Basic Math 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 there0834

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