Multiplying unit fractions: area model to expression

- [Instructor] We are told the area

of the entire figure
below is one square unit

so that's this entire thing.

Write a multiplication
expression to represent the area

of the striped piece, so
this area right over here.

So pause this video,

have a go at this before
we do this together.

Okay, so first of all, what is
a multiplication expression?

Well, we're really gonna
write something times

something else is going to
be equal to something else

on top of that, a third something.

So let's think about how to do this.

Well, we could think about
what we're multiplying

on each of these sides of this square.

So, on the left side here,

we have divided this square into

1, 2, 3, 4, 5 equal section.

So one way to think about it
is each of these are a fifth,

for example, that's a fifth.

That's a fifth, that's a fifth,
I guess I'll keep doing it.

That's a fifth and then
that is another fifth.

Five-fifths is equal to whole.

Now, if I look at the width up here,

I have 1, 2, 3, equal section.

So I could view that as a third.

This as a third, and then this is a third.

And so this area, the one that's striped,

that area is going to be
one-fifth times one-third,

one-fifth times one-third.

And then what's that going to be equal to?

Well, this whole thing is one square unit,

and this is one of the 15 that we see.

We can count them.

1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15.

This is one of the 15
equal areas we have here.

So this is gonna be one-15th
of the entire square.

So there we have it. There's
our multiplication expression.

One-fifth times one-third
is equal to 1-15th.

One-fifth times one-third
is equal to 1-15th.