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### Order of Operations

- The order of operations is a “road map” of what operations need to be done first in a problem.
- The order of operations tells us to do the following
- Work inside grouping symbols
- Simplify exponents
- Work on remaining multiplication and division from left to right
- Work on remaining addition and subtraction from left to right.
- You can memorize the order of operations by using PEMDAS. (Please Excuse My Dear Aunt Sally.)
- When working with large fractions you can think of the numerator and denominators as their own group. In other words simplify the top and bottom of the fraction before taking care of the division that the fraction represents.

### Order of Operations

^{2}− 3

^{3})/2

- 6 + (49 − 27)/2
- 6 + 22/2
- 6 + 11

^{2}− [(4 ×7) + (32/2)]

- 9
^{2}− [28 + 16] - 81 − 44

^{3}) ×21 + 6

^{2}

- (8 − 8) ×21 + 6
^{2} - 0 ×21 + 36
- 0 + 36

^{2}− 9)/(3 ×7 − 10)]

- [(5 + 3 ×16 − 9)/(3 ×7 − 10)]
- [(5 + 48 − 9)/(21 − 10)]
- [44/11]

- 3 + 14 ×2
- 3 + 28

^{2}− 4

^{3})/3] ×5 − 17

- [(100 − 64)/3] ×5 − 17
- (36/3) ×5 − 17
- 12 ×5 − 17
- 60 − 17

^{2}− 3(y

^{2}+ 4z)

- ( − 5)
^{2}− 3[(3)^{2}+ 4(2)] - ( − 5)
^{2}− 3[9 + 4(2)] - ( − 5)
^{2}− 3(9 + 8) - ( − 5)
^{2}− 3(17) - ( − 5)
^{2}− 51 - 25 − 51

^{2}+ 2 ×z)]

- [((5 ×12)/6 − 5)/(6
^{2}+ 2 − 8)] - [((60)/6 − 5)/(6
^{2}+ 2 − 8)] - [(10 − 5)/(6
^{2}+ 2 − 8)] - [5/(6
^{2}+ 2 − 8)] - [5/(36 + 2 − 8)]
- [5/(38 − 8)]
- [5/30]

**1**)/(

**6**)]

[36/(14 − x

^{3})] ×[y − 4x]

- [36/(14 − 2
^{3})] ×[13 − 4(2)] - [36/(14 − 8)] ×[13 − 4(2)]
- [36/(14 − 8)] ×[13 − 8]
- (36/6) ×[13 − 8]
- 6 ×[13 − 8]
- 6 ×5

^{3}− 15 ×4)/((8x + 22))]

**5**

^{3}−

**15**×

**4**)/(

**(**

**8**

**x**

**+**

**22**

**)**)]

^{3}− 15 ×4)/((9x + 22))]

- [(5
^{3}− 15 ×4)/((9 ×3 + 22))] - [(125 − 15 ×4)/((9 ×3 + 22))]
- [(125 − 60)/((9 ×3 + 22))]
- [65/((9 ×3 + 22))]
- [65/((27 + 22))]

**65**)/(

**49**)]

*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 0:00
- Objectives 0:06
- The Order of Operations 0:25
- Work Inside Parentheses
- Simplify Exponents
- Multiplication & Division from Left to Right
- Addition & Subtraction from Left to Right
- Remember PEMDAS
- The Order of Operations Cont. 2:27
- Example
- Example 1 3:55
- Example 2 5:36
- Example 3 7:35
- Example 4 8:56

### Algebra 1 Online Course

### Transcription: Order of Operations

*Welcome back to www.educator.com.*0000

*In this lesson we are going to take a look at the order of operations.*0002

*As we will see the order of operations is a great way that we can start combining numbers and figure out what we should do first.*0009

*This one involve things like what should we do at parentheses and exponents*0015

*and when should we do our multiplication, division, addition and subtraction.*0020

*When trying to simplify much larger expression with many different types of operations present, we have to figure out what to do first.*0027

*Our order of operations gives us a nice run back on what we should be doing.*0037

*The very first thing that we should do is work inside our grouping symbols.*0042

