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## Dividing fractions and whole numbers

# Dividing a fraction by a whole number

CCSS.Math:

## Video transcript

- [Instructor] Let's
see if we can figure out what 2/3 divided by five is equal to. Pause this video and see
if you can figure this out. Well, there is a couple of
ways that we can approach it. We can first do it in a conceptual way, think about it visually. To do that, let me represent 2/3, so let's say that what I'm drawing right over here is a whole. This is a square, and
it represents a whole. Now, I can divide into
three equal sections. I'm gonna try to hand-draw that. So, this is, that looks pretty good, three equal sections here. Each is 1/3, and we have 2/3, so we are really representing all of this stuff right over here. That is two of my thirds. Now, I wanna divide those 2/3 by five. Well, the way I could do this is I could divide it into
five equal sections. But, if I'm doing it, I might as well just divide everything, all the thirds, into five equal sections,
so let me do that. So, one, two, three, and then
four, and five equal sections. So, what is one of those
five equal sections of my original 2/3? Well, this right over here is one of those five equal
sections of my original 2/3. Notice I could draw that, I
could draw another one here, another one here, another one
there, and another one there, and I would have five equal
sections that make up those 2/3. But, what does just one of them represent? And if we figure out what
this represents of the whole, then we know what 2/3 divided by five is. Well, when I took my
thirds and I divided them into five equal sections, I
essentially constructed 15ths. How do I know that? Well, I had one, two, three thirds, and then I divided it into one, two, three, four, five sections, so each of these squares
right over here is a 15th. You have three times five, and you could count 'em if you like. And, what we have circled off
in red is two of these 15ths. We have 1/15 right over here, and then 2/15 right over there. So, this is going to be equal to 2/15. Now, another way that
you could think about, and over time this is the
way you will approach it, but it's nice to think
about it conceptually, when you divide by any number, it's the same thing as
multiplying by the reciprocal. So, five is the same thing
as five wholes, or 5/1. And so, 2/3 divided by
five is the same thing as 2/3 times the reciprocal of five, or the reciprocal of 5/1,
which is you just swap the numerator and the
denominator, which is 1/5. And so, another way of
thinking about this is this is 1/5 of 2/3, which
it once again will be this section right over here. The way you could compute this, conceptually, you see that this is 2/15, but you could also say well,
I could just multiply it. When I multiply fractions I can just multiply the numerators. Two times one is two. We do that same red color. Two times one is two, and then I could multiply
the denominators. Three times five is 15. And, hopefully, what we just drew out may help make sense of
why dividing by something is the same thing as
multiplying by the reciprocal. Then, when you multiply fractions, it's the same thing as
multiplying the numerators to get our new numerator,
and then multiplying the denominators to get
our new denominator.