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

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

### Integers and Order of Operations

#### Related Links

- Remember to solve using the order of operations:
- Parenthesis
- Exponents
- Multiplication/Division
- Addition/Subtraction

### Integers and Order of Operations

- 5 + 9 · - 2 ÷ 3 - 4

- − 5 + − 18 ÷3 − 4
- − 5 + − 6 − 4
- − 11 − 4
- − 11 + − 4

- 10 + 5 · - 6 ÷ 2 - 4

- − 10 + − 30 ÷2 − 4
- − 10 + − 15 − 4
- − 25 − 4
- − 25 + − 4

4

^{2}+ (5 − 6) ·2

- 16 + (5 − 6) ·2
- 16 + − 1 ·2
- 16 − 2

2

^{2}+ ( − 19 − 2) ÷3

- 4 + ( − 19 − 2) ÷3
- 4 + ( − 21) ÷3
- 4 + − 7

3

^{2}+ 12 − 3 ·4

- 9 + 12 − 3 ·4
- 9 + 12 − 12
- 21 − 12

( - 16 + 5) · ( - 5 - 1)

- − 11 ·( − 5 − 1)
- − 11 ·− 6

( - 15 + 5) ÷ (4 - 6)

- − 10 ÷− 2

( - 10 + 5) · ( - 3 + 6)

- − 5 ·( − 3 + 6)
- − 5 ·3

− (3

^{3}) |−9| − 8

- − (3 ·3 ·3) ÷|− 9| − 8
- − 27 ÷|−9| − 8
- − 27 ÷9 − 8
- − 3 − 8

− (2

^{3}) ·|−3| + 5

- − (2 ·2 ·2) ·|−3| + 5
- − 8 ·|−3| + 5
- − 8 ·3 + 5
- − 24 + 5

*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

### Integers and 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
- Combining Operations 0:21
- Solve Using the Order of Operations
- Extra Example 1: Evaluate 1:18
- Extra Example 2: Evaluate 4:20
- Extra Example 3: Evaluate 6:33
- Extra Example 4: Evaluate 8:13

### Basic Math Online Course

### Transcription: Integers and Order of Operations

*Welcome back to Educator.com.*0000

*For this next lesson on integers and order of operation,*0002

*now that we went over all the different ways we can solve integers,*0007

*we are going to put them together into the same problem and solve it by using order of operations.*0012

*Remember that when you solve, you have to solve in this order.*0023

*Parentheses is always, always first; then it is exponents.*0029

*Then after that, it is multiplication and division.*0035

*This is the same; you don't multiply before you divide.*0039

*You just do it in order from left to right.*0045

*If you have multiplication and division, then you would just solve it in that order.*0049

*You don't solve one over the other; same thing for addition and subtraction.*0053

*If you have something to subtract before you add, then you would just do that*0059

*in order from left to right instead of adding first and then subtracting.*0064

*Again parentheses; then exponents; then multiplication and division; then addition and subtraction.*0070

*The first problem is going to be -4 plus 8 times -3 divided by 6 minus 2.*0080

*Within all these operations, I have to multiply and divide first.*0091

*Multiplication and division, there is no order between those two.*0099

*I just have to solve it out whichever comes left to right.*0103

*I am going to solve this first right here; 8 times -3.*0107

*When you multiply integers, you have to look at how many negative signs there are.*0114

*There is only one negative sign; only this one has a negative.*0122

*My answer is going to be -24.*0126

*After you solve one thing out, write out the rest.*0133

*-4 plus the 8 divided by 6 minus 2.*0138

*I rewrote the whole problem with only this solved.*0146

*From here, my next step will be to divide these.*0150

*This is going to be -24 divided by 6.*0155

*Again the same rule applies for the negatives; negative sign here; positive here.*0159

*My answer is going to become a negative; that is going to be a -4.*0166

*This is not a divide; don't get confused with that.*0175

*-4; rewrite the whole problem again; plus that, minus that.*0178

*Don't forget to include these signs; this sign was included when we solved it.*0184

*This was part of this answer; but this wasn't.*0190

*You are going to write out that sign here when you rewrite the whole problem.*0194

*-4 plus a -4, I have the same sign.*0200

*When you add integers, if they have the same sign, then you are just going to add up the numbers.*0207

*Then you are going to give the same sign.*0213

*For this one, -4 plus -4 is -8.*0216

*I am going to write out this right here, -8 minus 2.*0223

*I have a minus; I am going to use the two-dash rule; one, two.*0227

*-8 plus -2 is -10; all of this became -10.*0234

*I know it looks like a lot of work.*0243

*But it is only a lot of work because you are doing one little step at a time.*0245

*But just remember, you are multiplying integers, then dividing, then adding, and then subtracting integers.*0249

