This is the video for lesson 53 on my web site, Order of Operations. This is a very important lesson so make sure that you pay close attention.
In math, we have rules that tell us the order in which we should calculations. We have an acronym that helps us remember those rules. It's called PEMDAS. Let’s take a look at what each of the letters in this acronym mean.
The P stands for parenthesis. What that means is that whenever we see parenthesis in the problem such as this one down here, we always do whatever is in the parenthesis first. It doesn’t matter whatever else is part of the problem. We immediately jump to the parenthesis and do the calculation that’s inside them.
Now after we do parenthesis, we’ll do E for exponent. You’ll going to learn more about exponents later. But in this lesson, I'll introduce to the very basics of how they work. Just keep in my mind for now that exponents will come after parenthesis. We always do parenthesis first.
Now after we’ve done those two assuming that we have any of those in a problem, we will then do multiplication and division left to right. Now this is important. In PEMDAS, even though M comes before D, it's a little bit of a fib.
Whenever the problem comes down to nothing but multiplication and division, we just do the multiplication and division left to right. What that means is that even if the division comes first, we will still do that first. We just work left to right if the problem comes down to nothing but multiplication and division.
Now, it is same as true for addition and subtraction. Even though A comes before S in PEMDAS, if we have a problem that’s nothing but addition and subtraction, we just work left to right. That’s important to remember. Let’s take a look at some examples.
In this example here, we have three plus four times five. Now it's very tempting to just start with the additions since it's on the left but we don’t do that. According to the order of operations, we must do our multiplication first so what I'm going to do is do the four times five which is 20 and it's a very good idea to get into the habit of bringing down the rest of the problems so that we don’t accidentally forget it. So now, we have three plus 20. We have nothing but addition so we can just do the addition and get 23. If we had added first and then multiplied, we would have gotten the wrong answer.
Let’s take a look at this problem here, four times three squared. Now you’ll learn more about the squaring in a later lesson. For now, let me just tell you that if you see something like this although a small little two next to a number, it means multiply the number times itself.
Now according to our order of operations, we must do exponents before multiplication. These little two is an exponent so I have to do three squared. We pronounce it as three squared which is nine. I've done my exponent first, I'll bring down the rest of the problem so I don’t forget it and we have four times nine which is 36 and that’s how we do that. Let’s take a look at this next problem here.
Now this is a little tricky. We actually have two sets of parenthesis. We have an inner set here surrounding the five plus three and then we have an outer set which very often you’ll see a square brackets but it’s really just a type of parenthesis. Now in a case like this, we always do the inner most parentheses first and then work our way out so all I'm going to do is focus on the five plus three. That gives me eight. Now I'm going to copy down the rest of the problem. This is very important. Don’t skip that step even if you think you can do it in your head. And we still have our outer brackets so we have to focus on what’s inside the parenthesis or in this case the brackets so let’s focus there.
Now we have to take a look at everything we have. We have nothing but addition and subtraction within the brackets. So according to our procedure, we do addition and subtraction left to right. In this case, the subtraction happens to come first but that’s okay. We’ll work left to right. We’ll do four minus one which is three. Bring down the plus eight and then three plus eight is eleven.
This is how I recommend you do all of your order of operations problems. Do them step by step, don’t skip anything. The common error in these problems is when you try to do things in your head or when you just incorrectly copy down previous parts of a problem. Just do it carefully and step by step and you’ll always get the right answer. I'm going to jump to this problem down here.
The first thing I see is parenthesis so I don’t look at anything else. I immediately do what’s in parenthesis, two plus six which is eight and I’ll copy down the rest of the problem, divided by four times three. By the way, for these examples, I'm using the slash to represent division. Sometimes you’ll see that.
Now in this problem I look at what’s left. I have nothing but division and multiplication. According to out order of operations, when we’re left with nothing but multiplication and division, we work left to right so I’ll do eight divided by four which is two. Bring down the times three, two times three is six. Okay. Now let’s take a look at this problem here. There are a lot of things going on but still according to order of operations, first I must do what’s in parenthesis, 12 divided by three is four and I'll bring down everything else that I see.
I know it looks like a lot but we’re going to take it step by step. Okay. We’ve done parenthesis. According to order of operations, we must now do exponents, two squared means two times two which is four so I've done my exponents. Bring down everything else that I see.
Okay. Now we continue taking a look. We have some subtraction here then multiplication, division and then some addition. According to order of operations, before we look at the addition and subtraction, we have to look at multiplication and division and we’ll do it left to right. We have 12 times two which is 24, bring down everything else. Okay.
We have to do the division before we do anything else, 24 divided by four is six so I now have 15 minus six plus four. Okay. According to order of operations, we’re left with nothing but addition and subtraction so we work left to right, 15 minus six is nine which is equals to 13 and that’s how we do that. That was many steps but we did it step by step, one step at a time and so we get the right answer.
This is a very important lesson. Make sure that you fully understand the order of operations. We have to add here to these rules in every single thing that we do in math so make sure that this lesson is fully clear. You’ll have—
Transcription by:
Scribe4you Transcription Services