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### Course: 6th grade > Unit 10

Lesson 3: Volume with fractions- Volume of a rectangular prism: fractional dimensions
- Volume by multiplying area of base times height
- Volume with fractions
- How volume changes from changing dimensions
- Volume of a rectangular prism: word problem
- Volume word problems: fractions & decimals

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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.

## Want to join the conversation?

- He doesn't really thoroughly explain the part where he multiplies all of the fractions. I got confused and now i have no clue how to do it, could someone help me?(78 votes)
- What he means is 7 * 3 * 3/6 * 5 * 7.

It's equal to 7/7 * 3/6 * 3/5.

That's 1 * 1/2 * 3/5, which equals 3/10.

Do you understand now? If you need more help, ask me!(17 votes)

- i didn't know geometry was so hard!(43 votes)
- true! its really fun though when you get the hang of it(26 votes)

- How do you express the answer?(24 votes)
- Any unit to the third power because we are talking about 3D volume units. E.g. cm^3 or inches cubed.(21 votes)

- I'm not sure if this is right but I think the equation is

Length x width x height

Tell me if I'm right or wrong by commenting or a upvote/downvote.(25 votes)- Yes, the volume of a rectangular prism is always length x width x height. Good job!(10 votes)

- What's the difference between V=bh and V=Bh?(12 votes)
- In geometric formulas, b usually refers to the length of the base of a 2-dimensional figure. B usually refers to the area of the base of a 3-dimensional figure. V=Bh is way should be written since V is measured in cubic units (u^3 = u * u * u), B is measured in square units (u^2 = u * u) and h is measured in linear units (u). I hope this helps.(13 votes)

- i do not under stand and i want to be able to ace most of my bench mark test(6 votes)
- It is basically the same as a regular rectangular prism. You multiply base and height (length x height x width).(12 votes)

- So basically we just multiply them all...(9 votes)
- Should you be able to do this without calculator ( I assume yes); if so - then why? provided number sense is already developed enough to understand the concept but not to memorize it. Thanks.(7 votes)
- In geometric formulas, b usually refers to the length of the base of a 2-dimensional figure. B usually refers to the area of the base of a 3-dimensional figure. V=Bh is way should be written since V is measured in cubic units (u^3 = u * u * u), B is measured in square units (u^2 = u * u) and h is measured in linear units (u).(7 votes)
- is there a difference if he didn't put a capital B for the v=Bh?(4 votes)
- Yes, in algebra, you have to use "b" instead of "B"

[Answered on May 3,2023

Sincerely, ShashrvatRB](7 votes)

## 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.