For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Order of Operations

#### Related Links

- Order of operations
- Parenth...theses .28 .29
- Exponentiation
- Nth root
- Multiplication
- Division
- Addition
- Subtraction

- 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

2 + 6 ×5

- 2 + 30

6 + 3 ×4

- 6 + 12

8 + (9 − 5)

- 8 + 4

18 − (2 + 3)

- 18 − 5

7 + (18 − 2)

- 7 + 16

10 − 3

^{2}

- 10 − 3 ×3
- 10 − 9

2 + 5

^{3}

- 2 + 5 ×5 ×5
- 2 + 125

30 − 4

^{2}

- 30 − 4 ×4
- 30 − 16

7 ×(6 − 2)

^{2}÷2

- 7 ×(4)
^{2}÷2 - 7 ×16 ÷2
- 112 ÷2

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.

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
- Please Excuse My Dear Aunt Sally
- 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
- Extra Example 2: Evaluating Expression
- Extra Example 3: Evaluating Expression
- Extra Example 4: Evaluating Expression

- 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

### Basic Math Online Course

### Transcription: Order of Operations

*Welcome back to Educator.com; 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 Educator.com.*0518

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.