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Volume of a rectangular prism: fractional dimensions

The video explains how to calculate the volume of a rectangular prism with fractional dimensions. It emphasizes that volume equals the area of the base times the height. To find the volume, multiply the length, width, and height. The video also shows how to simplify fractions during multiplication. Created by Sal Khan.

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Video transcript

- [Narrator] Let's see if we can calculate the volume of this rectangular prism or, I guess, you'd think this thing, the shape of a brick or a fish tank right over here. And what's interesting is now that the dimensions are actually fractions, we have a width or, I guess, yeah, we could call this the width. The width here is 3/5ths of a unit. The length here is 1 and 1/6th units, and the height here is 3/7ths of a unit. So I encourage you to pause this video and try to figure out the volume of this figure on your own before we work through it together. So there's a couple of ways to think about it. One way to think about it is you're trying to pack unit cubes in here. And one way to think about how many unit cubes could fit in here is to think about the area, is to think about the area of this base right over here. So sometimes you'll see volume is equal to the area of the base times the height, times the height. This right over here is the height. And let me make it clear, this is the area of the base. Area of the base times the height. Well, what's the area of the base? Well, the area of the base is the same thing as the length times the width. So you might see it written like that. You might see it written as area of base is going to be your length times your width, times your width. Width, length times width is the same thing as your area of the base. So that's that right over there. And, of course, you still have to multiply times the height. Or another way of thinking about it, you're gonna multiply your length times your width times your height. You're gonna multiply the three dimensions of this thing to figure out how many unit cubes could fit into it to figure out the volume. So let's calculate it. The volume here is going to be, what's our length? Our length is 1 and 1/6th units. Now, when I multiply fractions as I'm about to do, I don't like to multiply mixed numbers. I like to write them as improper fractions. So let me convert 1 and 1/6th to an improper fraction. So 1 is the same thing as 6/6ths plus 1 is 7/6ths. So this is going to be 7/6. That's my length times 3/5ths, that's my width. So times 3/5ths, times the height, which is 3/7ths times the height, which is 3/7ths. And we know when we multiply fractions, we can multiply the numerators. So it's gonna be 7 times 3 times 3 times 3. And the denominator, we can just multiply the denominators. So it's going to be 6 times 5, 6 times 5 times 7 times 7. Now, we could just multiply these out, but just to try to get an answer that is as simplified as I can make it. Let me, see, we have a 7 in the numerator and a 7 in the denominator. So let's divide the numerator and the denominator by 7. So let's divide the numerator and the denominator by 7. And what that does is that becomes 1 and those become 1. And we also see both the numerator denominator has 3. They're both divisible by 3. We see a 3 up here. We see a 3 over here. So let's divide both the numerator and the denominator by 3. So we divide by 3, divide by 3. 3 divided by 3 is 1. 6 divided by 3 is going to be equal to 2. So in our numerator, what are we left with? This is going to be equal to, where we're just left with that green 3, it's going to be equal to 3/2 times 5. 2 times 5 is 10, 2 times 5, right over here. So the volume over here is 3/10ths units cubed. Or we could fit 3/10ths of a unit cube inside of this brick or this fish tank or whatever you want to call it.