- [Instructor] So what we have here on this number line
that we've now marked off with the tenths
and you can see that this is three tenths here.
We can think about this as a multiplication of a decimal.
And so what is this representing?
And I'll give you a hint.
It's representing something times three tenths.
So pause the video and try to think about that.
Well, let's see.
We are going one times three tenths,
two times three tenths, three times three tenths,
and then four times three tenths.
So what's represented here is four times three tenths,
and so what is this going to be equal to?
Well you can see you go from three tenths,
to six tenths, to nine tenths,
and then you could view this as twelve tenths,
but twelve tenths is the same thing
as one, one and two tenths.
So you could view this as 1.2.
One and two tenths.
Let's do another example.
No, actually I'll do it on the same number line.
If we wanted to represent
three times 0.2
What would that look like on this number line?
And what would this be equal to?
So I'll put a little equal sign here.
Pause this video and see if you an figure that out.
All right, so let's think about where two tenths is
this is one tenth, two tenths is right over there.
This is 0.2, and we're gonna multiply it times three.
So, we're gonna multiply it times one,
then we're gonna multiply it times two,
that takes us to four tenths
and then we're gonna multiply it times three
to get us to six tenths, 0.6.
So it's six tenths just like that.
Now you could also visualize two tenths
as parts of a whole.
So for example, this represents two tenths.
I have this whole, this square is a whole
it's split into ten equal columns here
and we have two of them filled in.
So this represents two tenths.
So if you have three times two tenths,
Well this is one times two tenths,
this is two times two tenths,
and this is three times two tenths.
And so how many tenths do we now have?
Well we have one, two, three, four, five, six tenths.
Which is exactly what we have here, six tenths.
Let's do one more example,
that gets a little bit more involved.
So here we're told to multiply.
It says you many use the models shown
to help find the product.
And this is a screen shot from the exercise
on Khan Academy.
So pause this video
and see if you can figure out what this is.
All right, so they're saying 52 hundredths
times three, and they have 52 hundredths
depicted right over here
and then they have it depicted three times.
So the total number of hundredths depicted here
that is 52 hundredths times three,
because we have 52 hundredths here,
another 52 hundredths, and then another 52 hundredths.
So how many hundredths is that going to be?
Well, you could view this as 52 times three
and that will give you the number of hundredths we have.
So let's think about this.
So if we were to just say 52 times three,
well this is going to be two times three
is equal to six and then five tens times three
is 15 tens, which is the same thing.
We either just write it as 15 tens,
or that's 100 and five tens.
But either way if I have 52 of something
and I multiply that by three,
I now have 156 of that something.
And here the something is hundredths.
So if I say 52 hundredths times three
that's going to be 156 hundredths.
And how do we represent 156 hundredths.
Well there is a couple of ways to think about it
if this is the ones place, this is the tenths place,
this is the hundredths place.
Well we would write the six there, the five there,
and the one there.
So you could recognize this as hey look,
a hundred hundredths, let me color code it,
a hundred hundredths is the same thing as a whole
and I'll circle that in red, and fifty hundredths
is the same thing as five tenths,
and of course six hundredths is the same thing
as six hundredths.
So this is going to be equal to 1.56,
or you could view this as 156 hundredths,
or you could view this as a whole,
which is a hundred hundredths, and five tenths,
which is fifty hundredths, and six hundredths.