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Order of Operations - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Sometimes it's hard to know what to do first with a mathematical equation. The order of operations, sometimes called PEMDAS, is how we know what to operation to do first so that we always get the right answer. When adding, subtracting, multiplying, or dividing numbers, if we didn't use the order of operations we would get different answers for the same equation.

A lot of times students come to Math class ready to do problems like this. What I see is students sit down and start tracking through 8+8 is 16 then they go ahead and they divide by 4 and then take away 6. So the student just keeps going, says okay 16 divided by 4 is 4 take away 6 and gets the answer -2. Does that look right to you? See if you can think about that and see if you think that's a correct answer. I'm going to tell you that is actually Mathematically incorrect. Everything the student did was like a right answer like 8+8 is 16 and 2 times itself is 4 but there is something really tricky about Math and it's called the "Order of Operations".
Before I tell you what the Order of Operations is lets look at this one, this is the exact same problem but what if a student came at it like this, they said okay "8+8 I'll deal with that later. I'm going to start by doing I don't know 2 times itself is 4 and then take away 6." That's totally fine I mean like maybe the student started out like this, so they did 16 divided by 4 or first they did 4 take away 6 and said "okay that is going to be -2." So this person is doing all the right Math right. I mean 16 divided by 2 they got their answer was -8. Is that okay? You guys Math is like a total drag because of this, we wrote the same problem and you're doing everything Mathematically correct but you get 2 different answers they're totally different. So the thing I want to talk about today is what is called the Order of Operations most people remember it using this acronym "PEMDAS" which stands for Please Excuse My Dear Aunt Sally that's another way you could remember it. But each letter stands for a Mathematical thing, P stands for parenthesis, E is for exponents, M multiply, divide, add, subtract.

Before we go on I'm going to show one other trick to this PEMDAS business and that's these little arrows that help me because when you come to multiplying and dividing, or the adding and subtracting step you need to be really careful to move from the left to right. You do parenthesis first, then you do the exponents then you do multiplying and dividing from left to right then you do adding, subtracting from left to right. So why don't we visit this problem we started with only now lets do it the correct way. First we want to do parenthesis, there are none so that's okay, next thing we need to do is exponents because P E. E stands for exponents, 8+8 divided by 2 squared or times itself is equal to 4 and take away 6. So we've done parenthesis, we've done exponents now I need to multiply and divide from left to right. So look for a multiply or divide symbol and there it is right there, the first 8 stays the same, 8 divided by 4 is 2 and then take away 6.

My final step is to do the adding, subtracting from left to right. So I'll have 10 take away 6 which is 4, this is the correct answer. Both of those people got it wrong, they did the right Math just in the wrong order. It's really tricky and it's something that you're going to make mistakes on probably in your future so if you can really focus on learning to do the Order of Operations correctly now, it'll help you so much in your Math future. Before you start doing your homework or look at examples I want you to think about one more thing and that's how there's different kinds of parenthesis. Sometimes you see a parenthesis like this, sometimes you see them like that, sometimes you see them like these little swirly things, sometimes you get absolute value marks. These are all different kinds of parenthesis or groupings, you need to be careful that whatever kind of parenthesis grouping you have, you do that piece first before you move on to the exponents. So if you don't remember anything else from this video, I hope you guys remember PEMDAS, Please Excuse My Dear Aunt Sally or parenthesis, exponents, multiply, divide from left to right and subtract from left to right.

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