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Associative law of addition

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

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  • leaf green style avatar for user Karl Larsen
    Why do you need to KNOW the associative, commutative, and distributive laws?
    (33 votes)
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    • duskpin ultimate style avatar for user Katharine
      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)
  • starky ultimate style avatar for user Tezz
    So the law basically says it does not matter where the parentheses are when it comes to addition?
    (12 votes)
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  • male robot hal style avatar for user Oliver Davenport
    I worked this out as 77+5 = 70+12 = 82, is that still the associative law, or something else?
    (7 votes)
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  • female robot ada style avatar for user Jyotika
    do you need to put parentheses on each problem?
    (6 votes)
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  • blobby green style avatar for user kabir
    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)
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    • piceratops ultimate style avatar for user Mo
      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)
  • female robot amelia style avatar for user Sam
    At in the video, he practically says it doesn't matter how you associate the numbers... is that always true?
    (5 votes)
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  • leafers seed style avatar for user piggyluv912
    What is the associative property of addition?
    (3 votes)
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  • orange juice squid orange style avatar for user dan walker
    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)
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    • piceratops ultimate style avatar for user VanossGaming
      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)
  • hopper cool style avatar for user Eric
    Whats the difference between the associative and commutative laws? i dont understand.
    (2 votes)
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    • old spice man green style avatar for user SRC
      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)
  • mr pants teal style avatar for user Mala'kak Mundus Gubernavi
    why for addition its called "Associative", and for multiplication its "commutative"?
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      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.