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How many cups are in
3 and 1/2 gallons?

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So before even addressing this
question, let's just think

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about how large a cup is.

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Actually, I'll give you a little
bit of overview of how

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many cups there are in a pint,
how many pints in a quart, and

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how many quarts in a gallon.

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Let me just draw a cube here,
and let's imagine

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that this is a gallon.

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The most common time we see
a gallon is when you see a

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gallon of milk.

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So let's say that that whole
thing is a gallon.

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You can imagine if it had a
handle, it would be kind of a

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big gallon of milk.

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Now, there are 4 quarts
per gallon.

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Let me write this over here.

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There are 4 quarts per gallon.

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So if I were to draw the quarts
here, I could divide

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this gallon into 4 quarts, and
then each of these sections

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would be a quart.

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So you would have 4 quarts.

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So this right here that I've
just drawn in blue would be

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exactly 1 quart.

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And obviously, there's 4 of them
in this entire gallon.

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Now, you can divide the
quarts into pints.

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You have 2 pints per quart.

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So this quart that I drew here,
I can divide it into 2,

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like that, and this little
section that I'm highlighting

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in magenta is a pint.

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That is a pint right
over there.

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And then finally, there
are 2 cups per pint.

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So this pint right here, I can
divide it into 2, and each of

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these will be a cup.

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So this section right
here will be a cup.

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Now, we can go straight and
figure out exactly how many

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cups there are per gallon.

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Actually, that might be
an interesting way

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to think about it.

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If you have 4 quarts-- let's
multiply it right here.

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So you have 4 quarts per gallon

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times 2 pints per quart.

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What does this give you?

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This gives you 4 times
2 is equal to 8.

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And then the quarts cancel
out, and you

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have 8 pints per gallon.

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And that makes complete sense
because we had 4 quarts in

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this gallon, and then
each of those quarts

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have 2 pints in them.

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So 4 times 2.

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So 8 pints per gallon.

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And then we can multiply that
times 2 cups per pint.

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So I could just copy and
paste this right here.

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Actually, I should've
cut and paste.

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Let me select it again.

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I want to do that so I get
that real estate back.

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So edit, cut, edit, paste.

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There you go.

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So now you multiply this
times 2 cups per pint.

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And the reason why this will
work is because you have pints

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in the numerator.

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It cancels out with the pints
in the denominator.

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And you will be left with-- I'll
go back to the yellow-- 8

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times 2 is 16.

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In the numerator, we have
cups per gallon.

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Now, we just figured how many
cups there are per gallon.

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That makes sense.

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This section right here is
exactly 1/16 of this entire

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cube, this entire gallon.

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But we haven't even answered
our question.

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We want to figure out how
many cups there are

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in 3 and 1/2 gallons.

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So let's write it over here.

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So we're concerned with
3 and 1/2 gallons.

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I don't like working
with mixed numbers.

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I like to turn them into
improper fractions.

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3 and 1/2 is the same thing as
2 times 3 is 6, plus 1 is 7.

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This is the same thing as 7/2.

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If you divided 7 by 2, you would
get 3 with a remainder

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of 1, or this would be
3 and 1/2, so this is

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the exact same thing.

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So we want to know how many
cups are in 7/2 gallons.

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So what we want to do is end up
with cups, and we want the

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gallons to cancel out.

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So we have gallons in the
numerator right here.

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It's definitely not in
the denominator.

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And so we want to divide
by gallons.

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And then we're going to
have a numerator.

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We have cups in the numerator.

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And how many cups are
there per gallon?

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Well, we just figured
that out.

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There are 16 cups per gallon.

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When you multiply these two
quantities, the gallons will

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cancel out, and you'll just be
left with cups, and that's

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what we wanted.

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So it's going to be
7/2 times 16.

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So this is going to be
7 times 16/2 cups.

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You could divide 16
by 2 to get 8.

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2 divided by 2 is 1.

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So it just becomes 7 times 8
divided by 1, or just 7 times

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8, which is 56.

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So this is equal to 56 cups.

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And this should make sense.

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This should be a much larger
number because cups are a much

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smaller unit.

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So if you have 3 and 1/2
gallons, you will have many,

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many, many more cups in that
3 and 1/2 gallons,

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so this makes sense.