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### Course: Arithmetic > Unit 10

Lesson 9: Area of rectangles with fractional side lengths# Finding area with fractional sides 1

Learn how to calculate the area of rectangles with fractional side lengths. Watch examples of this concept in action and practice applying it to different problems. The video emphasizes understanding the process, not just getting the answer.

## Want to join the conversation?

- I STILL DONT GET IT they lose me at when they did the squares(1 vote)
- Sal showed 2 ways to figure out the area or the square

1): multiplying the width and height

2): is to take the numerator(the top number) of each fraction, and use that to make a grid.

Example: 5/9 is the height so top to bottom Sal separated the area into 5 sections

after doing that with height and width it made a grid each square being 1/9 by 1/8

He figured out the area by multiplying 1/9 by 1/8 (Which is 1/72)

then sal figured out the number of squares by multiplying the number top to bottom then left to right (height by width) that being 7x5(35)

and at the very end multiplied the number of squares (35)by the area or each squares(1/72) that is 35/72

(The thing about meters squared is just a poor example you don't have to understand it)(18 votes)

- When you are multiplying the height and width are you finding the area or the perimeter?(8 votes)
- You are finding the area width*height=Area

Perimeter=2*width+2*height(30 votes)

- I don't understand the relationship of 8 and 9.

7x5 seems logic however where did you get 8/9 from?(7 votes)- The 9 from the 5/9 and the 8 form the 7/8(0 votes)

- This is the death of fifth graders LOL☠(4 votes)
- 1:28clarify why you split the rectangle into 35 equal parts. It seems random. Please point out that you are using the numerators of both fractions to divide it into equal parts and why.(5 votes)
- Because of the following reason:

Let us pretend this is an addition

You can't do 7/8 + 5/9. The denominators are different. So you will find the MCP. The same is with multiplication.

Hope this is helpful.(0 votes)

- how ado you times a fraction by a normal number(3 votes)
- lets just say 3x 1/10, you would convert it into 3/1. 3/1 x 1/10 is 3/10.(1 vote)

- Guys, He said seconds instead of meters!

Guess Sal made a mistake!

Once in a lifetime mistake(2 votes) - At1:51why does it have to be 35 rectangles? Its very random in my opinion.(2 votes)
- Hi Austin!

It has to be 35 squares because that's the total amount of squares in the rectangle's area if you count each one on the screen. Each square has the same size/area of measurement and they distribute evenly (by "filling") the rectangle with no gaps or variations of size within the rectangle. Keeping each square the same size allows us to create a fraction that is from consistently measured data. If each square is consistently the same size then we know the fraction we create representing the total amount of squares (the 35 of 35/72) will be consistent and true as well.

You could also think of it as 7 columns of squares of 5 rows of squares = 35 total squares, or 5 rows of squares by 7 seven columns of squares = 35 total squares.

If anyone has another perspective with which to answer this question with, please feel free to add it.(1 vote)

- Your method does not work with the problem I have(1 vote)
- Why don't you try asking a question related to the problem that you have? Someone many be able to show you if the method does work or offer an alternate method.(2 votes)

- what is this i dont understand(1 vote)

## 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.