have a happy expression or frown to show a sad or an upset expression. Well, in math, a mathematical expression is a mathematical idea that's represented with symbols. Those symbols may include numbers, operations like we just talked about, addition, subtraction, multiplication or division. And it can also include variables which are represented with letters. So here's an example: two plus five. Now, you've seen problems like this many, many times, but you may not have thought of it as being a type of mathematical expression, but it does represent a mathematical idea. We're taking two of something and adding five more to it. We can also mix numbers and variables together to form an expression. So with this one we have 3y, which even though we don't see a symbol there, represents multiplication. So the three and y are being multiplied together. And then we can also have different variables combined together in an expression. Here we have x divided by y. But what we can see in all of these examples is that we have at least two different things, whether they're numbers or variables, and they're placed together using some type of operation, whether it's addition, multiplication or division. Now we're going to talk about what it means to simplify an expression. Have you ever had a friend that tells really long stories and they go on and on and on and you just want to say, hey, can you hurry up and just give me the simplified version of the story? It's kind of like that in math sometimes too. Sometimes we have really big, long expressions showing many different numbers and variables and operations, but we really just want to simplify it and make it easier to understand. So when we're simplifying expressions, we're going to write the expression in the shortest or most efficient way. The result represents the same value as the original expression. So we haven't changed what the expression represents, we're just representing it in a shorter or more efficient way. And performing the operations that are shown in the expression will help us to simplify it. So here's an example that we looked at before. Two plus five. Now, we know that two plus five is really just equal to seven. But what we're doing is simplifying that expression. We're performing the operation by adding the two and five together. Now, our result is just one number seven. So our original expression had two numbers in it, the two and five. But once we performed that addition operation, we were able to simplify it to just seven.