*It means if you see parentheses or brackets work inside of those first.*0047

*Then move on to simplifying your exponents, things raised to a power.*0052

*Once you have both these in care, move on to your multiplication and division.*0058

*If you see lots of multiplication and division next to each other, remember to work these ones from left to right.*0063

*Now you have to do any remaining addition and subtraction.*0072

*And again when it comes to which of those is more important simply work those from left to right as well.*0074

*One handy way that you can remember of this entire list of that is the order of operations is to remember PEMDAS.*0081

*PEMDAS stands for parentheses, exponents, multiplication, division, addition and subtraction.*0090

*Let us try it out.*0096

*A great way that you can remember these is Please Excuse My Dear Aunt Sally.*0105

*I often heard a lot of my students use that one to make sure that they came out straight.*0110

*Start with your parentheses and then move on to exponents.*0116

*Be very careful if you are using this to memorize what to do first because sometimes when using it, it looks like multiplication is more important.*0120

*But work these ones from left to right.*0129

*The same thing applies to your addition and subtraction, work those from left to right.*0135

*Sometimes you will deal with a larger expression that has a fraction in it.*0150

*Even though you might not see some grouping symbols, think of the top and bottom as their own group.*0157

*That means work to simplify the numerator and get everything together up there.*0163

*And work to simplify your denominator, get everything together down there before we continue on with the simplification process.*0166

*As a quick example, let us look at this slide.*0173

*We have (-2 × 5) + (3 × -2) / (-5-3).*0176

*I'm going to work on the top part as its own group, and the bottom part as its own group.*0183

*Let us see what does this, -2 × 5 would give me -10, 3 × -2 =-6.*0191

*On the bottom in that group I have that -5 -3 =-8.*0202

*Okay -10 - 6=-16 and on the bottom I still have a -8.*0212

*We worked to look inside each of those groups and simplify them using our order of operations in there.*0220

*I simply have a -16 / -8 and that is a 2.*0226

*Watch for those large fractions to play a part.*0232

*Let us try some examples now that we know more about the order of operations and see how we can bring these into a much simpler expression.*0237

*This one is ((5 - 2) ^{2} + 1))/ -5, we also write down PEMDAS.*0245

*This will act as our roadmap as we are going through the problem.*0257

*I want to look for grouping symbols or parentheses to see where I need to start.*0261

*That 5 - 2 looks like a good area, we will do that first, 5 - 2 is 3.*0266

*The only other grouping that I'm concerned with is the top and bottom of the fraction.*0278

*There is only one thing on the bottom so I'm just going to now focus on the numerator.*0283

*I can see that I have some exponents, I have a 3 ^{2} in there.*0290

*And now let us do that, 3 ^{2} is 9, it is getting better.*0294

*I want to move on to my multiplication and division.*0302

*Looking at the top and bottom of the fraction individually I do not see any multiplication or division, I can move on.*0306

*Addition and subtraction, why I do have some addition on the top, I put those together to get 10/-5.*0314

*We are looking at 10 ÷ -5 and now I can say that my result is a -2, this one is done.*0322

*You can see how we move through that order of operations as our road map.*0330

*In this next one we want to evaluate a (-12 × -4/3) - (5 × 6) ÷ 3, let us go over the map.*0338

*I do not see too much in terms of grouping but I do have this group of numbers over here.*0354

*Let us go ahead and take care of those.*0361

*Inside I have (5 × 6) ÷ 3, what should I do in there? I got multiplication and division.*0363

*Those ones remember we are working from left to right.*0370

*On the left side there I have multiplication then we actually do the division.*0374

*5 × 6 is a 30, now do the 30 ÷ 3 and get 10.*0383

*We have taken care of that grouping.*0394

*I'm just going to copy down some these other things and then we will continue on.*0396

*Our grouping is done, now on to exponents.*0406

*I do not see any exponents here so now on to multiplication and division.*0410

*We will do multiplication I got a -12 × -4/3.*0416

*A negative × a negative would give me a positive, multiplying on the top that would be 48/3.*0421

