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### Course: Arithmetic>Unit 2

Lesson 8: Associative property of multiplication

# Using associative property to simplify multiplication

Sal uses the associative property to multiply 2-digit numbers by 1-digit numbers.

## Want to join the conversation?

• I was doing some problems along with him to see if I got different answers, when he did 15x3 I broke it up into 8x3x7 which equals 168, but 15x3 is 45.

I broke the 15 up into two parts {8 and 7 = 15} then I took the 3 and put it in-between {8x3x7} does not equal 45, where did I go wrong?
• You split 15 into 2 numbers that add to 15. You need to split it into 2 numbers that multiply to 15.
15 = 5*3
So, you could have done: 5*3*3

Hope this helps.
• Can't we do like that 3*21 = (3*20)+(3*1)=60+3=63
For me it is much more easier to do them
like 83 *4 =(80*4)+(3*4)=320+12=332?
• You are actually using the distributive property, not the associative property.
You split 21 into 20+1 to get to 3(20+1)
Then, you distributed the multiplication across addition to get 3(20)+3(1). This is what the distributive property allows us to do.

The video is showing how to use the associative property to multiply. Associative property lets you regroup numbers being multiplied. It is all multiplication (no addition like you used).

Your teacher will likely want you to know the difference between the different properties.
• Honestly? It's sort of hard depending on how you're thinking about things. Maybe the entire concept of this flew over my head and I'm doing it the wrong way but whenever I see 14x5 my brain just multiplies 5 by whatever comes to mind that's easiest to remember.

14x5=
5x5 + 5x5 + 5x4
so
25+25+20= 70
• I say do whatever way is easier for you

For me, I'm pushing myself to relearn a bunch of old math concepts because I slept way too much in math class in grade school lol

Anyways I think what helped me build splitting up multiplication problems to do them easier was practicing the base concept of multiplication

Where 2 x 3 = 3 + 3

And Distributive Property where 2 x 3 = 2(3+3)

At first is seems pointless to do but when you practice it enough and slowly start doing bigger numbers like 6 x 9 = 6(10-1) = 60 - 6 = 54

It'll make doing math quicker not just on paper but even in your head

I just say keep practicing trying to solve math problems with different techniques and even if you got the answer in another way force yourself to solve it differently so you get the sense of different solutions
• Does it matter, if you wrote the answer to be 15 x 3 = (3x3) x 5 = 9 x 5 = 45. / video time.
• Good question!

It doesn't. In multiplication, the product will be the same no matter what order you write the numbers:

3x4x5 = 5x3x4 = 4x5x3 = 3x5x4 = 60
• Can we only split even numbers up? :)
• We can split up odd numbers too, if they're not prime. In other words, for any number that can be evenly divided by another whole number (other than itself and 1), we can split it up. For example, in the following expression:

`15 × 5`

...15 is an odd number, but we could split it up into 3×5:

`3 × 5 × 5`

Then we could multiply it out as follows:
` 15 × 5`
`= 3 × 5 × 5`
`= 3 × (5 × 5)`
`= 3 × 25`
`= 75`
• I kinda couldn't understand this whole lesson. Can somebody help me out?
• In a nutshell, this is about breaking up two-digit numbers into multiplication of one-digit numbers, changing the order of multiplication (using the associative property), and making the problem easier.
It's just a tiny thing you can do to make the problem a lot, lot easier to solve.
Hope that helps