- [Instructor] Welcome.
So let's see if we can figure out
what eight divided by 0.4 is.
Pause this video and see if you can work through that.
All right.
So we're trying to figure out what eight ones
divided by four tenths is.
And so one way to think about it
is to think about everything in terms of tenths.
So eight ones.
One one is equal to 10 tenths,
so eight ones is equal to to 80 tenths.
So this is equal to 80 tenths.
And I'm dividing it by four tenths.
So divided by four tenths.
So if I have 80 tenths,
and if I wanna divide it into equal groups of four tenths,
how many equal groups am I going to have?
Well I am going to have 20 equal groups of four tenths.
That would make up 80 tenths.
80 divided by four is 20.
So eight divided by four tenths is equal to 20.
Another way that we could've approached that
is we could've thought about it in terms of fractions.
We could've said, hey, eight divided by four tenths,
that's the same thing as eight
divided by four tenths,
which is the same thing when you divide by a fraction.
It's the same thing as multiplying by the reciprocal.
So this is the same thing as eight times
10 over four,
or you could view it as the same thing as eight over one.
Eight ones times 10 over four.
Times 10 over four.
In your numerator you get eight times 10,
so that is going to be equal to,
I'll do it in this orange color,
eight times 10 is equal to 80.
And then in our denominator
we're going to have one times four.
I didn't circle the one.
You're going to have the one times the four.
So that's just going to be equal to four.
So 80 fourths, or 80 divided by four,
once again that is going to be equal to 20.
Let's do another example, but in this case,
let's deal with hundredths.
So draw a line here.
And so let's say that someone walks up to you on the street
and says, "Quick,
"what is 48
"divided by
"0.24?"
Pause this video and see if you can figure that out,
and I'll give you a little bit of a hint.
The techniques we just did might apply.
Although now we're dealing with hundredths.
All right now let's work on this together.
Well one way to work on it is you could view this as 48.
You could just convert everything to fractions.
As 48, and actually I can just write it as 48 over one,
divided by
24 hundredths
24 hundredths.
This division sign looks a little bit weird.
Let me make it look a little bit more normal.
There you go.
And so when you divide by a fraction
that's the same thing as multiplying by the reciprocal.
We've seen that before.
So this is equal to 48 over one
times 100 24ths.
And so our numerator here
is going to be equal to 48 times 100.
Actually I'm just gonna write that out as 48 times 100
in the numerator.
And then our denominator is going to be 24 times one.
Well that's just would equal to 24.
And so what is this going to be equal to?
48 times 100 divided by 24.
Well we could divide the numerator
and the denominator by 24.
If we did that, 48 divided by 24 is two.
And 24 divided by 24 is one,
so we're left with two times 100 divided by one.
Well two times 100 is equal to 200.
And then you divide that by one, you still get 200.
So there you have it.
This is equal to 200.
Now another way that you could have approached this
is you could've thought about everything again,
in terms of hundredths.
And so 48 ones is the same thing as 4800 hundredths.
So it's equal to 48.
4800 hundredths.
So let me write that down.
Hundredths.
Divided by 24 hundredths.
So if I have 4800 or 4,800 hundredths,
and if I wanna divide it into equal groups of 24 hundredths,
how many of those equal groups would I have?
Well you would have 4,800 divided by 24 equal groups.
So this is going to be equal to
4,800.
Divided by 24.
Now 4,800 is exactly what we had up here.
And so we already saw
that 4,800 divided by 24 is equal to 200.
And if you just got to this point,
and if you said, hey, how could I work on this?
You could just say, hey, let me divide
the numerator and the denominator by 24.
You could try to re express 4800 as 48 times 100.
Or you could even say that 48 is 24 times two,
and then you're gonna multiply that times 100
to get to 4,800.
And then the division is a little bit more straightforward.
But the big picture here is to realize
that dividing by decimals is not some mysterious thing
when you think about it in terms of place value
or when you think about it in terms of fractions.