Basic Math Dividing Decimals

Welcome back to Educator.com; this lesson is on dividing decimals.0000

Make sure, when you are dividing decimals, that you apply the correct rules for it.0010

Don't get confused between when you add and subtract decimals and when you multiply decimals.0018

Dividing decimals is actually very different.0023

Before we begin, let's go over some words--divisor and dividend.0027

When divide two numbers together, if I have let's say 10 divided by 2,0034

this top number is the one that is going to go inside the box.0043

That is called the dividend.0050

This top number, the number that goes inside the box, is called the dividend.0052

The bottom number, the one that goes outside the box, is called the divisor.0057

Here is a divisor; here is a dividend.0063

When we divide decimals together, we have to make sure that the divisor becomes a whole number.0068

If this number right here is a decimal, then we have to change it into a whole number.0075

The way you do that is by multiplying both the divisor and the dividend by the same multiple of 10.0080

We don't care if this number is a decimal; it is only the divisor.0090

Let's say that the divisor is 0.2; it is 10 divided by 0.2.0096

That is a little high; 0.2; this is not a whole number.0105

We have a decimal; we have a number behind the decimal point.0114

I count how many numbers are behind that decimal point.0118

There is only one; there is one number.0122

That means I need to multiply this number by 10.0124

0.2, multiply it by 10 so that this will become a whole number0129

because 0.2 times 10 will just become 2.0138

If I have 0.22, I have two numbers behind the decimal point so I have to multiply it by 100.0143

There is two numbers behind the decimal point.0153

I have to have two 0s here as a multiple of 10.0155

That way this will become 22 or 22.0, same thing.0160

We will do a few examples of those.0170

For this one, I have to change the divisor to a whole number.0172

0.2, I have to multiply this by 10.0176

But that means I have to multiply the dividend by 10 also.0179

I can't just multiply one of these numbers by 10.0182

If I multiply 0.2 by 10, it becomes 2; 10 times 10 is 100.0185

This becomes 2; this becomes 100; this will be the actual problem.0193

When you find the answer for this, it is still going to be the same answer as if you were dividing this.0199

That is the rule; you have to make sure that this becomes a whole number.0208

Place the decimal point in the same place right above the dividend; the decimal point here.0213

We don't see a decimal point because it is a whole number.0219

If it is a whole number that doesn't show a decimal point, it is at the end.0222

It is right there; let me make this longer.0226

As long as it is behind the decimal point and at the end of a number,0231

I can add as many 0s as I want.0235

I can add one 0; I can add ten 0s.0237

I can add a million 0s; it doesn't matter.0239

100.0 is the same thing as 100; here is a decimal point.0243

I am going to place a decimal point right above, right there.0247

I know that my answer is going to go on top here.0251

Let me give myself some room.0257

When I solve this, I know 2 goes into 10 five times.0267

0, bring down the 0; 2 goes into 0 zero times.0275

My answer just becomes 50; 2 times 50 is 100.0280

Or if I bring down this 0, again 2 goes into 0 zero times.0285

It is just going to be 50; the answer will be 50.0291

Again the first rule when you divide decimals together is to make the divisor a whole number by multiplying it,0295

multiplying this number and this number to the multiple of 10.0305

That decimal point will go behind the number; it becomes a whole number.0309

Once you multiply that same number to the dividend, you place a decimal point right above here.0315

Then you just divide it the same way.0321

Let's do a few examples; 26.2 divided 0.4.0323

The first number, this is the dividend; this is the divisor.0331

The dividend goes inside the box, 26.2; and then 0.4.0335

I have a decimal in my divisor; I have to make it a whole number.0346

In order to make this 0.4 a whole number, I have one number behind the decimal point.0353

I have to multiply it by 10; 0.4 times 10 is going to be 4.0359

Since I have one 0, I can move the decimal point one time to make it bigger.0368

It becomes 4.0374

If I am going to multiply this by 10, then I have to multiply the dividend by 10.0377

If you want to think of it this way, you can do that.0384

Or a shortcut would be just to move the decimal point once here.0388

Then move the decimal point for the dividend once also.0393

Let me just rewrite this; this becomes 4.0401

My dividend is 262 because the decimal point moved behind the 2.0404

It is right there; then I can place a 0 at the end of it.0412

The next thing I do is to make sure I bring up the decimal point so it is lined up.0418

Then I can just divide it the same way.0424

I know that 4 does not go into 20427

I can put a 0 there; or you don't have to.0429

4 goes into 26; 26 divided by 4.0431

How many times does 4 go into 26?0435

4 times 6 is 24; I am going to write that number right there.0439

24 subtracted; I get 2; I bring down this 2.0451

4 goes into 22 five times; that becomes 20.0457

Subtract again; 2; bring down this 0.0463

This 0 was not there; I placed it there.0468

Because it is behind the decimal point and it is at the end of a number, I can place as many 0s as I want.0471

I can bring down the 2; 4 goes into 20 five times.0477

That becomes 20; then I have 0.0483

I am done with the problem; my answer then becomes 65.5.0488

This is my answer; 26.2 divided by 0.4 is 65.5.0493

Sharon bought six CDs for 42 dollars and 8 cents.0505

How much does each CD cost?0508

If she has this much and she buys the six CDs, each CD costs the same amount.0512

