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

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

### Adding Integers

#### Related Links

- On the number line, start at the first number
- Use the second number to move spaces
- If it is a positive number, move to the right
- If it is a negative number, move to the left
- The number you land on is the answer
- Remember that opposites add to zero
- If both numbers are the same sign, then add the numbers and keep that sign
- If they are opposite signs, then find the difference of their absolute values and take the sign of the greater number

### Adding Integers

- 9 + - 15

- 1 + - 5

16 + - 8

- 16 + 2

3 + - 20

- |16| = 16
- |−5| = 5
- 16 + 5

- |−12| = 12
- |−9| = 9
- 12 + 9

*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

### Adding Integers

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
- Using a Number Line 0:04
- Example: 4 + (-2)
- Example: 5 + (-8)
- How to Add Integers 3:00
- Opposites Add to Zero
- Adding Same Sign Numbers
- Adding Opposite Signs Numbers
- Extra Example 1: Add the Integers 8:21
- Extra Example 2: Find the Sum 10:33
- Extra Example 3: Find the Value 11:37
- Extra Example 4: Add the Integers 13:10

### Basic Math Online Course

### Transcription: Adding Integers

*Welcome back to Educator.com; this lesson is on adding integers.*0000

*To use a number line, we can add integers using a number line here.*0007

*What we are going to do is start with the first number.*0012

*If I give you a problem, 4 plus -2.*0014

*I am going to start off at this number right here, 4.*0023

*Let me just write out the numbers on this number line.*0026

*Here is 0, 1, 2, 3, 4; I can just do a few more on this side.*0028

*Here are my negatives; this is -4.*0037

*I start at this first number 4; 4 is right here.*0045

*I am going to start right here and then use the second number to move spaces.*0051

*This number right here is how many spaces I am going to move.*0061

*If it is positive, I am going to move to the right because this is the positive direction.*0064

*If it is negative, I am going to move to the left because left is always negative.*0073

*Since I have a negative number, -2, I am going to be moving to the left two spaces.*0078

*The negative and the positive is to just see which direction you are going to go, to the right or to the left.*0085

*I am going to move this many number of spaces.*0092

*We are starting at 4, moving to the left two spaces.*0095

*I am going to go 1, 2; his is where I land.*0099

*This number right here is 2; my answer is 2.*0104

*Let's do another example; if I have let's say 5 plus -8.*0111

*Again I am going to start off at 5; here is 5 right here; I start right here.*0122

*I am going to move 8 spaces to the left because it is negative.*0129

*Negative is going to make me go left.*0134

*If this was a positive, I would move 8 spaces to the right.*0136

*8 spaces to the left is going to be 1, 2, 3, 4, 5, 6, 7, 8.*0142

*This is where I am going to land.*0151

*That is -3 because it is -1, -2, -3.*0154

*The number I land on is the answer; my answer here is -3.*0157

*That is how you use a number line to add integers together.*0164

*Again integers are all positive and negative whole numbers.*0168

*No decimals, no fractions, just whole numbers and their opposites.*0174

*Another way to add integers without using the number line... first let's remember that opposites add to 0.*0183

*If I have +5 and I have a -5, then they are going to become 0.*0194

*A 5 plus a -5 equals 0; 5 and -5 are opposites.*0203

*As long as they are opposites, if I add opposites together, then my answer becomes 0.*0210

*If both numbers are the same sign, then you are going to add the numbers and keep that sign.*0219

*If they are opposite signs, we will talk about that in a second.*0225

*But let's do an example of this one--if I have -2 plus -3.*0229

*They are both negative; they have the same sign.*0238

*This is negative and this is negative.*0240

*I am just going to add up the numbers and I am going to keep that sign.*0245

*My answer is -5.*0250

*If I have -1 plus -10, then my answer is -11.*0253

*As long as I have the same sign, I am adding two numbers to the same sign,*0260

*then I am just going to add it and keep that sign; that is it.*0265

*Same thing goes with positive numbers.*0269

*If I have 3 plus 6, this is a positive number and this is a positive number.*0271

