Simplifying Expressions with Addition and Subtraction

We just learned about the order of operations which we used to help us simplify expressions. So first we're going to see how we can apply the order of operations to simplify expressions that have addition and subtraction in them. So let's simplify the following expression. Twelve plus three, minus five plus six. Now we can see we have two different things going on here. We have four different numbers and we have addition signs. We have a subtraction sign. So let's make sure that we are doing this in the proper order. So as a reminder, here's our order of operations to the left here. That's going to help us remember what we need to do when. Okay, remember, we start with parentheses, but we don't have any of this problem. We also don't have any exponents. There's no multiplication and division signs, but we do have addition and subtraction. Remember, addition and subtraction get done at the same time. So when there is only addition and subtraction involved, we start at the left and proceed to the right. We're going to do this all in one step. We'll break it down and do each piece separately, but it's really doing everything all together because addition and subtraction get done at the same time. So it's going to be kind of like we're reading a sentence, start left and move to the right. So first we start with our twelve plus 3, 12 plus three gives us 15. Now we're going to subtract five from that. So we had 15, we'll subtract five. Now we have ten. Now we go to our last step, which is adding the six. So we have ten, add six to it, that gives us 16. So that means that this expression simplifies to 16. Let's look at one more. We have twelve plus three minus now we have some parentheses. We have five plus six inside the parentheses. But remember, we have to make sure that we follow the order of operations to know what we should do first. So we do have some addition and subtraction here, but we have the parentheses that we mentioned before as well. If we start in the beginning of our order of operations tells us to first start with the parentheses. So let's focus on just what's inside that parentheses. That's what we're going to solve first. Five plus six, which gives us eleven. Now to help you keep track of simplifying expressions that involve more than one step, it helps to be able to write the simplified version underneath. And we're going to write one step at a time. Don't try to do too much in your head because it's really easy to make mistakes and get things mixed up. So we're going to solve this one step at a time and move from one line to the next as we keep simplifying it. So for now, I'm not even going to do anything to the twelve and three yet. I'm just going to bring them down. Okay, so now I have twelve plus three minus eleven. Now if we look at this expression, it is partially simplified. Now we just have the addition and subtraction left. Now remember, when we have just addition and subtraction left, we start left and move right. So we do the twelve plus three, which will give us 15. And then we subtract the eleven. We keep moving on to the right and that'll give us four. So the result of this step is four. And that is our final simplified answer.