42 dollars and 8 cents divided by 6.0520

Do 42 dollars and 8 cents divided by 6.0526

I don't have a decimal point here.0537

It is at the end; but I have a whole number.0540

I don't have to worry about changing this number, changing my divisor.0542

I can go ahead and just divide.0547

The next step would be to bring out the decimal point; don't forget that.0550

Then I can divide; 6 goes into 42 how many times?0555

Seven; 6 times 7 is 42; that becomes 0.0562

I have to bring down the other number 0.0568

6 goes into 0 zero times; that is 0; 0.0572

Bring down the 8; 6 goes into 8 one time; 6; 2.0577

I can add a 0 at the end of this0588

because it is behind the decimal point and it is at the end of a number.0590

I can bring down another 0.0593

I don't have to; I can just leave it like this.0595

But if I want to round this number, then I can just do the next step.0597

I can just do one more time; 6 goes into 20 how many times?0604

Three; that becomes 18; 2; I can just stop there.0610

Since I know I am dealing with money, I want to see how much each CD costs.0617

I know it is going to be in dollars.0622

Dollars only go to my hundredths place.0624

I only have two numbers after my decimal point.0627

How much is each CD going to cost?--7 dollars and 1 cent.0632

The only reason why I did one more number here was to see0639

if this was a 5 or greater, then this can round up to 2.0643

But it is smaller than 5; I can keep this as a 1.0648

It becomes 7 dollars and 1 cent; that is the cost of each CD.0652

My next example, 77.44 or 77 and 44 hundredths divided by 11.0660

77.44 divided by 11.0668

Rule number one, make sure this divisor is a whole number.0676

It is a whole number.0679

Step two, raise up my decimal point right there; now I can divide.0682

11 goes into 77 seven times; I subtract; this becomes 0; bring down the 4.0689

Fits into this number zero number of times; that becomes 0; subtract it.0701

I get 4; bring down this 4; 11 goes into 44 four times.0707

I get 0; 77.44 divided by 11 becomes 7.04.0716

My next example, I am going to do 45.218 divided by 0.23.0730

Or I can read this as 45 and 218 thousandths divided by 0.23 or 23 hundredths.0737

Remember the first rule in dividing decimals is to make sure that this number, my divisor, is a whole number.0756

It is not a whole number because there is numbers behind the decimal point.0763

I am going to count to see how many numbers I have behind the decimal point.0767

It is two; I have two numbers here.0772

What I am going to do is take that number, 0.23,0775

and multiply it by a multiple of 10 with this number many of 0s.0783

There is two numbers; multiply it by 100 with two 0s; this becomes 23.0789

If multiply my divisor by that number, I have to multiply my dividend by that number also.0795

I can just take this number, move it two places this way.0804

That is the same thing as multiplying it by 100.0807

Then I have to take this decimal point; I have to move it two places.0810

This was where my decimal point was originally.0817

It moves right there, two numbers.0821

Whatever you do to one number, you have to do to the other one.0825

If I write this over, it is going to be 4521.8 divided by 23.0830

When I divide this and get my answer, it is going to be0847

the same thing as if I divide that and get my answer.0850

My second rule is to bring up the decimal point; then I can go ahead and divide.0854

23 goes into 45 one time; this becomes 23.0862

I subtract it; I get 22; I bring down the 2.0871

How many times does 23 go into 222?0876

If you round this to 25, I know that 25 goes into 100 four times.0881

This is 200 and something; I can... let's see.0888

If I just try let's say 9; 23 times...0891

Or if I do 23 times 10, it is 230; that is too big.0900

I know it is going to be a little bit less than that which is 9.0905

23 times 9 is 27; 18, 19, 20... 207.0910

9 goes there; 207 goes there; subtract it; I get... I have to borrow here.0919

This is 12; this is 1; you subtract it; I get 5; this is 1 and 0.0931

What is my next number?--1; I am going to bring down the 1.0941

Again let's see how many times does 23 fit into 151?0945

Again 25 into 100 is four times; let's say 4; let's try 6.0952

On the side, I am going to do 23 times 6; 18.0962

Then let's try the next one; 23 times 7; that is 21... 14, 15, 16.0970

Which one do you think it is?0978

Is it going to be 6 or is it going to be 7?0979

We know it is going to be 6 because 7 is too big.0982

This number is too big; it can't be bigger than this number.0986

I am going to write the 6 here; it is 138.0990

If I subtract it... let me give myself some more room.0997

If I subtract it here, this will be 3... I am just borrowing.1010

This is 4; this becomes 11; 13; what happens next?1017

I have to bring this 8 down; 23 goes into 138 how many times?1025

Look at this; it is the same number.1035

I know that 23 times 6 is 138; 6 there.1037

Let me rewrite this right here; 138; 23 times 6 was what?1044

138; if I subtract it, then I get 0.1049

I have no more numbers to bring down.1054

I have no remainder; my answer is 196.6.1056

That is it for this lesson on dividing decimals.1065

Thank you for watching Educator.com.1068