*We know that 3 plus 6 is 9; +9; you kept the same sign.*0278

*If the signs are opposite, the two numbers that you are adding together have opposite signs, then that becomes a little tricky.*0285

*If I have 2 plus a -3, this one I know is a positive number because integers can only be positive or negative.*0294

*There is no negative sign here so I know it is positive.*0306

*It is +2 plus a -3.*0308

*Since they are opposites, what I am going to do is take the absolute value of both numbers.*0313

*The absolute value, if you don't remember absolute value, then take a look at the lesson right before.*0321

*Absolute value asks me for the distance from 0.*0326

*On the number line, how far away is 2 from 0?*0333

*I know it is 2; the absolute value of 2 is 2.*0336

*The absolute value of this is 3.*0340

*I am actually going to take their absolute values... or I am going to subtract them.*0348

*Basically I am going to just do 3... because the absolute value of -3 is 3... and -2.*0357

*I am going to find the difference; that becomes 1; 3 minus 2 is 1.*0364

*You are going to keep the sign of the number that is greater, with the greater absolute value.*0372

*For this one, this has a negative sign.*0380

*I am going to keep that negative sign; this is a little confusing.*0384

*But just keep in mind that when you have the same sign,*0387

*then it is like you are adding the two numbers and you are keeping that sign.*0392

*When you have opposite signs, it is like you subtract the numbers.*0395

*Then you take on the sign with the greater absolute value.*0400

*Another way you can do this is think of positive numbers as dogs.*0409

*I like to use dogs and cats; you can use anything.*0416

*You can use stars; you can use different colors.*0419

*Let's say positive numbers are like dogs and negative numbers are cats.*0429

*If I am adding dogs and cats together, I am going to add a D for dog and C for cat.*0436

*It is going to be dog and a dog because there is 2 of them, and then 3 cats.*0442

*That is cat, cat, and cat; because it is -3, it is 3 cats.*0447

*Each dog and cat cancels out; they are like opposites, add to 0.*0453

*Dog and cat cancels out; these cancel out; what do I have left?*0460

*I have 1 cat; remember a cat is a negative number; it is a -1.*0465

*I can also use colors.*0472

*If I have a positive, then let's say I am going to use blue.*0475

*Blue circle, blue circle; -3 is going to be red circles.*0478

*Each time I have a blue and a red, I am going to cancel it out; cancel it out.*0488

*What do I have left?--1 red; that makes a negative.*0494

*Let's do a few more examples; add the integers.*0501

*If I have -4 plus -2, I am adding two negative numbers together.*0507

*You can just add up the two numbers and keep the same sign.*0516

*-4 plus -2 is going to be -6.*0520

*If I want to draw it out, -4... red circles because it is negative; -4 plus a -2.*0529

*I don't cancel this out because I only cancel out a blue and a red or opposites.*0541

*These are not opposites; they are the same.*0547

*I can't cancel them; instead I have to add them all together.*0549

*1, 2, 3, 4, 5, 6; 6 and it is red; it is -6.*0553

*Next one, I have -3 plus 8; 3, negative, that is red.*0559

*Then +8; +8 is blue; 1, 2, 3, 4, 5, 6, 7, 8.*0571

*The blue and the red cancels out; cancels out; cancels out.*0582

*Then I have 1, 2, 3, 4, 5 left; blue is positive; it is +5.*0589

*I can leave it like this; or I can write +5.*0598

*Again another way to think of this, you can take the absolute value of each number.*0603

*The absolute value of this is going to be 3.*0608

*The absolute value of this is 8; I just find the difference.*0611

*I subtract them; I can just do 8 minus 3 is 5.*0616

*I take on the sign of the greater number which is 8.*0623

*That is a positive so this becomes a positive.*0629

*The next couple of examples; find the sum; that just means to add them up.*0634

*-15 plus -10; we have a negative number and a negative number.*0639

*I just add them up; my answer is also a negative number, -25.*0650

*The next one, I have a positive number and a negative number.*0660

*Again I take the absolute value.*0666

*I am just going to think of both of these as positive numbers; 37 minus 25 which is 12.*0667

