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Volume of a rectangular prism: fractional dimensions

CCSS.Math:

Video transcript

let's see if we can calculate the volume of this rectangular prism or using this thing that's 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 we I guess yeah we could call this the width the width here is 3/5 of a unit the length here is 1 and 1/6 units and the height here is 3/7 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 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 going to multiply your length times your width times your height you're going to multiply the three dimensions of this thing to figure out how many unit cubes could fit in into it fit 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 1/6 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 1/6 to an improper fraction so 1 is the same thing as 6 six plus one is seven sixths so this is going to be 7 over 6 that's my length times 3/5 that's my width so times 3/5 times the height which is 3/7 times the height which is 3/7 and we know when we multiply fractions we can multiply the numerators so it's going to 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 a answer that has a slightly lower that has a 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 we also see what the numerator denominator has 3 they're both divisible by 3 we see 3 up here we see a 3 over here so let's divide both the numerator and the denominator by 3 so divided by 3 divided 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 what we're just left with that Green 3 it's going to be equal to 3 over 2 times 5 2 times 5 is 10 2 times 5 right over here so it's going to the volume over here is 3/10 units cubed or we could fit 3 tenths of a unit cube inside of this brick or this fish tank or whatever you want to call it