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Lecture Comments (23)

0 answers

Post by Kyoung-Hee Kim on October 7, 2014

educator helps alot 100%

0 answers

Post by Eileen Rothenhausler on June 16, 2014

isn't (3)2 equal to 6?

0 answers

Post by Babatunde Thomas on March 9, 2014

you have to solve what's in the parenthesis before the exponent. 5 and 2 are two numbers in one variable

1 answer

Last reply by: Simon Holland
Wed Aug 5, 2015 4:53 AM

Post by aljona brahaj on January 21, 2014

in the example of (5-2)power 2 I am little confuse Because I thought since we have parenthesis both number are on power can you??? explain this please

1 answer

Last reply by: Kyoung-Hee Kim
Tue Oct 7, 2014 7:29 PM

Post by tom late on September 25, 2013

Thanks allot :)

1 answer

Last reply by: Professor Pyo
Sat Aug 10, 2013 12:20 AM

Post by Qing Wang on August 2, 2013

6*9/9=6*1=6 ? If there only exist M and D in operation, there is no order for M and D. Is that true?

4 answers

Last reply by: Victor Quispe
Mon Feb 3, 2014 6:33 PM

Post by Vasyl Golub on June 14, 2013

in the example of 6*9/9 you said that there is no order for multiplication and division... but... how about this one: 6/2*3=?
If I choose to do first the multiplication or division, as a result we'll have a different number.

2 answers

Last reply by: Kyoung-Hee Kim
Tue Oct 7, 2014 7:17 PM

Post by Corinne Lee on July 25, 2011

thank you it helped alot

3 answers

Last reply by: brandon smith
Mon Apr 22, 2013 6:16 PM

Post by MICHAEL JOHNSON on April 10, 2011

Overall, this was a great lesson. However, it was a bit confusing when Professor Pyo went through PEMDAS. She continued to explain that M-D and A-S were the same. I felt that a little more explanation on what she meant by “the same” would have been helpful. The amount of examples helped to learn the concept of order of operations.

Order of Operations

Related Links

  • Order of Operations: The order of which operations to do first.
  • To help you remember the order of operations, use “Please Excuse My Dear Aunt Sally”
    • P: Parenthesis
    • E: Exponent
    • M: Multiply
    • D: Divide
    • A: Add
    • S: Subtract
  • First solve within parentheses; then, solve exponents; then, multiply and divide, etc.

Order of Operations

Evaluate each expression
2 + 6 ×5
  • 2 + 30
Evaluate each expression
6 + 3 ×4
  • 6 + 12
Evaluate each expression
8 + (9 − 5)
  • 8 + 4
Evaluate each expression
18 − (2 + 3)
  • 18 − 5
Evaluate each expression
7 + (18 − 2)
  • 7 + 16
Evaluate each expression
10 − 32
  • 10 − 3 ×3
  • 10 − 9
Evaluate each expression
2 + 53
  • 2 + 5 ×5 ×5
  • 2 + 125
Evaluate each expression
30 − 42
  • 30 − 4 ×4
  • 30 − 16
Evaluate each expression
7 ×(6 − 2)2 ÷2
  • 7 ×(4)2 ÷2
  • 7 ×16 ÷2
  • 112 ÷2
Evaluate each expression
6 ×(7 − 4)2 ÷3
  • 6 ×(3)2 ÷3
  • 6 ×9 ÷3
  • 54 ÷3

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.


Order of Operations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Please Excuse My Dear Aunt Sally 0:07
    • Step 1: Parenthesis
    • Step 2: Exponent
    • Step 3: Multiply and Divide
    • Step 4: Add and Subtract
    • Example: Please Excuse My Dear Aunt Sally
  • Extra Example 1: Evaluating Expression 3:37
  • Extra Example 2: Evaluating Expression 4:59
  • Extra Example 3: Evaluating Expression 5:34
  • Extra Example 4: Evaluating Expression 6:25

Transcription: Order of Operations

Welcome back to; this lesson is on the order of operations.0000

For order of operations... operations we know are multiplying, dividing, adding, subtracting, things like that.0009

Those are all called operations; we are going to look at the order.0017

When we have several different operations we look at within a single problem,0023

there is an order of which ones we have to do first.0028

To help you remember the order of operations, there is this phrase right here.0034

