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### Course: Class 6 (Old) > Unit 2

Lesson 3: Commutative property# Commutative law of addition

Commutative Law of Addition. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- but in my school i learned it a different way isn't it actually going to be what ever calculation you have for example: 2 times 4 and i know the answer is :8 so when we swap the number it becomes 4 times 2 and so my answer: is 8 so when we swap the numbers around its going to be the same answer(9 votes)
- That is called commutative property! The commutative property also exists for multiplication(5 votes)

- Why is there no law for subtraction and division?(4 votes)
- The properties don't work for subtraction and division.

For example: 7 -2 is not the same as 2 - 7, so commutative property does not work for subtraction.

AND, 8 / 2 is not the same as 2 / 8, so commutative property does not work for division.(7 votes)

- what is 5+5+9 and 9+5+5

and 5+9+5(4 votes)- It is the communative property of addition. Refer to t(2 votes)

- is there any other law of addition(3 votes)
- Keep watching videos, the associative law is coming up. Then there is the additive inverse.(2 votes)

- Are laws and properties the same thing?(0 votes)
- Laws are things that are acknowledged and used worldwide to understand math better. Properties are qualities or traits that numbers have. For example, the commutative law says that you can rearrange addition-only or multiplication-only problems and still get the same answer, but the commutative property is a quality that numbers and addition or multiplication problems have.(5 votes)

- What's the difference between the associative law and the commutative law?(2 votes)
- What does arithmetic mean(1 vote)
- Arithmetic means basic math, or the use of numbers.

Numbers like: 5 + 4, 7 - 3, 2 x 4, etc.

Hope this helps! :)(2 votes)

- well, I just learned about this in class and have a quiz on it in (about) 3 days. I have a question though, how many properties are there? I know we ahve not learned them all but I would like to know!! please help (i just want to know)(0 votes)
- Commutative law of addition: m + n = n + m . A sum isn’t changed at rearrangement of its addends.

Commutative law of multiplication: m · n = n · m . A product isn’t changed at rearrangement of its factors.

Associative law of addition: ( m + n ) + k = m + ( n + k ) = m + n + k . A sum doesn’t depend on grouping of its addends.

Associative law of multiplication: ( m · n ) · k = m · ( n · k ) = m · n · k . A product doesn’t depend on grouping of its factors.

Distributive law of multiplication over addition: ( m + n ) · k = m · k + n · k . This law expands the rules of operations with brackets(4 votes)

- how do u do 20-5? please answer(1 vote)
- You are taking 5 away from 20 of something : 5 taken away from 20 therfore 20-5=15(2 votes)

- This video is for grade 9 people right?(1 vote)
- No, it is meant for Pre-Algebra, or about middle school grade (6-8). It may still be in higher grade math as a refresher of what you've learned.(2 votes)

## Video transcript

Use the commutative law of
addition-- let me underline that-- the commutative law
of addition to write the expression 5 plus 8 plus 5
in a different way and then find the sum. Now, this commutative law of
addition sounds like a very fancy thing, but all it means
is if you're just adding a bunch of numbers, it doesn't
matter what order you add the numbers in. So we could add it as
5 plus 8 plus 5. We could order it as
5 plus 5 plus 8. We could order it
8 plus 5 plus 5. These are all going to add up
to the same things, and it makes sense. If I have 5 of something and
then I add 8 more and then I add 5 more, I'm going to get
the same thing as if I had took 5 of something, then added
the 5, then added the 8. You could try all
of these out. You'll get the same thing. Now, they say in a different
way, and then find the sum. The easiest one to find the sum
of-- actually, let's do all of them. But the easiest one, just
because a lot of people immediately know that 5 plus 5
is 10, is to maybe start with the 5 plus 5. So if you have 5 plus
5, that's 10, plus 8 is equal to 18. Now, let's verify that these two
are the same exact thing. Up here, 5 plus 8 is 13. 13 plus 5 is also 18. That is also 18. If we go down here,
8 plus 5 is 13. 13 plus 5 is also equal to 18. So no matter how you do it and
no matter what order you do it in-- and that's the commutative
law of addition. It sounds very fancy, but it
just means that order doesn't matter if you're adding
a bunch of things.