Pattern when dividing by tenths and hundredths

- [Instructor] Let's see if we can figure out what two divided by 0.1 or one tenth is. Pause this video and see if you can figure that out. All right, now let's work through this together. And there's a couple of ways that we can approach it. One way is to think about everything in terms of tenths. So two wholes is how many tenths? Well, a whole is equal to 10 tenths, so two wholes is equal to 20 tenths. So I could write the two, rewrite the two, as 20 tenths. And so that's going to be 20 tenths divided by, and instead of writing it this way, I could, instead of just writing it as 0.1, we know this is the same thing as one tenth. So divided by one tenth. And so if I have 20 of something and if I divide it by, into groups of one of that something, how many groups am I going to have? Well, I'm going to have 20 equal groups of one. So 20 tenths divided by one tenth is equal to 20. Another way that you could approach that is you could rewrite the 0.1, the one tenth, as a fraction. We could rewrite this as two divided by, divided by, instead of writing one tenth like this, I could write it as a fraction, divided by 1/10. Well, we know that dividing by a tenth is the same thing as multiplying by 10. So this is going to be equal to two times, two times 10. And that gets us to the same place that we had before. What is two times 10? Well, that is going to be equal to 20. That's good, that we got to the same answer, otherwise these would not be equivalent methods. Let's do another example. So let's say we wanted to figure out what six divided by one tenth is. Pause this video and see if you can figure that out. All right, well, you could do the same idea. Six wholes is equal to how many tenths? It's equal to 60 tenths. So I'll rewrite this as 60 tenths, divided by one tenth, is equal to how many, is equal to what? Well, if I have 60 of something and if I divide it into groups of one of that something, I'm gonna have 60 equal groups of one. So this is going to be equal to 60. So you might see a pattern. When we divide it by a tenth, we end up multiplying by 10. When we divide by a tenth, we are multiplying by 10. And you could do the same thing as we saw up here. You could take, you could say six divided by one tenth is the same thing as six divided by one tenth written as a fraction, which is going to be equal to six times, you could say six times 10 or six times 10 over one, either way. Six times 10 over one. Or, which is the same thing as 10, which is once again going to be equal to 60. So I think you see the general pattern. Divide by a tenth, same thing as multiplying by 10. Now, what about if we dealt with hundredths? So let's say we wanna figure out what seven divided by a hundredth is. What would this be? Pause the video and try to figure it out. All right, well, we can do the same drill. So seven wholes, one whole is equal to a hundred hundredths, so seven wholes is equal to 700 hundredths. So this is equal to, I'll write it like this, 700 hundredths, hundredths, divided by, divided by one hundredth, one hundredth. If I have 700 of something and if I'm dividing it into equal groups of one of that something, I'm gonna have 700 equal groups. So this is going to be equal to 700. So you divide by a hundredth, is the same thing as multiplying by a hundred. Now, you could also rewrite this as fraction if you like, so that some of the principles we saw up here still apply. So we could rewrite this as seven divided by 1/100, and so this is going to be the same thing as seven times a hundred over one, or seven times a hundred. Seven times 100, which, once again, will get you to 700. So I think you see a pattern. Divide by a tenth, same thing as multiplying by 10. Divide by a hundredth, same thing as multiplying by a hundred.