*Because of my fraction there, I do have some division I could take 48 and divided by 3 = 60.*0434

*On to addition and subtraction 16 – 10 = 6.*0444

*I have completely simplified this one and I can call it done.*0451

*This next one I have (12 ÷ 4) × (√5 - 1).*0458

*Starting with my grouping symbols and parentheses, I could consider everything underneath the square root as its own little group.*0469

*Let us work on simplifying that, I'm writing here 5-1 is a 4,12÷ 4 × √4, taking care of the square root entirely.*0475

*I'm looking at 12 ÷ 4 × 2, moving on do I see any exponents? No exponents.*0499

*On to multiplication and division, this is that tough one.*0509

*It is tempting to say that multiplication is more important but it is not.*0512

*Simply work these guys from left to right.*0516

*In this case, we are going to do the division first, 12 ÷ 4 is 3.*0519

*Then we are actually taking that and multiply it by 2 and get 6, this one is completely simplified.*0527

*Let us look at our example that involves lots and lots of different things.*0538

*I have (8 × 4) - (3 ^{2} × 5) + (2 × the absolute value of -1) / (-3 × 2/3) +1*0542

*With so many different things in here we have to be careful in what to do first.*0562

*I'm dealing with a fraction here I want the top as its own group and the bottom as its own*0567

*and work inside each of those and try to simplify them.*0572

*Let us look at the top a little bit.*0575

*Inside of that I do not see any additional grouping symbols so I will try and do any exponents on the top.*0578

*I do have a 3 ^{2}, let us change that into a 9.*0587

*I have the absolute value of -1, might as well we go ahead and take care of that as well.*0594

*We are doing a little bit of simplifying on the top, let us see if there is any exponents in the bottom.*0602

*83 × 2 ^{3} and change out into -3 × 8 and of course we still have the + 1.*0607

*Continuing on, looking at the top I do not have any additional parentheses, I do not have any additional exponents, multiplication and division.*0621

*A lot of multiplication on the top, 4 × 8 would give me 32, 9 × 5 =45, 2 × 1=2.*0629

*On to the bottom, -3 × 8=-24 and then +1, multiplication and division done.*0644

*On to addition and subtraction and we are going to do this from left to right.*0655

*I will do 32 - 45, what do we got from there?*0660

*Let us imagine our technique for combining numbers that have different signs.*0665

*I'm just subtracting here, I get a result of 13.*0673

*The one that is larger in absolute value is the -45 so my result is a -13.*0677

*Looking at the bottom-23 almost done.*0685

*-11 at the top divided by -23, this one is completely simplified as 11/23.*0693

*When dealing with multiple operations it is important that we do have a roadmap in order to get through all of these.*0705

*Feel free to use PEMDAS also that you keep everything in order.*0711

*As you use PEMDAS, if you get down to your multiplication and division then use them from left to right.*0715

*If you get down to your addition and subtraction, again use those from left to right.*0720

*Thank you for watching www.educator.com*0725

1 answer

Last reply by: Professor Eric Smith

Tue Aug 18, 2015 1:19 PM

Post by Terrance Goins on August 17, 2015

Evaluate if x = âˆ’ 5, y = 3, and z = 2x2 âˆ’ 3(y2 + 4z)

In this problem i am confused is it any error that the # 2 has disappeared from the problem shouldnt it be.

2(-5)second power -3 (3second power + 42) = ?

0 answers

Post by Mohamed Elnaklawi on April 11, 2014

Thank you! This lesson was very helpful, and you have a good way of teaching! :-)

0 answers

Post by Professor Eric Smith on October 30, 2013

You are right, the large number is 16, but since we are taking away a smaller number 10, we will still be left with a positive number, or in this case a positive 6.

If the number were switched around, with say the larger number second like 10 - 16, then it would be -6. Keep an eye on subtraction, the order makes a huge difference! :^D

0 answers

Post by Asia Hassan on October 23, 2013

in example 2 the answer you told is 6 and I think it should be -6 because we are subtracting and the big number is 16 therefore and should have negative sign. I might be wrong, so plz tell me. Thanks.