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Lesson 3: Associative property of multiplication

# Associative property of multiplication

Let's explore the associative property of multiplication! This video demonstrates that the order of multiplying numbers doesn't affect the result, using examples like 4 x 5 x 2. The associative property simplifies math.

## Want to join the conversation?

• Is there a difference between the associative and commutative laws? They seem to say the same thing--order does not matter.

The only difference I see is the parentheses in the associative law which is explicitly "associating" two numbers together.
• The commutative property lets you change the order of the numbers. This is the one that tells you that the order does not matter.
Example: 2 * (3 * 5) = (3 * 5) * 2
In this example: the "2" moved, but the parentheses still contain their same numbers.

The associative property tells use that we can regroup (move parentheses).
Example: 2 * (3 * 5) = (2 * 3) * 5
In this example, we regroup by moving the parentheses to now contain 2*3 rather than 3*5

The combination of these 2 properties lets us regroup and change the order of numbers being multiplied and we still get the same result.
• what is the direct simplification of the defenition of what the associative property is? I don't understand this definition.
• The associative property of multiplication let's us move / change the placement of grouping symbols. It does not move the numbers.
For example: (2 x 4) x 5 can be changed into 2 x (4 x 5)
Both expressions create the same result.
• This means that
(5 X 3) X 4 = (5 X 4) X 3 = (4 X 3) X 5
Is is correct ?
• (5x3) x4 = (5x4) x3 = (4x3) x5
The above statement is true.
• How do you use Associative property of Multiplication with 4 nummbers
• you do the same thing, like 3x2x9x7 = 378 7x2x9x3 = 378
• I just do not get it. Can you make another video like that to explain it to me.
• When doing mathematical operations, we put parentheses around the parts that need to get done first. For example, when we put parentheses around (4 × 5) in the following expression:

`2 × (4 × 5)`

...it just means we have to multiply the 4×5 first, before multiplying by 2. So we solve it as follows, by first multiplying 4×5:

`2 × (4 × 5) = 2 × 20`

...and then we can finish it off by multiplying by 2:

`2 × (4 × 5) = 2 × 20 = 40`

When they're talking about the "associative property of multiplication," all they really mean is that when you multiply things together, you can group them into parentheses any way you want, because the result will be the same. And because the part in parentheses gets done first, this means that you can use parentheses to do whichever part of the multiplication you want to do first. For example, all of these expressions give the same final result, even though the parentheses are in different places:

` 2 × 4 × 5 = 8 × 5 = 40`
`(2 × 4) × 5 = 8 × 5 = 40`
` 2 × (4 × 5) = 2 × 20 = 40`
(1 vote)
• Thank you this helped me so much
• Does that mean that it could be written in different order and still be the same answer?
(1 vote)
• YES that is exactly what it means!
(1 vote)
• what Associative property of multiplication?
(1 vote)
• The associative property of multiplication means that any order you multiply in, it will equal the same answer.

For example, 2*3*4=24, and 4*2*3=24, and 4*3*2=24, and 3*2*4=24, and 3*4*2=24.

They are all equal because it is multiplying the same numbers, just in a different order each time. This is the associative property of multiplication.
(1 vote)
• Does it need to be only odd or even?
• Every number that exists is either odd or even, so yes. You can mix odd and even numbers, or have two of the same. I hope this helped! Comment if you have any questions!
• Use the associative property of multiplication to find the missing number 2x(8X3)=(2x8)x
• 2 × (8 × 3) = (2 × 8) × ?

The associative property of multiplication says
2 × (8 × 3) = (2 × 8) × 3

This gives us
(2 × 8) × 3 = (2 × 8) × ?

So, now it says that multiplying (2 × 8) by 3
is the same thing as multiplying (2 × 8) by "?"

Thereby, "?" must be equal to 3.