Basic Math Adding and Subtracting Decimals

Welcome back to Educator.com; this lesson is on adding and subtracting decimals.0000

When you add and subtract decimals, there are some rules to follow.0008

The first thing, the most important thing, is to align the decimal points.0013

Whenever you have decimal numbers and you have to add or subtract them, make sure the decimal point is lined up.0018

For example, if you are going to add 4.1 with 3.2,0027

you have to make sure that the decimal points, this and this, line up.0036

We are adding these numbers together; this becomes 3; this is 7.0047

After you add them, you have to make sure you place a decimal point in the same place.0055

You just align them straight down right here.0059

4.1 plus 3.2 is going to be 7.3; check by estimating.0065

4.1 is very close to 4; 4 is the whole number that it rounds to.0073

4 plus 3; this 3.2 rounds to 3; so it is about 7.0077

That is what it means to check by estimating.0085

Let's do a few problems; add 3.45 plus 7.835.0088

Again the first rule, the very important rule, is to line up the decimals.0099

Make sure you align them; 3.45.0103

The next number, we don't see a decimal point here.0110

7 doesn't have a decimal point; it actually does; we just can't see it.0114

If we have a whole number that doesn't show a decimal point, then the decimal point is right behind it.0118

It becomes 7.0; 7 is the same thing as 7.0.0126

If you have a whole number with no decimal point, that does not show a decimal point,0132

just place the decimal point at the end of it, right behind it.0136

I need to make sure that the decimal point goes right there; align them.0141

This one, 0.835; again 0.835, align the decimal.0149

That is all that matters; when you add them or subtract them, this is the main thing.0159

You don't line up the numbers; you line up the decimals.0165

We are adding these together.0169

Here, whenever I have decimals, I can place 0s at the end of them.0170

As long as it is behind the decimal and it is at the end, we can add as many 0s as we want.0176

Here it is behind the decimal point and it is at the end.0182

I can put 0s here to fill in those blanks.0186

If I add straight down, this becomes 5; 5 plus 3 is 8.0191

4 plus 8 is 12; 7 plus 3 plus 1 is 11.0197

My answer is 11.285 or 11 and 285.0206

The next problem, find the difference.0215

This is--write the first number--351 and 4 tenths, minus... be careful here.0217

If I write it like this, this would be wrong; this is wrong.0229

I have to make sure not to line up the numbers but line up the decimals.0242

65 and 25 hundredths; I have space right here; I have to put something there.0251

It is behind the decimal point and it is after the number so I can place a 0 there.0266

I can only place 0s if it is behind the decimal point and it is at the very end.0272

0 minus 5, remember I have to borrow; this becomes 3; this becomes a 10.0277

Get 5; 3 minus 2 is 1; decimal point comes down.0284

Again I have to borrow here; this becomes 4; this becomes 11.0291

11 minus 5 is 6; 4, again I have to borrow; this becomes a 2.0298

14; this becomes 8 and then 2; this is the answer.0305

Make sure your decimals are lined up.0314

Don't forget again if you have any empty spaces, you have to place 0s in them0318

because it is behind the decimal point and it is after the number so you can place 0s there.0325

Let's do a few more examples.0331

The next one, we want to add these two numbers, 123.1 and then 140.0334

We have a whole number that does not show a decimal point.0343

In that case, we are just going to place it at the very end.0346

It is going to be 140.0; adding these numbers.0350

It is 1; bring the decimal point down; 3; 6; and 2.0358

Next example, Sarah has 90 dollars and 75 cents.0371

Running shoes cost 55 dollars and 45 cents.0377

How much money will Sarah have left after buying the running shoes?0381

If she is going to buy something that costs 55 dollars and 45 cents, this is how much she has.0386

We have to see how much she will have left; we have to subtract the numbers.0392

She has 90 dollars and 75 cents; she spent 55 dollars and 45 cents.0401

I am going to subtract them; this will be 0; 3.0412

Again I have to borrow; this is 8; this is 10.0421

10 minus 5 is 5; this is 3.0424

After buying the running shoes, Sarah will have 35 dollars and 30 cents left.0429

The next example, we are going to subtract these two numbers.0442

Just write it out; 7 minus... be careful here.0449

The decimal place has to line up with this decimal place.0455

I am going to write 9 under the 2; 91 and 386 thousandths.0458

Again I have an empty space right here that I have to fill in with a 0.0469

Don't forget that; the reason why you have to place that 0 there.0476

If I don't have a 0... let's say I don't have a 0.0480

When you subtract this, this seems like it would be a 6 right here.0486

It seems like you would write a 6 here.0491

But if you place a 0 there, then you know that you have to borrow.0494

This is actually 10 minus 6.0497

If I borrow this, this is going to become 6; 10; 4.0501

Borrow again; 7; 16; there is 8.0507

7 minus 3 is 4; bring down the decimal point.0514

I am going to make this a 10; this becomes 11; this becomes 5.0520

10 minus 1 is 9; 11 minus 9 is 2.0527

5 minus 0 is 5; there is my answer.0533

If you want to check your answer by estimating, this is about 600.0540

If you just round it to the nearest hundreds, it is 600.0546

Here, this is about 90 or maybe let's say 100.0550

600 minus 100 is about 500; we have 500 something; it sounds right.0554

If we had let's say 50 something as our answer, we know that is wrong0562

because we know that if we estimate, it should be around 500.0566

The last example, adding these decimals together.0573

We have 8 and 215 dollars and 49 cents and 75 cents.0578

Remember the rule when we add or subtract decimals is to line up the decimal point.0586

That is very, very important.0591

When we have a whole number that is not showing a decimal point,0593

then we can place a decimal point at the end of it.0597

Just because it is not showing a decimal point does not mean it does not have one.0601

This is 8 point... and then I can add 0s to it.0607

8 dollars is the same thing as 8.00.0610

Then I am going to add 215 and 49 cents; line up the decimal point.0614

It is going to go 215.49; 75 cents here is going to be 0.75.0621

Going to add these all up together; 9 plus 5 is 14.0637

1 plus 4 is 5; 5 plus 7 is 12.0646

Bring down the decimal point; come straight down.0655

1 plus 8 is 9; plus 5 is 14; 1 plus 1, 2; and 2.0660

We are adding money together; don't forget your dollar sign.0669

This is your answer--8 dollars plus 215 dollars and 49 cents plus 75 cents becomes 224 dollars and 24 cents.0674

That is it for this lesson on adding and subtracting decimals.0686

Thank you for watching Educator.com.0689