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- How many cups are in 3 and 1/2 gallons?
- So before even addressing this question, let's just think
- about how large a cup is.
- Actually, I'll give you a little bit of overview of how
- many cups there are in a pint, how many pints in a quart, and
- how many quarts in a gallon.
- Let me just draw a cube here, and let's imagine
- that this is a gallon.
- The most common time we see a gallon is when you see a
- gallon of milk.
- So let's say that that whole thing is a gallon.
- You can imagine if it had a handle, it would be kind of a
- big gallon of milk.
- Now, there are 4 quarts per gallon.
- Let me write this over here.
- There are 4 quarts per gallon.
- So if I were to draw the quarts here, I could divide
- this gallon into 4 quarts, and then each of these sections
- would be a quart.
- So you would have 4 quarts.
- So this right here that I've just drawn in blue would be
- exactly 1 quart.
- And obviously, there's 4 of them in this entire gallon.
- Now, you can divide the quarts into pints.
- You have 2 pints per quart.
- So this quart that I drew here, I can divide it into 2,
- like that, and this little section that I'm highlighting
- in magenta is a pint.
- That is a pint right over there.
- And then finally, there are 2 cups per pint.
- So this pint right here, I can divide it into 2, and each of
- these will be a cup.
- So this section right here will be a cup.
- Now, we can go straight and figure out exactly how many
- cups there are per gallon.
- Actually, that might be an interesting way
- to think about it.
- If you have 4 quarts-- let's multiply it right here.
- So you have 4 quarts per gallon
- times 2 pints per quart.
- What does this give you?
- This gives you 4 times 2 is equal to 8.
- And then the quarts cancel out, and you
- have 8 pints per gallon.
- And that makes complete sense because we had 4 quarts in
- this gallon, and then each of those quarts
- have 2 pints in them.
- So 4 times 2.
- So 8 pints per gallon.
- And then we can multiply that times 2 cups per pint.
- So I could just copy and paste this right here.
- Actually, I should've cut and paste.
- Let me select it again.
- I want to do that so I get that real estate back.
- So edit, cut, edit, paste.
- There you go.
- So now you multiply this times 2 cups per pint.
- And the reason why this will work is because you have pints
- in the numerator.
- It cancels out with the pints in the denominator.
- And you will be left with-- I'll go back to the yellow-- 8
- times 2 is 16.
- In the numerator, we have cups per gallon.
- Now, we just figured how many cups there are per gallon.
- That makes sense.
- This section right here is exactly 1/16 of this entire
- cube, this entire gallon.
- But we haven't even answered our question.
- We want to figure out how many cups there are
- in 3 and 1/2 gallons.
- So let's write it over here.
- So we're concerned with 3 and 1/2 gallons.
- I don't like working with mixed numbers.
- I like to turn them into improper fractions.
- 3 and 1/2 is the same thing as 2 times 3 is 6, plus 1 is 7.
- This is the same thing as 7/2.
- If you divided 7 by 2, you would get 3 with a remainder
- of 1, or this would be 3 and 1/2, so this is
- the exact same thing.
- So we want to know how many cups are in 7/2 gallons.
- So what we want to do is end up with cups, and we want the
- gallons to cancel out.
- So we have gallons in the numerator right here.
- It's definitely not in the denominator.
- And so we want to divide by gallons.
- And then we're going to have a numerator.
- We have cups in the numerator.
- And how many cups are there per gallon?
- Well, we just figured that out.
- There are 16 cups per gallon.
- When you multiply these two quantities, the gallons will
- cancel out, and you'll just be left with cups, and that's
- what we wanted.
- So it's going to be 7/2 times 16.
- So this is going to be 7 times 16/2 cups.
- You could divide 16 by 2 to get 8.
- 2 divided by 2 is 1.
- So it just becomes 7 times 8 divided by 1, or just 7 times
- 8, which is 56.
- So this is equal to 56 cups.
- And this should make sense.
- This should be a much larger number because cups are a much
- smaller unit.
- So if you have 3 and 1/2 gallons, you will have many,
- many, many more cups in that 3 and 1/2 gallons,
- so this makes sense.

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