Basic Math Integers and the Number Line

Welcome back to Educator.com.0001

We are going to talk about integers and the number line.0003

What are integers?--integers are all positive and negative whole numbers.0008

Whole numbers are all numbers that are whole; no decimals, no fractions.0016

Numbers like 4, 5, 10, 20, 100, 0, those are all whole numbers.0024

All whole numbers and their opposites...0034

Opposites just mean that if I have a whole number like 5, the opposite would be -5.0037

It is basically all whole numbers because whole numbers are only positive numbers including 0.0045

When you say whole numbers and their opposites, integers include whole numbers0053

and the negative of the whole numbers; positive and negative whole numbers.0060

-3 is an integer; -5 is an integer; and so on.0068

If I have a number line right here, this is a number line.0076

I am going to make that 0 right in the middle.0083

All of my numbers to the right of it are going to become positive.0089

If this is 1, 2, 3, 4, 5, 6, 7, 8, this right here then on the other side of 0 are negative numbers.0095

This one is going to start off at -1, -2, and so on, -3, -4, -5, -6, -7, -8.0111

It is going to keep going; this is 1, 2, 3, 4, 5, 6, 7, 8.0123

This is -2, -3, -4, -5, -6, -7, -8, right there.0129

This is a number line that includes positive numbers and negative numbers.0136

The opposite of 8 is going to be -8.0143

But all of these together are called integers.0149

Absolute value is the number's distance from 0; distance from 0.0156

If I ask you what is the absolute value of 3?0165

How many units or how far away is 3 from 0?0169

If it is 0 right here and 3 is right here, the absolute value of 3 will be 3.0177

It is 3 units away from 0.0182

If I ask you the absolute value of -3, the distance away from 0 is going to be 3.0185

Distance we know cannot be a negative number.0195

Whenever they are asking for a distance, make sure that the number is a positive number.0199

In this case, when I ask for absolute value of a number,0203

whether it is positive or negative, it is going to have to be positive.0206

This is how you would write it; absolute value of x.0213

You are going to write a 1, but make sure it is a little bit longer.0216

Then you are going to write the number inside.0221

Two bars, in between two bars, and then the number inside; this is the absolute value of x.0224

If I ask you what the absolute value of 5 is, then my answer is 5 because it is 5 units away from 0.0234

If I ask you what the absolute value of -5 is, again -5 is right here.0246

It is 5 units away from 0; this is also 5.0254

It is just asking how far is it from 0; that is absolute value.0261

Whenever you have an absolute value of a number, you are just taking the positive of it.0267

You are making it positive.0272

Let's go over a few examples; let's compare the integers, 3 and -5.0276

I just want to know which one is bigger than the other.0282

3 and -5; negatives are very small.0289

Positive numbers I know are bigger than negative numbers.0296

If you have the number line again, as the numbers go to the right, they become bigger.0300

This way is bigger; if the numbers go this way, then it gets smaller.0311

Positive numbers are big; negative numbers are small.0321

If one number is positive and one number is negative, I know...0324

By the way, this doesn't have a plus sign in front of it to show that it is positive.0328

But if there is no negative sign, then that means it is positive.0333

+3 and -5, I know that +3 is greater no matter what these numbers are because this is negative.0338

This is positive; this is negative.0349

Positive numbers are always greater than negative numbers.0351

The next one, -2 and -4, they are both negative.0356

But I want to see which one is greater, which one is bigger, which one is smaller.0361

If I make this 0, then here is -2.0370

Here is -4 because it goes -1, -2, -3, -4.0375

Remember the numbers that go this way, that are on the right side of it, are bigger.0382

The numbers that are on the left side are smaller.0388

-2 is on the right side.0391

It is closer to 0 or to the positive side than -4 is.0395

So I know -2 is bigger than -4.0400

In this case, -2 is greater than -4.0405

You can also think of this as money.0410

If you want to think of it that way, you can.0416

-2 means that maybe you owe money.0420

A negative, you either owe 2 dollars or you can owe 4 dollars.0427

You know that owing 4 dollars is worse than owing 2 dollars.0435

If you owe 2 dollars, then that means that you have more value or that it is bigger0441

because you owe less, because the more you owe, the worse it is.0449

So -2 is going to be bigger than -4.0452

10 and -10; 10 is +10; this is -10.0457

Automatically 10 is greater because this is positive and this is negative.0466

I would rather have 10 dollars than owe 10 dollars.0475

The next one, this is positive; it is +8.5 and -8.9.0479

Don't get confused with these numbers because... just look at this line.0487

This is a positive number; this is a negative number.0490

I know that this number is bigger.0494

What if I make this number negative, -8.5 and -8.9?0496

Let's see; let me draw this out a little bit bigger.0509

If I have a number line, if I make the 0 right here, here is -8 and here is -9.0511

I know that both numbers are going to be in between -8 and -9.0522

Which one is closer to -9?--which one is closer to -8?0530

-8.5 would be right in the middle of -8 and -9.0535

-8.9 is actually very close to -9, right here.0542

This number of -8.5 would be greater because it is closer to the right.0548

It is on the bigger side; this one is going to be greater than -8.9.0556

Write an integer to represent each; 200 feet below sea level.0566

This is the keyword here, below.0573

If it is below, then I know it is going to go negative.0575

If it goes above, then it is positive.0578

200 feet below sea level is going to become -200 feet or -200.0582

I don't have to write the feet; it is just write an integer.0590

A gain of 30 yards, if you are gaining something, then it is a positive value.0594

Here is the keyword, gain; that is +30.0601

The next one, a decrease of 100 points.0606

Decrease, the keyword, means you are losing it; increase means you are gaining.0610

Decrease would be negative; -100.0619

12 degrees below 0; below so it is going to become -12 degrees.0625

Write the opposite integer; remember we talked about opposites.0640

How if you have a number line, then it is going to be on the other side of 0.0644

The opposite of -3 is going to become +3; or I can just write 3.0650

+94, the opposite is going to become -94; -50, +50 is the opposite.0659

Again this doesn't have a plus sign in front of it.0670

But I know it is a positive because numbers can only be positive or negative.0672

There is no negative sign; it has to be positive; this is -48.0678

The fourth example, find the absolute value of these numbers.0689

Absolute value remember again was the distance from 0.0697

How far away is that number from 0?0700

Distance, if I am asking you how far away something is, we know we can't have a negative number.0705

We have to have a positive number; distance can only be positive.0710

The absolute value of 45 is 45; 45 units away from 0.0715

+98, 98; absolute value of 10 is going to become 10.0728

Here the absolute value of 726 is 726.0741

If I have the absolute value of -10, on the number line, -10 is to the left of 0.0748

It is on the negative side.0759

Again if I am asking you how far away -10 is from 0,0762

then it is just 10 because it is 10 spaces away from 0.0766

Whether it is to the right or to the left, it is still 10 units, 10 spaces.0771

If I have an absolute value of a negative number again, then it becomes positive.0775

We can never have a negative distance.0780

Even if you find the absolute value of a negative number, then it is still going to be positive0785

because you are just finding the distance; that is it.0791

That is it for this lesson on absolute value and introducing integers.0796

Thank you for watching Educator.com.0803