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### Course: 3rd grade > Unit 7

Lesson 3: Associative property of multiplication- Associative property of multiplication
- Properties of multiplication
- Understand associative property of multiplication
- Associative property of multiplication
- Using associative property to simplify multiplication
- Use associative property to multiply 2-digit numbers by 1-digit

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# 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?(0 votes)- 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.(3 votes)

- 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?(28 votes)- 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.(1 vote)

- 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(6 votes)- 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(8 votes)

- Does it matter, if you wrote the answer to be 15 x 3 = (3x3) x 5 = 9 x 5 = 45.4:15/4:30video time.(6 votes)
- 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(6 votes)

- Can we only split even numbers up? :)(4 votes)
- 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`

(7 votes)

- i know this this but i apreceate that you still teach it to learners thank you. :)(1 vote)
- why how what when were(1 vote)
- What is the difference between Associative law and Associate property please ?(0 votes)
- A law and a property mean the same thing in math.(4 votes)

## Video transcript

- [Instructor] In this video,
we're gonna think about how we can use our knowledge of multiplying single digit
numbers to multiply things that might involve two digits. So for example, let's start
with, what is five times 18? And you can pause the video
and see how you might try to approach this, and
then we'll do it together. All right, so if we're trying
to tackle five times 18, one strategy could be to
say, hey, can I re-express 18 as the product of two numbers? And the one that jumps
out at me is that 18 is the same thing as two times nine, and so I could rewrite five times 18. This is the same thing as five times, instead of 18, I
can write two times nine. Now, why does this help us? Well, instead of multiplying
the two times nine first to get the 18, and then
multiplying that by five, what we could do is we
could multiply the five times the two first. And you might be thinking,
wait, wait, wait, hold on a second. Before, you did the two times nine first, and now, you're telling me that you're going to change the order? That you're going to say, hey, let's multiply the five times
two first, is that okay? And the simple answer is, yes, it is okay. If you are multiplying
a string of numbers, you can do them in any
order that you choose, and so this is often known as the associative
property of multiplication. We can associate the
two with the nine first. We can multiply those first, or we can have an association
with the five and the two. We can multiply those two first. Now, why is that helpful? Well, what is five times two? Well, that's pretty straightforward. That's going to be equal to 10. So this is going to be equal to 10. We're doing that same color. 10 times nine. Now, 10 times nine is a
lot more straightforward for most of us than five times 18. 10 times nine is equal to 90. Let's do another example. Let's say we wanna figure
out what three times 21 is. Pause this video and see if
you can work through that. There's multiple ways to do it, but see if you can do it the way we just approached this first example. Well, as you could image,
we want to re-express 21 as the product of smaller numbers. So we could rewrite 21 as
three times seven maybe? And so if we rewrite it
as three times seven, and now, we do the
three times three first. So I'm just gonna put parenthesis
there, which we can do because the associative
property of multiplication. Fancy word for something that is hopefully a little bit intuitive. Well then, this is going to be equal to, what's three times three? It is nine, and then times seven,
which you may already know is equal to 63. Let's do another example. This is kinda fun. Let's say we wanna figure
out what 14 times five is. Pause this video and see
if you can figure that out. Well, we could once
again try to break up 14 into the product of smaller numbers. 14 is two times seven, so we can rewrite this as two times seven or as seven times two, and I'm writing it as seven times two, because I want to associate
the two with the five to get the 10 times five, and then I can multiply
the two times five first. And so this is going to
give us seven times 10, seven times 10, which is
of course equal to 70. One more example. Let's say we want to
calculate 15 times three. How would you tackle that? Well, we can break up 15
into five times three. Five times three, and then we can multiply that,
of course, by this three, and then we can multiply
the threes together first, and then this amounts to five times nine. And five times nine, you might already be familiar with this. This is going to be equal to 45. Another way to get to
45, you can say, hey, five times 10 is 50. So five times 9 is going
to be five less than that, which is also 45.