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

Lesson 4: Associative property# Associative law of addition

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

## Want to join the conversation?

- Why do you need to KNOW the associative, commutative, and distributive laws?(33 votes)
- It's important if you want to understand the structure of mathematics. It really only becomes very important when you try to look at subsets of numbers (like the numbers on a clock, for example) and talk about how to add or multiply that subset of numbers. (For example, on a clock, 11 + 3 = 2).

If someone has already proven that any subset of numbers that have a certain property will have some other property, than you don't have to prove everything again for each new set; you just have to prove that it has the first property and the rest will follow.(36 votes)

- So the law basically says it does not matter where the parentheses are when it comes to addition?(12 votes)
- Yes, in addition you can put the parentheses in any order over any numbers and your'll still get the same answer.(24 votes)

- I worked this out as 77+5 = 70+12 = 82, is that still the associative law, or something else?(7 votes)
- No that is something else, im not rlly sure what that is..

But the associative is when you move the parentheses in an equation

Ex. (4x3)+5=17 but 4x(3+5)=32

According to the order of operations the answers will not be the same..(1 vote)

- do you need to put parentheses on each problem?(6 votes)
- YOU have to do that because you are telling that you have been adding these two numbers first(3 votes)

- can anybody explain to me what is a parantheses i am from india and here i think parantheses is similar to bodmas -bracket off division multiplication addition subtraction. and i think in india bodmas is another version of parantheses.so can anybody please help me understand it a bit more clearly(4 votes)
- A parenthesis just tells you to solve the equation inside of them before solving anything outside of them. If they are around a single number like -3 it is usually just to keep you from getting confused with a subtraction sign. If you have a problem like 3(5+4) you solve 5+4=9, then multiply by three. If there is no sign outside the parenthesis it means multiply.(4 votes)

- At1:45in the video, he practically says it doesn't matter how you associate the numbers... is that always true?(5 votes)
- Yes it does not mater how you group the numbers it will always come out with the same number.

6+5+2=13

// 5+6+2=13

// 2+6+5=13

// 2+5+6=13

It will always work out the same no matter how you group them.(2 votes)

- What is the associative property of addition?(3 votes)
- (13 + 4) + 8 = 13 + (4 + 8) = 25

Associative Property (for addition) is the rearranging of parentheses -( and ) - which does not effect the sum of the equation(4 votes)

- could some one please explane what the brackets do. Do you do the brackets first? or do you multiply what is in the brackets before you do the sum(3 votes)
- You do whatever is in the brackets like (5*6)+(8*7)= you would do the brackets then do the addition/subtraction/division/multiplication but always follow these rules

B: brackets

I: Indices (exponents)

D: division

M: multiplication

A: addition

S: subtraction

When you come to division it isn't always division then multiplication for example in 5*12/12 you would do multiplication first then division and vice versa for addition and subtraction. Hope this helps :).(1 vote)

- Whats the difference between the associative and commutative laws? i dont understand.(2 votes)
- The commutative law means you can do the problem with the digits in any order, eg.

1+4+9 or 4+9+1 or 9+1+4. No matter how you order the numbers, you are still going to get the same answer (14).

The associative law means to change the order of the digits but show that you still have the same answer, eg. (6+7)+2=(7+2)+6. Both ways equal 15. If you haven't already, I would recommend that you watch the video above and the video Commutative Law of Addition, they are both in the section Number Properties. I hope this helps, this is just my understanding of the laws.(5 votes)

- why for addition its called "Associative", and for multiplication its "commutative"?(3 votes)
- Both addition and multiplication has commutiative properties that tell you that you can add/multiply in any order.

Addition: 2+3 = 3+2

Multiplicaiton: 2(3) = 3(2)

They also both have associative property which tells us that we can regroup (move parentheses) and still get the same result.

Addition: 2+(3+5) = (2+3)+5

Multiplicaton: 2*(3*5) = (2*3)*5

Hopefully you can see, commutative property and associative property are not the same.(3 votes)

## Video transcript

Use the associative law of
addition to write the expression. We have a 77 plus 2 in
parentheses, plus 3, in a different way. Simplify both expressions
to show they have identical results. So this associative law of
addition, which sounds very fancy and complicated, literally
means that you can associate these three numbers
in different ways or you can add them in different orders. Now let me just make
that clear. So the way they wrote it right
here, they wrote it 77 plus 2 in parentheses, and then
they wrote plus 3. These parentheses mean
do the 77 plus 2 before you add the 3. So if you were to evaluate
this, you would evaluate what's in the parentheses first.
So you would say, well, 77 plus 2, that's 79, so
everything in the parentheses just evaluates to 79. And then you still
have that plus 3. And 79 plus 3 is 82, so
this is equal to 82. That's if you just evaluate
it the way that they gave it to us. Now, the associative law of
addition tells us it doesn't matter whether we add 77 and 2
first or whether we add 2 and 3 first. We can associate
them differently. So this is going to be
the exact same thing. This is the exact same
thing as-- we could write it this way. Let me write them all. 77 plus 2 plus 3. If we have no parentheses here,
this is actually the same thing as this over here,
because we'd go 77 plus 2 is 79 plus 3 is 82. But the associative law tells
as, well, you know what? I could do 77 plus 2 plus 3. I could add this first and then
add it to 77, and it's going to be the exact same thing
as if I added these two guys first and then add the 3. Let's verify that
for ourselves. So 2 plus 3 is 5, so this
evaluates to 77 plus 5. And 77 plus 5, once
again, is 82. So it doesn't matter how you
associate the numbers. Either way, you get 82. And that's the associative
law of addition.