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## Arithmetic (all content)

### Unit 5: Lesson 21

Multiplying fractions- Intro to multiplying 2 fractions
- Multiplying 2 fractions: fraction model
- Multiplying 2 fractions: number line
- Multiplying fractions with visuals
- Multiplying 2 fractions: 5/6 x 2/3
- Multiplying fractions
- Finding area with fractional sides 1
- Finding area with fractional sides 2
- Area of rectangles with fraction side lengths
- Multiplying fractions review

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# Finding area with fractional sides 1

CCSS.Math:

Sal finds the area of a rectangle with fractional side lengths.

## Video transcript

- [Voiceover] So we've
got a rectangle here, it's five-ninths of a meter tall, and seven-eighths of a meter wide. What is its area? And I encourage you to pause the video to think about that. Well one way to think about it, is you can say our area, our area is just going to be
the width times the height. We're just going to multiply
these two dimensions. And so the width is
seven-eighths of a meter. So it's going to be
seven-eighths of a meter times the height, times the height which is five-ninths of a meter. Times five-ninths of a meter. And what's that going to get us? Well, that's just going
to be equal to the meters times the meters give us square
meters, so meters squared. We could write it like that. And then we're going have,
and then we're going to have seven times, this in a new color, we're going to have seven
times five in the numerator to get us 35, and then in the denominator, in the denominator we are
going to have eight times nine to give us 72. And we'd be done. This is the area of this rectangle here. It's 35-72nds of a square meter. What I want to do now is
think a little bit deeper about why that actually makes sense. Or just really another
way of thinking about it. And to do that, what I'm going to do is I'm going to split this
region into equal rectangles. So let's split it into equal rectangles. And we see that we have seven,
if we go in the horizontal direction we have one,
two, three, four, five, six, seven or you could say
in each row we have seven of these rectangles. In each column you have
one, two, three, four, five of these rectangles. So you can see we have
five times one, two, three, four, five, six, seven. So we have five times
seven of these rectangles. So, we have--so 35, we have 35 rectangles. I'll just write this, 35 rectangles. And what's the area of
each of those rectangles? Well, if this is
seven-eighths meters wide, and this is divided into
seven equal sections in the horizontal direction,
that means that each of these is exactly one-eighth of a meter wide. And by that same logic, each of these, if this whole thing is five-ninths, and the height of each
of these is one-fifth because we have five
rectangles per column, then the height of each
of these is going to be one-ninth of a meter. So what's the area of just
this character right over here? Well, it's going to be
one-ninth of a meter times one-eighth of a meter. So this area, this area right
over there is just going to be one-ninth of a meter times
one-eighth of a meter which is equal to one times one is one, nine times eight is 72,
and meters times meters is square meters. So the area of each of these 35 is one-72nd of a square meter. So, if I say 35, so the
area of all of them combined is going to be 35 times
the area of each of them. 35 times one-72nd of a square meter. And what's that going to be? Well, that's going to be
exactly what we got up here. 35 times one-72nd of a
square meter is going to be 35, 35-72nds of a square meter. And this 35 is the same
one that we had in yellow. That's this one right over there. So once again, you can
just multiply five-ninths times seven-eighths to
get what we have got here. But hopefully when we
thought about the area of each of these rectangles, it might make a little
bit more intuitive sense where this number came from.