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## Topic C: Use equations and inequalities to solve geometry problems

Current time:0:00Total duration:4:15

# 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 I guess you think this thing
is 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. 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 of this base right over here. So sometimes you'll
see volume is equal to the area of the
base 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. 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 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 1/6 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 6/6. Plus 1 is 7/6. So this is going
to be 7/6-- that's my length-- times
3/5-- that's my width-- 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. And the denominator, we can
just multiply the denominators. So it's going to be
6 times 5 times 7. Now, we could just
multiply these out, but just to try to get an
answer that has as simplified as I can make it,
let me-- we 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. And what that does is that
becomes 1, and those become 1. We also see what the numerator
and the denominator has 3. They're both divisible by 3. We see a 3 up here. We see of 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
what we were 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-- the volume
over here is 3/10 units cubed, or we could fit 3/10 of a unit
cube inside of this brick, or this fish tank, or
whatever you want to call it.