Please excuse my dear aunt sally.0040

That is just an easy way for you to remember the order of operations.0044

Try to say it out loud a few times; please excuse my dear aunt sally.0049

That just means p for parentheses, e for exponent, m to multiply, d for divide, a for add, and s for subtract.0057

No matter what, you are always going to solve within the parentheses first.0077

If you have parentheses, then always solve that first.0082

Then e for exponent; you are going to do the exponents next.0086

For m and d, multiplying and dividing, they are actually the same.0091

When it comes to multiplying and dividing, you are just going to multiply or divide across whichever ones come first.0099

Multiplying and dividing are actually the same; adding and subtracting are also the same.0107

For multiplying and dividing, there is no order.0114

It is just whichever comes first when it comes to these two.0117

For adding and subtracting, also the same.0121

If there is something you have to subtract before you have to add, then you just go ahead and do that.0125

They are the same; there is no order in here.0130

But please excuse my dear aunt sally is just an easy way for you to remember the order of operations.0135

Make sure you say it a few times and try to remember those.0139

We just went over variables so I have some variables here to help us with the order of operations.0147

A plus in parentheses B minus C plus D squared plus E times F.0154

First thing we have to do is parentheses; this right here would be number one.0164

That is the first thing you would have to do.0172

When you have a number B minus a number C, that is the first thing you are going to solve out.0175

The second thing you are going to solve out is exponent.0181

This; this will be the second thing for you to solve out.0185

Then you are going to just rewrite this problem with that part solved.0189

The next would be to multiply; E times F.0196

That is going to be the third step; you are going to multiply those two first.0200

All you are going to have left are adding and subtracting.0208

You are going to just do that last; you will get your answer that way.0211

Let's do a few examples; let's look at this; 2 plus 3 times 5.0216

My order of operations is P-E-M-D-A-S.0224

That is PEMDAS--please excuse my dear aunt sally.0231

I don't have parentheses; I don't have any exponents.0237

But I do have a multiplication; you are going to do this first.0240

Even though this comes first, you would have to multiply before you add.0248

You are going to do 2 plus... 3 times 5 is 15.0256

This is going to become 17.0265

If you were to add first, if we don't follow the order of operations rule, 0271

let's say you just did 2 plus 3 and then you times 5.0276

2 plus 3 is 5; times 5 is 25.0280

See how that is a different answer; this is a wrong answer.0288

You have to make sure you follow this rule so that you can get the correct answer, 17.0291

Another example would be A plus in parentheses 4 minus 2.0298

We know always, always solve within the parentheses first.0304

This is going to be solved first.0310

I am going to write this because I am not going to do anything to that.0313

4 minus 2 is 2; 8 plus 2 now is 10.0318

When you follow the order of operations, you are going to get the correct answer of 10.0328

Another example, 9 minus 2 squared.0334

We just discussed in the last couple lessons on exponents.0338

2 squared is the same thing as 2 times 2; or 2 times 2 like that.0345

Exponents come after parentheses; we are going to have to solve this before subtracting.0355

2 times 2 is 4; I am going to write 9 minus the 4.0365

9 minus 4 is 5; 9 minus 2 squared is 5.0375

This next example, kind of long, I have a few operations I can perform to this.0387

But remember we have to stick with the order.0392

I am just going to write PEMDAS so I can see the order.0394

Always, always parentheses first; I have a parentheses right here.0404

I am going to write everything else out; solve the parentheses out.0413

5 minus 2 is 3; that is 3 squared divided by 9.0419

Here what is my next operation?--exponents.0430

Since I have an exponent right here, I would have to solve this out before I do anything else.0435

This is going to be 6 times... this remember is 3 times 3.0440

3 squared is the same thing as 3 times 3.0448

3 times 3 we know is 9; then divided by 9.0451

I am just rewriting this out; then multiplication and division right here.0459

When we have only these two, they are actually going to be the same.0468

There is no order for multiplication and division.0473

You are just going to solve out whichever comes first when it comes to multiplying and dividing.0476

For this problem, it just happens to be multiplication.0480

We are just going to solve this out; 6 times 9 is 54.0485

54 divided by 9; I am just rewriting this; 54 divided by 9 is 6.0491

My answer to this, 6 times 5 minus 2 squared divided by 9, as long as you follow the order of operations, your answer will be 6.0504

That is it for this lesson on order of operations.0515

Thank you for watching