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### Course: Class 7 (Foundation) > Unit 2

Lesson 2: Properties of whole numbers# Associative law of multiplication

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

## Want to join the conversation?

- Is it possible to mix multiplication with addition??(78 votes)
- It's possible but if you know the order of operations then you know that multiplication comes before addition(6 votes)

- Also,can you mix associative with commutative?(6 votes)
- Yes. You can group and change the position of the numbers at your will, making any possible combination.(15 votes)

- Why are the associative law and the commutative law considered two different laws? The commutative law states that 12 x 3 x 10 = 3 x 10 x 12. The associative law states that (12 x 3) x 10 = 12 x (3 x 10). But that is doing the exact same thing! Doing the parentheses first is the same thing as removing the parentheses and putting the numbers inside at the beginning of the equation! So what is the difference?(10 votes)
- Can you mix subtraction with Addition?(6 votes)
- The associative law only applies to addition and multiplication. It does not work with subtraction or division.

Associate Law = A + (B + C) = (A + B) + C

1 + (2 + 3) = (1 + 2) + 3

1 + 5 = 3 + 3

6=6

I'll try the same formula with subtraction.

1 - (2 - 3) = (1 - 2) - 3

1 - - 1 = -1 - 3

2 = - 4

Simply put, the order in which things occur make a difference. Hope that helps!(8 votes)

- whats the difference between the commutative and the associative property?(7 votes)
- Communitive property is when you change the order of numbers:

A+B = B+A

A*B = B*A

Associative Property is when you change the location of the parenthesis:

A+(B+C) = (A+B)+C

A(BC) = (AB)C(2 votes)

- Why can't there be an associative property of division or subtraction?(4 votes)
- The reason why is because if you try and regroup the numbers, different answers will occur. I hope this will help you!(4 votes)

- For the associative property to work, do you have to keep the numbers in the same order or can they be in a different order?(4 votes)
- The associative property
**only**moves parentheses. It will not move the numbers.

For example: 2 x (3 x 5) can be changed to (2 x 3) x 5

If you want to both move the numbers and move the parentheses, then you need to apply both the commutative property and the associative property.

For example: 2 x (3 x 5)

With the commutative property, we can swap the 3 and the 5: 2 x (5 x 3)

With the associated property, we can not make this into: (2 x 5) x 3

Hope this helps.(5 votes)

- Can you add and multiply in the same question?(3 votes)
- yes as long as you use the order of operations(PEMDAS)(5 votes)

- Why does anyone need to know this?(3 votes)
- Can you change the order of the factors and their parentheses? For example, in the problem in the video, it's (12*3)
**10 and it was changed to 12**(3*10) but can it become (12*10)*3? I'm guessing no, because that never seems to happen, but it's still equal and I'm still not so sure....(2 votes)- Actually, you can do that! As long as you are only multiplying and you have the same factors, regardless of the parentheses and order of the factors, the product will be the same. This means all of the following is equal (a, b, and c are numbers):

abc, a(bc), (ab)c, (a)bc, a(b)c, ab(c), acb, a(cb), (ac)b, (a)cb, a(c)b, ac(b), bac, b(ac), (ba)c, (b)ac, b(a)c, ba(c), bca, b(ca), (bc)a, (b)ca, b(c)a, bc(a), cab, c(ab), (ca)b, (c)ab, c(a)b, ca(b), cba, c(ba), (cb)a, (c)ba, c(b)a, cb(a)

I hope this helps!(3 votes)

## Video transcript

Use the associative law of
multiplication to write-- and here they have 12 times 3 in
parentheses, and then they want us to multiply that times
10-- in a different way. Simplify both expressions
to show they have identical results. So the way that they wrote it
is-- let me just rewrite it. So they have 12 times 3 in
parentheses, and then they multiply that times 10. Now whenever something is in
parentheses, that means do that first. So this literally
says let's do the 12 times 3 first. Now, what
is 12 times 3? It's 36. So this evaluates to 36, and
then we still have that times 10 over there. And we know the trick. Whenever we multiply something
times a power of ten, we just add the number of zeroes that we
have at the back of it, so this is going to be 360. This is going to be
equal to 360. Now, the associative law of
multiplication, once again, it sounds like a very
fancy thing. All that means is it doesn't
matter how we associate the multiplication or it doesn't
matter how we put the parentheses, we're going to get
the same answer, so let me write it down again. If we were to do 12 times 3
times 10, if we just wrote it like this without parentheses,
if we just went left to right, that would essentially be
exactly what we just did here on the left. But the associative law
of multiplication says, you know what? We can multiply the 3 times 10
first and then multiply the 12, and we're going to get the
exact same answer as if we multiplied the 12 times
the 3 and then the 10. So let's just verify
it for ourselves. So 3 times 10 is 30, and we
still want to multiply the 12 times that. Now, what's 12 times 30? And we've seen this several
times before. You can view it as a 12 times
3, which is 36, but we still have this 0 here. So that is also equal to 360. So it didn't matter how we
associated the multiplication. You can do the 12 times 3 first
or you can do the 3 times 10 first. Either way, they
both evaluated to 360.