– [Instructor] So, what we’re gonna do is get a little bit of practicing

multiple numbers together and we’re gonna discover some things. So, first I want you to figure out what four times five times two is. Pause the video and try to

figure it out on your own. Alright, so whatever your answer is, some of you might have done it this way, some of you might have said hey, what is four times five and then you multiplied it by two, so what you would really have done is you would have done

four times five first, so that’s why I put

parentheses around that and then you would have multiplied by two and what would you have gotten? Weil, the four times five part, that is of course 20 and then you multiply that times two and you would get 40 which of course would be correct, four times five times two is indeed equal to 40. Now, what I want you to do now is as quickly as possible try to figure out what five times two times four is. Really quick, pause the

video, try to figure that out. Well, some of you might have tried and you might have done

it in a similar way where you tried to figure

out five times two is first and you said okay, five times two is equal to 10 and then I’d multiply that times four and then you would say well, gee, this is same thing as I got last time. Is there something interesting going on? And the interesting thing that you might realize is in both cases we’re multiplying the same three numbers. We are just doing it in a different order. Here we multiplied four times, we wrote it out in a different order, four times five times two. Here we wrote five times two times four. Here we did the four times five first, here we did the five times two first but notice we got the same result. Now, I’d encourage you, pause this video. Try to multiply these numbers in any order, maybe you do two times four first. In fact, let’s just do that. Let’s do two times four, two times four and then multiply that by five. What is this going to be equal to? Well, you might notice again this is two times four is eight, you multiply that times five. Well, once again, we got 40, so you might see a pattern here. It doesn’t matter which order

we multiply these things in. In fact, you could write

four times five times two. You could do the four times five first, four times fives times two or you could do four times five times two, so you could do four times five times two. So, it doesn’t matter which order you multiply these things in. In every case you are going to get 40. Now, there’s a very fancy term for this, the associative property of multiplication but the main realization

is and it’s not just true with the three numbers, in fact, you’ve seen something similar with two numbers where it doesn’t matter what order you multiply them in but what you see with three numbers and even if you tried it with four or five or really 1,000 numbers being multiplied together, as long as you’re just

multiplying them all, it doesn’t matter what

order you’re doing it with. It doesn’t matter in what order you associate them with. Here we did four times five first, four times five first, here we did five times two first but in either case we got the same result and I’d encourage you, after this video, try to draw it out. Try to think about why that

actually makes intuitive sense, why this is true in the world and it’s nice because

it simplifies our life when we’re doing mathematics and not only now but in our

future mathematical career.

## 8 Comments

## Ruby P

WOOHOO I'm first comment!! OH YEAH!

## Lรฉa LEPETIT

Hi ! I'm looking for the software used to make this video if someone know the name

## chen adam

Which playlist can I find the new uploaded videos in khan academy ?

## Stephen Psalm Lozano

Fourth

## Lion Alesso

The numbers can be changed in any order in multiplication and also in addition.

## Hope Solberg

hi

## Jahrid Geonzon

Wow love your vid thanks for helping๐๐๐๐๐๐๐๐๐๐๐

## aaron salomon

Angry cats