*I take the sign of this number because 37 is bigger than 25.*0680

*That has a sign of negative.*0690

*That means I am going to give this that same sign.*0691

*It is going to be -12.*0694

*Find the value; this one right here, I am looking for x.*0699

*To find x here, -2 plus something is going to give me -7.*0703

*-2 plus what is going to give me -7?*0711

*If I give myself 5 circles or 5 cats, what do I have to add to this?*0722

*Plus what is going to give me 7?--how many more do I need?*0730

*I have 5 here; I have 7 here; how many more do I need?*0738

*I need 2 more, 2 more red.*0744

*That is -2 because red I know is negative; I have to add -2 more.*0748

*The next example, the absolute value of 15 plus the absolute value of -9.*0761

*The absolute value of 15 is 15; the absolute value of -9 is 9.*0767

*My answer is 24; that is a positive.*0778

*Again if it is a positive number, you don't have to write the plus sign, the positive sign.*0784

*You can just leave it as 24.*0788

*The next couple, add the integers.*0791

*Again we have a negative number here plus a negative number here.*0796

*As long as they have the same sign... in this case, they both have a negative sign.*0800

*Then we can just add the numbers together, 12 and 20.*0807

*Or you can add the absolute values together.*0813

*It is 12 plus 20 which is 32.*0815

*You are going to give it the same sign.*0820

*Negative plus a negative equals a negative; -12 plus -20 equals -32.*0823

*The next one, 8 plus -6.*0831

*Again 8 is a positive number even though there is no sign written there*0834

*because numbers can only be positive or negative.*0838

*We know it is not negative so it has to be positive... plus a negative number.*0842

*Again if I want to draw a visual representation of this, this is going to be 2, 3, 4, 5, 6, 7, 8.*0851

*The blue represents the positive number; that is +8.*0862

*My red is going to represent the negative number, -6; 3, 4, 5, 6,*0867

*Each time I have a blue and a red, an opposite, I am going to cancel it out.*0875

*All of these cancel out; what do I have left?--2.*0880

*That is positive because blue is positive; it is +2.*0887

*Or you can just take the absolute value of these numbers.*0893

*The absolute value of 8 is 8; the absolute value of -6 is 6.*0897

*We are going to subtract those numbers; 8 minus 6 is going to be 2.*0903

*This is only when the signs are opposite; so 2.*0909

*Then this was an absolute value of 8 and this was 6.*0914

*The bigger number is 8; that has a sign of positive.*0920

*You are going to give that same sign to the answer which is 2.*0925

*It is going to become +2.*0932

*Again you take the absolute value of each number; subtract them.*0935

*It is 8 minus 6 because absolute value of 8 is 8.*0939

*Absolute value of -6 is 6; 8 minus 6 is 2.*0944

*Then you are going to give it the same sign as the bigger number.*0948

*That is a positive; your answer becomes +2.*0955

*That is it for this lesson on adding integers.*0960

*We will see you next time; thank you for watching Educator.com.*0963

3 answers

Last reply by: mohamed bulhan

Thu Jun 26, 2014 1:50 PM

Post by Noor Mohammad ibrahimi on August 15, 2013

In Adding integers in extra example 3: find the Value: there is an example as follow:

15 + - 9 = 24

I think the answer should be = 6

please let me know if I wrong.

thanks,

Noor

0 answers

Post by Jeanette Akers on October 22, 2012

This is a GREAT visual presentation. MANY years ago I tried to explain how to add and subtract integers to an 8th grade and failed miserably. Had I explained it the way this presentation does, the child would probably have understood how to do this.

1 answer

Last reply by: Milan Ray

Fri Apr 18, 2014 3:43 PM

Post by judy lee on August 22, 2011

I am having struggles with adding and subtracting positive and negative numbers.

Can you help?