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  • - [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.

- [Instructor] Let's see if we can figure out

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