- [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.
Alright, now let's work through it 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 rewrite the two as 20 tenths.
And so that's gonna be 20 tenths divided by,
instead of writing it this way,
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 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 one tenth.
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.
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 six divided
by one tenth is.
Pause this video and see if you can figure that out.
Alright.
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 divided by a tenth, we ended 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 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 can 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.
Alright, 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 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 100.
Now you could also rewrite this as a 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 one hundredth.
And so this is going to be the same thing as seven times
100 over one.
Or seven times 100.
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 100.