Relate multiplication and division
- [Voiceover] Let's say someone walks up to you on the street and says to you, 50 divided by five, 50 divided by five is equal to blank, is equal to blank. How can you think about this as a multiplication problem? Well, whatever blank is, whatever blank is, if you multiply it by five, if you multiply by five, you should get 50. You should get 50. You should get 50. So one way of thinking about it, you could say "what times five is 50?" Well, 10 times five is 50. 10 times five is 50, so 50 divided by five is going to be 10. Hopefully you see the relationship here. If 50 divided by five is 10, then 10 times five is 50. 10 times five is 50. And you could do it the other way around. What is 50 divided by 10 going to be? 50 divided by 10, well that's going to be equal to five. 50 divided by 10 is going to be equal to five. How do I know that? Well, five times 10, five times 10, five times 10, is equal to 50. Is equal to 50. So let's keep thinking about this. If someone walked up to you in the street again, and said blank, blank, divided by, divided by two, blank divided by two is equal to, is equal to nine. How would you figure out what blank is? Something divided by two is equal to nine. Well, one way to think about it, and if we just follow here, if you said 50 divided by five is 10, you could say 10 times five is 50, so right over here we could say well, nine times two, nine times two, must be equal to blank. Must be equal to our blank. Well we know what nine times two is, that is 18, so this must be 18. 18 divided by two is nine. And that's really describing how 18, two, and nine relate to each other. Two nines is 18, or nine twos is 18, or if I were to divide 18 into two groups, each group would have nine. Or if I were to divide into groups of two, you would have nine groups. Any way you look at it, 18 divided by two is nine, nine times two is 18. Let's do one more of these. So, someone walks up to you on the street, and tells you, and tells you that 12 divided by, divided by blank, 12 divided by blank is equal to three. Is equal to three. What is blank going to be? Well one way to think about this is three times blank is going to be equal to 12. Three times blank, three times this unknown number, is going to be equal to 12. And three times what is equal to 12? Well three times four is equal to 12, so 12 divided by four is equal to three.