Order of Operations

"PEMDAS"



PEMDAS is a handy mnemonic to help students remember the order of operations. This video explains the order of operations: parentheses, exponents, multiply, divide, add and subtract. It then shows students how to use it on an example equation. Follow our astronaut through space as he guides you through PEMDAS.



I’ve been first and I’ve been last,
Either way I keep the order with PEMDAS.
First it’s parentheses, then it’s exponents,
Multiply, divide, add, subtract, yeah you know this. (x2)


When I evaluate expressions, I have some patience,
I just follow the order of operations.
I simplify to see what they equal,
PEM comes first and DAS is the sequel:
PEMDAS. Yeah, that’s the acronym,
We’ll break it down, just to see what is happening.
P is parentheses, search for them first,
Whatever is inside them, you need to do the work.
E is exponents, so raise them (raise them) up,
Or get down with the roots
like Questlove does.
MD - multiplication and division,
I do them left to right
, yes, that’s my decision.
AS - addition and subtraction,
You learned them first, do it last, that is the fashion.
Some say, “Please Excuse My Dear Aunt Sally,” some say, “PEMDAS,”
Either way the order is important just like swim class.

I’ve been first and I’ve been last,
Either way I keep the order with PEMDAS.
First it’s parentheses, then it’s exponents,
Multiply, divide, add, subtract, yeah you know this. (x2)


OK, OK, let’s say that we’ve got this: 42(17 – 15) / (3 + 1) – 5
Let’s use PEMDAS, see what we accomplish.
First we do what we see in the parentheses,
17 – 15 that is 2 indeed.
3 + 1 that is 4, yes I’m brilliant,
Now exponents is what we’ll be dealing with.
4 to the 2nd means 4 · 4,
That equals 16, and yes I am sure.
Next we multiply and we divide,
16 · 2 = 32, oh my.
32 / 4 = 8,
And then we add or subtract OK?
8 – 5 = 3,
Which is easier than writing 42(17 – 15) / (3 + 1) – 5 to me.
Cut through your operations just like a surgeon,
Flocab, yeah we keep it working.

I’ve been first and I’ve been last,
Either way I keep the order with PEMDAS.
First it’s parentheses, then it’s exponents,
Multiply, divide, add, subtract, yeah you know this. (x2)


When you see 1 + 1, you know you need to add. With 845 · 952, your product may be messy, but it's clear that you need to multiply.

So what happens when you see 42(17 – 15) / (3 + 1) – 5 ? What do you do first? This song will help you remember the order of operations, and soon evaluating an expression like this one will be no sweat.

1. Parentheses

First you need to evaluate everything inside the parentheses. That's these guys:
( )
If there are multiple operations to be completed inside the parentheses, they also follow the order of PEMDAS.

2. Exponents & Roots

After you complete parentheses, it's time for exponents. Reminder: don't multiply the base by the exponent. Multiply the base by itself, as many times as the exponent says. If your expression has any roots, this is also the time to solve them.

3. Multiplication & Division

Next up? Multiplication and division. If you have a few numbers or terms to multiply and divide, the order you multiply or divide them in doesn't matter. So a good rule of thumb is just to go from left to right to make sure you didn't miss any. And always divide from left to right.

4. Addition & Subtraction

The final step includes the operations you probably learned first: addition and subtraction. At this point in your evaluation process, you should only have to add and subtract the remaining terms. If there are any other operations left--like a stray parenthesis or something to multiply--you missed a step. If you have multiple terms to add or subtract, solve from left to right to make sure you don't forget any.

The mnemonics PEMDAS or Please Excuse My Dear Aunt Sally can help you remember the order of operations. But often the best mnemonics are the ones you make up yourself.

Can you think of your own phrase to help remember the order of operations?
Phelps Earned Mucho Dinero After Swimming? Picky-Eating Monsters Don't Allow Sardines? You try!
Even if your expression doesn't have every type of operation, the order of operations is still the same. If it is missing one, just skip it and move on to the next operation. No parentheses in your equation? Skip the P and use EMDAS. No addition? Have we got a PEMDS for you!
What does the mnemonic PEMDAS stand for?
Parentheses Exponents Multiplication Division Addition Subtraction
What does PEMDAS help you remember?
The order of operations
What is the other operation you can do at the exponent step?
Roots
Evaluate 2 + 3 · 4
2 + 3 · 4 = 14
Evaluate (2 + 3) · 4
(2 + 3) · 4 = 20
Evaluate 23(6 + 3) / (4 - 1) – 4
23(6 + 3) / (4 - 1) – 4 = 20

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