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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 6

Lesson 6: Adding decimals: standard algorithm# Adding decimals: 9.087+15.31

Sal solves 9.087+15.31 using the "standard algorithm". Created by Sal Khan.

## Want to join the conversation?

- how did you get the decimals to line up with each other and why do you put a number off to the side(206 votes)
- You line up the
*decimal points*.

Wrong`1.23`

+45.6

-------

0.579

Correct`1.23`

+45.60

--------

46.83(524 votes)

- how does this help us in a real life situation(17 votes)
- You have to use decimals when go shopping. because if something cost 28.34 and then you also get another thing that costs 15.24 you have to add them so u know how much u spending(23 votes)

- how do you do it(11 votes)
- ★
**Use the decimals to guide the place value alignment.**

• line up the decimals above and below,

•*then add each column of numbers*,

• empty spaces are equal to zero

9.087 + 15.31 = ?`9.087`

+ 15.31

—————————

24.397 ←🥳 answer

★In**Addition**order doesn't matter, because it's**Commutative**,*meaning we can rearrange addition and get the same answer*,

1 + 7 = 8

7 + 1 = 8

So**either decimal value can be first or second**, but*always line up the place values*.`15.31`

+ 9.087

—————————

24.397 ←🥳 same answer

★This method works for more than two values as well, as long as we*always line up the decimals so that the place values form columns*!

2.14 + 0.3421 + 3 + 11.2 = ?`2.14`

0.3421

3

+ 11.2

——————————

16.6821 ←🥳 answer

Rearranged,

with place keeper zeros…`11.2000`

3.0000

0.3421

+ 2.1400

——————————

16.6821 ←🥳 same answer

★ Just remember: we**must**throughout the calculation,*line up the decimals*and keep the place values aligned**move the decimal straight down,**, then it's just adding the columns like usual…*so it is aligned in the answer too*

Start adding in the far right column, carry values to the left, etc…

(ㆁωㆁ) Hope this helps someone!(14 votes)

- I made a chart and placed them into the chart to solve it, is that smart?(5 votes)
- yes, it is very smart! i learned how to solve it using a chart, and it's good that you still use it as a strategy! ^^(6 votes)

- is it allowed to add an zero at the whole number?(5 votes)
- I mean I get ur question. You can add a zero at a whole number. HOWEVER it won't change the answer. For example, 5+0=5. But it is allowed but no use.(6 votes)

- hi can i have a upvote(6 votes)
- yes u can :>(3 votes)

- Is it compulsory to line the decimals(4 votes)
- Corresponding place values must be added together, the decimals naturally align when the columns are in the correct order.

Therefore aligning the decimals is an easy way to align the place values correctly into columns for manual addition.

So, when creating accurate addition columns, it is also compulsory to line up the decimals.(0 votes)

- Do you align the decimals even if you are multiplying decimals(3 votes)
- if you are multiplying decimals, you do not have to line up the decimal points. You keep the decimal points in the correct space in the numbers, but otherwise, write it out like a normal multiplication problem. You solve it like a normal problem too. so if it is 1.5 X 3.4, you would write it out like a normal multiplication problem:

2

3.4

x1.5

--------

1

1 7 0

+3 4 0

-------

5 1 0, but to put in the decimal point, you have to think of the original numbers, which were 1.5, and 3.4, 1.5 had one number to the right of the decimal point, so note that, and 3.4 also had one number to the right of the decimal point, So note that as well, add that up and it means that you have to put the decimal point in the problem so that it is to the left of two numbers, so the answer is not 510, it is 5.10.(2 votes)

- bruh when will this matter in life it's not like i am going to have 9.087 dollars.That's impossible.(5 votes)
- you line up your decimal in subtraction also(4 votes)
- Yes, you line the decimals up in addition and subtraction.(2 votes)

## Video transcript

Let's see if we can
add 9.087 to 15.31. And I encourage you
to pause the video and try to do it on your own. So I'm assuming you have
tried to do it on your own. And now let's see how we
could actually tackle this. Now, one thing I want to
point out, some of you all might have seen
these numbers all lined up and immediately want
to say, hey, 7 plus 1 is 8, and 8 plus 3 is 11, carry
the 1, et cetera, et cetera. And if you did that, you
would be making a mistake. Because, you see,
right over here, these decimals aren't lined up. Here, if you did that, you would
be adding the 7 thousandths to 1 hundredths. You would be adding
0 tenths to 5 ones. You would be adding 9 to 1
tens, or essentially, this is a 10 right over here. So the places would
be all mixed up. So what you need to do is to
actually align the decimals so that your place
values are aligned. So what you want to do is
you want to align things up. So we could write 9.087. And then we want to
align the decimal. So let's align the decimal. This is what has to match up. And this is going to be 15.31. And this should hopefully
make sense to you as well. This is 9 point something
plus 15 point something so it's going to be--
If you add 9 to 15, it will be 24 point something,
give or take a little bit. And you see that here. Here you have a 9 plus the 15. So you have lined up the
appropriate place values. And now we are ready to add. It's a good idea to start
with the smallest place value, so if you have any extra
at a certain place, you can bring something
into the next place value. So here you say 7 plus--
well, this is 7 thousandths. It's in the thousandths place. And you might want to-- you
say, well, what do I add it to? There are no thousandths
right over here. And you're right. There are no thousandths. So we could literally
write 0 thousandths. So 7 thousandths plus 0
thousandths is 7 thousandths. 8 hundredths plus 1
hundredth is 9 hundredths. 0 plus 0 tenths plus
3 tenths is 3 tenths. We got our decimal. Then you have 9 ones
plus 5 ones is 14 ones. Well, 14 ones is the same
thing as 4 ones and 1 ten. So we'll carry that
1 right over there. This is just 1 ten plus
4 ones, which is 14. And so then finally, you have
1 ten plus another ten is 2. So we get 24.397.