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## Algebra basics

### Unit 1: Lesson 8

Operations with decimals- Adding decimals: 9.087+15.31
- Adding decimals: 0.822+5.65
- Adding decimals: thousandths
- Subtracting decimals: 9.57-8.09
- Subtracting decimals: 39.1 - 0.794
- Subtracting decimals: thousandths
- Multiplying decimals example
- Multiplying challenging decimals
- Decimal multiplication place value
- Dividing decimals with hundredths
- Dividing by a multi-digit decimal
- Dividing decimals: hundredths

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# Adding decimals: 0.822+5.65

CCSS.Math:

Sal solves 0.822+5.65 using "standard algorithm". Created by Sal Khan.

## Want to join the conversation?

- hi

can you divide the ten by the two hundred(0 votes)- yes bc it will turn out to be 2000 thing for asking(5 votes)

- When exactly the "standard algorithm" happens in this solution?(4 votes)
- To use the
**standard algorithm**, follow these steps in order:**Line up the decimal points**`36.413`

12.5

+ 30.08

------------**Fill in the blank spots with zeros**`36.413`

12.500

+ 30.080

------------**Add, beginning with the smallest place first***thousandths*: 3+0+0=3*hundredths*: 1+0+8=9*tenths*: 4+5+0=9*ones*: 6+2+0=8*tens*: 3+1+3=7**Be sure to drop the decimal down into the answer**`36.413`

12.500

+ 30.080

------------

78.993

Hope this helps!(2 votes)

- Why do you put the smallest decimal on top and the longest decimal on the bottom?(0 votes)
- it does not matter you just have to line up the decimals(1 vote)

- Why do decimals seem so complicated all the time?(3 votes)
- I guess it's cause they are kinda big and right away you think ,"UH-OH!"(1 vote)

- 1️⃣Listen, there are 2 types of operations: Commutative and NOT commutative. WHAT DOES THAT MEAN? Here... Commutative: the operations that u can switch numbers in, and when you do so, they give you the same answer. These operations (+ and x) Addition and multiplication.🙌🏻 NOT commutative: the operations that you CAN'T switch between them, and if you do so, it would change the answer and these are the operations. (- and ÷) 🙌🏻 -⏩BY THE WAY, it's NOT wrong to do it the first way, it's just easier, since we have 4 digits and 3 digits, the better is to change to make the addition process easier, that's all!🌻⭐ 2.10+ 10.25// It's better to switch the digits just to make the addition easier. (✅IT'S NOT WRONG TO DO IT THIS WAY❌)👍🤓 It can be written as: 10.25+2.10 // this is called the commutative property.😊📜 10.25+2.10= 12.35 You might find it FASTER this way!😄🤝🏻 HOPE THAT HELPED YOU! #YouKhanLearnAnything!💪It doesn't matter which decimal value is longer or shorter to write, or which comes first or second… In the video Sal arranged the higher valued decimal on top, (he placed the value with 5-whole over the 0-whole), and says it is just his preference, and it would add the same either way.0:10because… ★ Addition is Commutative, (able to be rearranged and still add the same). 2 + 5 = 7 5 + 2 = 7 ★We can have either decimal value on top or bottom, but… ★ We must LINE UP THE DECIMALS to keep each place value aligned throughout the calculation. 0.822 + 5.65 = ? 0.822 + 5.65 ———————— 6.472 ←same answer 5.65 + 0.822 ———————— 6.472 ←same answer ★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. (ㆁωㆁ) Hope this helps someone!(2 votes)
- It doesn't matter which decimal value is longer or shorter to write, or which comes first or second…

In the video Sal arranged the higher valued decimal on top, (he placed the value with 5-whole over the 0-whole), and says it is just his preference, and it would add the same either way.0:10

because…

★ Addition is Commutative, (able to be rearranged and still add the same).

2 + 5 = 7

5 + 2 = 7

★We can have either decimal value on top or bottom, but…

★ We must LINE UP THE DECIMALS to keep each place value aligned throughout the calculation.

0.822 + 5.65 = ?

0.822

+ 5.65

————————

6.472 ←same answer

5.65

+ 0.822

————————

6.472 ←same answer

★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.

(ㆁωㆁ) Hope this helps someone!(3 votes)

- Is'nt the 0.822 suppose to go above the 5.65(2 votes)
- It doesn't matter which one goes on top. It only matters that you line up the decimal points.(0 votes)

- Do you have to wuch thes veteos(3 votes)
- No, but it is usually good to watch them as they might help you or teach you something you didn't know yet.(1 vote)

- It doesn't matter which decimal value is longer or shorter to write, or which comes first or second…

In the video Sal arranged the higher valued decimal on top, (he placed the value with 5-whole over the 0-whole), and says it is just his preference, and it would add the same either way.0:10

because…

★ Addition is Commutative, (able to be rearranged and still add the same).

2 + 5 = 7

5 + 2 = 7

★We can have either decimal value on top or bottom, but…

★ We must LINE UP THE DECIMALS to keep each place value aligned throughout the calculation.

0.822 + 5.65 = ?

0.822

+ 5.65

————————

6.472 ←same answer

5.65

+ 0.822

————————

6.472 ←same answer

★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.

(ㆁωㆁ) Hope this helps someone!(2 votes)- It is plagiarism if you just copy another person's work and act like it is your own. Seed something wrote this 4 months ago, and you just copied word for word. Please delete(2 votes)

- why do the assignments have due dates(1 vote)
- It doesn't matter which decimal value is longer or shorter to write, or which comes first or second…

In the video Sal arranged the higher valued decimal on top, (he placed the value with 5-whole over the 0-whole), and says it is just his preference, and it would add the same either way.0:10

because…

★ Addition is Commutative, (able to be rearranged and still add the same).

2 + 5 = 7

5 + 2 = 7

★We can have either decimal value on top or bottom, but…

★ We must LINE UP THE DECIMALS to keep each place value aligned throughout the calculation.

0.822 + 5.65 = ?

0.822

+ 5.65

————————

6.472 ←same answer

5.65

+ 0.822

————————

6.472 ←same answer

★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.

(ㆁωㆁ) Hope this helps someone!(4 votes)

## Video transcript

We're asked to
add 0.822 to 5.65. So let me rewrite this. And when I rewrite it, I
want to line up the decimals so that we add the right
place to the right place. And so we could write
either number first, although I like to write
the larger number first. So let's write 5.65. And remember, the
important thing is that we line up
the decimal points. So if we write 0.822-- so
we line up the decimal. Let me line up
the decimal first. So I'll write the decimal
right below the other decimal. And it is 0.822. And now we are ready to add. So let's see what's
going on here. So I like to start in
the smallest place. That way, the carrying
works out well. So you might say, wait,
I need to add this 2 thousandths to something. I don't see anything up here. Well, you could say there's just
a 0 thousandths right up here. Then it makes it very clear. Well, 0 thousandths
plus 2 thousandths is going to be 2 thousandths. 5 hundredths plus 2
hundredths is 7 hundredths. 6 tenths plus 8
tenths is 14 tenths. Well, 14 tenths is the same
thing as 4 tenths and 1 one. Another way of thinking about
it is you're carrying the 1. But really, what you're saying
is, look, this is 14 tenths. I could write it as 4 tenths
and a 1, or a ones place, a 1 in a ones place. Then you have 1 plus 5 is 6. And of course, you cannot
forget the decimal. The decimal goes right there. And this is 6.472.