*The next one, 3 ^{2} plus 2 minus 5 times 6.*0261

*I have parentheses; parentheses always, always, always comes first.*0270

*I am going to solve this first; I have a minus problem, 2 minus 5.*0276

*I am going to use the two-dash rule to make this minus to a plus, the subtraction problem to an addition problem.*0282

*It would be one, two.*0289

*They have different signs; I am going to find the difference of their absolute values.*0293

*This is a 2; the absolute value of -5 is 5.*0298

*The difference will be 3.*0303

*I am going to give it the same sign as the 5.*0306

*That is a negative so this is a negative.*0308

*Then I am going to rewrite the whole problem.*0312

*This is 3 ^{2}; don't forget this plus; then times 6.*0316

*The next step on the order of operations is exponents.*0325

*I have to solve this exponent next; 3 ^{2} is 9; plus -3 times 6.*0330

*Then after that, I have adding and I have multiplying; multiplying comes first.*0339

*That will be again one negative sign here; my answer will be -18.*0346

*Write everything else out; you don't have to write everything out.*0355

*But that is the best way to do it because that prevents any mistakes that you might make.*0358

*9 plus -18; again we are adding integers.*0368

*They have different signs; you find the difference.*0372

*This is a 9; absolute value of this is 18.*0376

*If you find the difference of those, you get 9.*0380

*Give it the sign of the 18; that will be your answer, -9.*0383

*This next problem, I have parentheses that I have to solve out first, -15 plus 4.*0397

*Again we are adding integers; they have different signs.*0406

*Find the difference of their absolute values.*0410

*Absolute value of -15 is 15; absolute value of 4 is 4.*0413

*If you find the difference of those, it is 11 with a negative sign.*0419

*Then times another parentheses that I have to solve out.*0429

*Here is a minus problem; use the two-dash rule; one, two.*0433

*Again two-dash rule, do not apply it to any other negative signs.*0438

*This negative sign, you are not going to touch that.*0441

*The two-dash rule only changes the minus to a plus.*0444

*Then this number to either a negative or a positive.*0449

*-2 plus -8; they have the same sign; -2 and -8.*0454

*You are going to add the numbers, their absolute values; then give it that same sign.*0459

*-2 plus -8 is going to be -10.*0464

*-11 times -10; I have two negative signs.*0472

*That is going to make my answer a positive; 11 times 10 is 110.*0479

*That is it for this problem; that is the answer.*0488

*The fourth example, let's see, I have a negative.*0494

*This, divided by absolute value of that minus a -7.*0501

*The first thing I want to solve out is the parentheses which is right here.*0507

*2 ^{3}; 2^{3}, be careful, 2^{3} is not 2 times 3.*0513

*This is 2 times 2 times 2; I can just rewrite the whole thing.*0519

*Absolute value of -8 minus a -7; I have to solve this out first.*0530

*2 times 2 is 4; 4 times 2 is 8.*0536

*I am going to make this an 8.*0541

*-8 divided by absolute value of -8 minus a -7.*0544

*I want to solve this out too because absolute value is like parentheses.*0555

*Just solve that out first before you divide and do anything else.*0560

*Absolute value of -8 is 8 because the distance from 0 is 8.*0567

*I am going to write everything else out; don't forget these signs.*0580

*Minus a -7; write everything else out exactly the way it is.*0584

*-8 divided by 8 minus -7; I have to divide before I subtract.*0590

*Do this next; -8 divided by 8 is -1.*0597

*Because I have one negative sign, that is going to make my quotient a negative.*0602

*Then I am going to write all this out again; minus a -7.*0608

*I am subtracting integers; I am going to apply the two-dash rule.*0612

*Make this a plus; make that a plus; -1 plus a 7 here.*0617

*Again I have different signs so I am going to find the difference of their absolute values.*0625

*The absolute value of -1 is 1; absolute value of 7 is 7.*0630

*That is 6; then I am going to give it the sign of the 7.*0635

*That is it; that is your answer.*0642

*If any of these problems were confusing to you, if you forgot how to do some of these*0646

*like either dividing or multiplying, maybe adding and subtracting integers,*0653

*then just go back to the previous lessons and review over it.*0657

*Then try to come back here and figure out these problems too.*0660

*That is it for this lesson; thank you for watching Educator.com.*0665

1 answer

Last reply by: Peter Spicer

Wed Jun 18, 2014 1:47 PM

Post by Milan Ray on April 15, 2014

2 plus -5

Equals -

7 right so when it was 2 plus -5 why did you put -3

0 answers

Post by Daniel Eckert on April 11, 2014

a few of the practice questions are done incorrectly. wrong order of operations and they add a division sign to a question in step 2 but its not in the original question.

0 answers

Post by Crystal Curry on September 25, 2012

nice

0 answers

Post by Arpana Duggal on June 15, 2012

really good video. my favorite one so far.

0 answers

Post by earl west on January 19, 2011

Your basic math instruction is excellent. I love your teaching style.