Area with fraction division example

- [Instructor] We're told a yoga mat is 3/5 of a meter wide. It has an area of 1 and 2/25 square meters. What is the length of the mat? Well, we know that length times width is going to give you area, or another way of thinking about it, if the product of two numbers gives you a third number, if you take that third number and divide it by one of these, you're going to get the other one. So another way of thinking about it is length would be the same thing as area divided by width. So we're trying to figure out the length here. We have the area, we have the width. So our length is going to be 1 and 2/25, 1 and 2/25 divided by 3/5. Now this is going to be the same thing as, let me write this as an improper fraction, it's gonna be easier to do some arithmetic with it. So one is the same thing as 25/25, plus 2/25, this is 27/25 divided by 3/5. And we've already talked about how this is saying how many 3/5 can fit into 27/25. And we've given the intuition why this is the same thing as just multiplying 27/25 times the reciprocal of 3/5, which is 5/3. And so this is going to be equal to, and actually I'm gonna factor this out a little bit to simplify things a bit. 27 is 3 x 3 x 3. 25 is 5 x 5. So this is going to be equal to, in our numerator we're gonna have 3 x 3 x 3 x 5. 3 x 3 x 3 x 5. And then in our denominator we're gonna have 5 x 5 x 3. 5 x 5 x 3. And then we can reduce this a little bit. We can divide both the numerator and the denominator by five. We can divide both the numerator and the denominator by three. So in the numerator, we're gonna 3 x 3, which is 9/5. So this is all going to be equal to 9/5. So the yoga mat is 3/5 of a meter wide and 9/5 of a meter long. Now let's make sure that this makes sense. So I'm gonna make a grid. So this right over here is 1/5 of a meter. 1/5 of a meter in that dimension and 1/5 of a meter in that dimension. And then we can see, well, if this is 1/5 of a meter, then the width right over here is 3/5 of a meter. Our length right over here, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, fifths. It is 9/5. Now each of these units, what is its area? Well, it is 1/25 meter squared. And how many of these do we have? Well, we can see, we have three rows of nine, which is 27 of these 25ths, so we're gonna have 27/25 square meters, which is the same thing as 1 and 2/5 square meters.