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Current time:0:00Total duration:3:47

CCSS.Math:

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 I encourage you to pause the video to think about that well one way to think about it you can say okay our area our area we is just going to be the width times the height we're just gonna 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 to have and then we're going to have seven times I'm just 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 seventy-two and we'd be done this is the area of this rectangle here it's thirty five seventy seconds of a square meter but 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 this region into equal rectangles so let's split it into equal rectangles and we see that we have seven if we go and 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 1 2 3 4 5 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 3035 we have 35 rectangles 30 others right is 35 rectangles and what's the area of each of those rectangles well if this is 7/8 meters wide and this is divided into seven equal sections in the horizontal direction that means that means that each of these is exactly 1/8 of a meter wide and by that same logic each of these if this whole thing is five nines and the height of each of these is 1/5 because we have five five rectangles per column then the height of each of these is going to be 1/9 of a meter so what's the area of just this character right over here well it's going to be 1/9 of a meter times one eighth of a meter so this area this area right over there is just going to be 1/9 of a meter times 1/8 of a meter which is equal to 1 times 1 is 1 9 times 8 is 72 and meters times meters is square meters so the area of each of these 35 is 172nd of a square meter so I could say 35 so the area of all of them combined is going to be 35 times the area of each of them 35 times 172nd 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 172nd of a square meter is going to be 35 35 70 seconds 70 seconds 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 7/8 to get what we have got here but hopefully when we thought about the area of each of these each of these rectangles it might make a little bit more intuitive sense where this number came from