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Order of Operations: Introduction

Order of Operations: Introduction

Author: Colleen Atakpu
Description:

In this lesson, you will learn the basics of ordering operations. 

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Today we're going to talk about order of operations. Order of operations tells us the order in which we do different math operation. So operations like adding, subtracting, multiplying, or dividing. We're going to start by looking at an acronym called PEMDAS to help us remember the order in which we do our different operations, and then we'll do some examples.

So behind me is the word PEMDAS. PEMDAS is an acronym that we use to remember the order in which we need to do our different math operations. And PEMDAS stands for Parentheses, Exponents, Multiplying, Dividing, and Adding and Subtracting.

So let's look at a little bit about each of those different operations. So parentheses-- parentheses most commonly look like this. But can include other types of grouping symbols like square brackets, or curvy brackets, or absolute value signs.

Exponents can include a regular exponent, such as a two or square, but also include radicals like the square root or the cubed root.

Then we've got multiplying and dividing and adding and subtracting. And the thing to know about multiplying, dividing, adding and subtracting is that they are done together from left to right. So you are going to evaluate your multiplication and division together from left to right. It doesn't actually matter which one between multiplying and dividing comes first. You're going to do them together from left to right.

And similarly for adding and subtracting, these two things are done together from left to right. So it doesn't matter whether adding or subtracting comes first. You're going to do them together from left to right. So let's look at some examples using different expressions and how we would evaluate them with the order of operations.

So here's my first example. I've got negative 24 divided by 6 times 4, minus 5, and in parentheses 3 plus 6. I rewrote PEMDAS, or our acronym for order of operations, on the side so we can refer to it as we go through our examples.

So we're going to start with P for parentheses. And you'll notice that I actually have parentheses around this negative number, 24, and around the 4. But here, we just use parentheses because it's a negative number and we don't want to confuse this negative sign with a minus.

And here, we use parentheses to signify multiplication between the 6 and the 4. So there's not actually any operation to do within either of these sets of parentheses.

So we're actually going to start with this parentheses and our operation inside of those parentheses is adding. So we're going to start by adding 3 plus 6. Which will give me 9. And I'm going to bring down the rest of my problem.

All right, so now I have dividing, multiplying, subtracting, and multiplying. I don't have any exponents, so I'm going to start with multiplying and dividing. And remember, we do these together going from left to right.

So I've got dividing and multiplying and multiplying. So, again, I'm going to go from left to right. So negative 24 divided by 6 is going to give me a negative 4. I'm going to bring down the rest of my problem.

Continuing multiplying from left to right, negative 4 times 4 gives me a negative 16. And 5 times 9 gives me 45. And I can bring down my subtraction sign. So now all I have left is subtracting. So I'm going to subtract a negative 16 minus 45. And that's going to give me a negative 61.

For my second example, I've got in square brackets which we know are also a form of parentheses, 2.3 plus a negative 6 divided by 5. And adding to that a negative 2.5 plus 1.2.

So here I've got two sets of parentheses. And so I know that's where I'm going to start. And it doesn't matter which set of parentheses we start with first.

So let's start with this first set of parentheses. Inside, I've got adding and dividing. So looking at our order of operations, I know I need to do the dividing before I do the addition.

So negative 6 divided by 5 is going to give me a negative 1.2. I'm going to bring down the rest of my problem.

Now I need to finish evaluating inside of these first parentheses. 2.3 plus a negative 1.2 is going to give me a positive 1.1. Bringing down the rest of my problem.

So I finished evaluating my first parentheses. I can move on to my second set of parentheses. Inside, I only have one operation which is addition. So I'm just going to go ahead and add negative 2.5 plus 1.2 is going to give me a negative 1.3.

I'm going to add to that my 1.1 from my first set of parentheses. And now I've got 1.1 plus negative 1.3, which is going to give me a final answer of negative 0.2.

So before we do our last example, if you're feeling pretty confident with order of operations, go ahead and try this one on your own. And then check back with us and see if you got the right answer.

All right, so I've got negative 7 minus in brackets. 6 times 4 minus 8, divided by 3. And then a plus 2 on the outside.

So looking at order of operations, I know I'm going to start with my parentheses. Which means I need to evaluate inside of here first.

I also have another set of parentheses inside of the square brackets. And when you have two sets of parentheses, you're going to start with parentheses that are on the most inside.

So we're going to start with these parentheses. 4 minus 8 is going to give us a negative 4. I'm going to bring down the rest of my problem.

Continuing inside of my second set of parentheses or the square brackets, I've got multiplying and dividing. And I know that I can just do that from left to right. So 6 times negative 4 is going to give me a negative 24. And now I can finish doing my last operation. Negative 24 divided by 3 will give me a negative 8.

All right, so I finished evaluating my parentheses. Now I've got subtracting and addition. And I know that I can just do addition and subtraction together from left to right. It doesn't matter that subtraction actually comes first.

So I have negative 7 minus a negative 8 which is going to give me a positive 1. Bring down my plus 2. And now I just need to add 1 plus 2. Will give me a final answer of 3.

So let's go over our key points from today. Make sure you get these in your notes if you don't have them already so you can refer to them later.

So we talked about order of operations as being the way that we know the order that we need to complete different map operations. And we talked about PEMDAS, which is the acronym that we use to remember that order of operations.

And there were a couple of things that were important to remember. Number one is that multiplication and division are actually done together moving from left to right. And also, addition and subtraction are done together just moving from left to right.

So I hope that these notes in these examples helped you understand a little bit more about order of operation. Keep using your notes and keep on practicing. And soon you'll be a pro. Thanks for watching.

TERMS TO KNOW
  • PEMDAS

    An acronym to remember the order of operations: parentheses, exponents, multiplication and division, addition and subtraction.