Pattern when dividing by tenths and hundredths

Let's see if we can figure out what 2 divided by 0.1, or 1/10, is. Pause this video and see if you can figure that out.

All right, now let's work through it together. There are 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 ten tenths, so two wholes is equal to twenty tenths. I could write the two as twenty tenths. That's going to be twenty tenths divided by—and instead of writing it this way, I could write it as zero point one. Now, this is the same thing as 1/10. So, divided by 1/10.

If I have 20 of something and I divide it into groups of 1 of that something, how many groups am I going to have? Well, I'm going to have 20 equal groups of one. So, twenty tenths divided by one tenth is equal to twenty.

Another way that you could approach that is you could rewrite the zero point one, the one tenth, as a fraction. We could rewrite this as 2 divided by—instead of writing 1/10 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 2 times 10. That gets us to the same place we had before. What is 2 times 10? Well, that is going to be equal to 20.

And 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 6 divided by 1/10 is. Pause this video and see if you can figure that out.

All right, well, you could do the same idea. 6 wholes is equal to how many tenths? It's equal to sixty tenths. So I'll rewrite this as sixty tenths divided by one tenth. This is equal to how many? Well, if I have 60 of something and if I divide it into groups of one of that something, I'm going to have 60 equal groups of one. So this is going to be equal to 60.

You might see a pattern: when we divided by a tenth, we end up multiplying by ten. When we divide by a tenth, we are multiplying by ten. You could do the same thing as we saw up here. You could say six divided by one tenth is the same thing as six divided by 1/10 written as a fraction, which is going to be equal to 6 times 10 over 1. Either way, 6 times 10 over 1—which is the same thing as 60—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 want to figure out what seven divided by a hundredth is. What would this be? Pause this video and try to figure it out.

All right, well, we could do the same drill. So seven wholes—one whole is equal to a hundred hundredths. So seven wholes is equal to seven hundred hundredths. So this is equal to—I’ll write it like this—seven hundred hundredths divided by one hundredth. If I have 700 of something and if I’m dividing it into equal groups of one of that something, I’m going to 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 a fraction if you like, so some of the principles we saw up here still apply. We could rewrite this as seven divided by one hundredth, and so this is going to be the same thing as seven times a hundred over one, or seven times a hundred, which once again will get you to seven hundred.

So I think you see a pattern: divide by a tenth, same thing as multiplying by ten; divide by a hundredth, same thing as multiplying by a hundred.