Understanding the Order of Operations
Video Lessons > Understanding the Order of Operations
The order of operations serves as a guide to ensure that when we simplify expressions in math, all operations are performed in the proper order. In this video lesson, we will explain why understanding the order of operations is essential for simplifying expressions and discuss a useful acronym (PEMDAS) to help you remember the proper order.
Before beginning the lesson, it's important to understand operations and expressions.
Let's look at the details of the lesson including the steps of the order of operations and how you can easily remember them.
When solving mathematical problems, often there is more than one step involved. It is important to know the sequence in which these steps should be executed to solve problems correctly. This sequence is known as the order of operations.
Why do we need the order of operations?
The order of operations dictates the sequence in which operations should be tackled in a mathematical expression. It breaks down to four steps:
After following the steps in the correct order, the expression will be completely simplified. Note that the order of operations applies to both numeric and algebraic expressions.
To easily remember the order of operations, we can use the acronym PEMDAS:
Now you know what the order of operations is, and why we need it to simplify expressions. You also have a nifty acronym, PEMDAS, to help you remember the steps.
In our next video lesson, we will look at how the order of operations can be used to simplify different kinds of expressions. By understanding and applying the order of operations, you will gain a valuable tool for tackling complex mathematical problems with confidence and accuracy.
Try this practice activity to see what you learned. Drag the steps to put them in the correct order.
Now we'll look at the order of operations. Sometimes when we're solving a problem, there's more than one step for us to perform. But it's important for us to know what step we need to do first or second or third. So we can follow the order of operations to make sure that we do everything in the proper order and get the correct answer.
Let's look at this problem. 36 divided by three. Simple enough, right? Just one step, one operation to perform. But what if there was more to this problem? Now we have 36 divided by three minus four times five. There's a lot going on here.
Where do we start? How do we know what to do first? We could start with the division, but we could start with the multiplication. Or we could even start with the subtraction. Do we get to choose or is there a proper way to do this? It turns out that there is a proper way to do it. It's called the order of operations.
So let's look at what the order of operations tell us we need to do first to solve this problem. With the order of operations, the first thing that we'll always start with are parentheses. Now, not every problem is going to have parentheses. In fact, most of the ones that we see probably won't for this course. But if you ever do have a problem with parentheses, you always solve what's inside the parentheses first. So that's our step one.
Our step two is to solve the exponents. Now, if you haven't seen exponents before, it's represented as a number written a little smaller and a little higher than the number that it sits next to. If you haven't learned them yet, don't worry. It's a topic that we normally study once we get further into algebra. So we really won't see this much at all.
The next step includes multiplication. Now, multiplication can be represented with different symbols, so keep your eyes open for that. We might see the little x, the little cross to represent multiplication. We might see just a dot between the numbers to show multiplication. But sometimes we might even see parentheses. Whenever you see a number written right next to parentheses, that means that number is going to be multiplied by whatever's inside the parentheses. So with this example, the two that's on the outside is going to get multiplied by the three that's on the inside.
Step three also includes division. So division can be represented different ways. We can see the division symbol, or sometimes division is also represented as a fraction. So the fraction two thirds can also be thought of as two divided by three. Now notice, step three includes multiplication and division. So that means when we are simplifying expressions, we're going to perform the multiplication and division during the same step.
Step four includes addition and subtraction. We'll also perform addition and subtraction at the same time, once we get to that step.
Now, to help us remember the order of operations, we can use this little acronym. First, we start with the P for parentheses. Then our next step is E for exponents. Our third step, we can have M and D to represent multiplication and division. And then our fourth step we can use AS to show addition and subtraction.
So you can put that together and just remember the word PEMDAS to remember the order of operations. Now, in our next lesson, we're going to look at how we can apply the order of operations to help us simplify expressions.
Related Standards: Common Core 5.OA.A.1, 6.EE.A.1
Hi, I'm Mia!
With over 12 years of experience as a classroom teacher, tutor, and homeschool parent, my specialty is easing math anxiety for students of all ages. I'm committed to empowering parents to confidently support their children in math!