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### Course: Arithmetic (all content)>Unit 3

Lesson 3: Properties 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.
• Does that mean that it could be written in different order and still be the same answer?
• YES that is exactly what it means!
• does anyone just love math after once hating it and saying that you would hate it for eternity
• I problably did. Without Sal, I would be hating it right now.
• Thank you this helped me so much
• I just do not get it. Can you make another video like that to explain it to me.
(1 vote)
• 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`
• How do you use Associative property of Multiplication with 4 nummbers