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CCSS.Math:

A local hospital recently
conducted a blood drive where they collected a total of 80
pints of blood from donors. The hospital was hoping to
collect a total of 8 gallons of blood from the drive. Did they meet their goal? How much more or less
than their goal did the hospital collect? So really, they collected
80 pints. We just need to figure out how
many gallons that is, and then say, well, is that going to be
more or less than 8 gallons? So we start with 80 pints. And we can take it
step by step. You may or may not know how
many pints there are per gallon, so let's just go
straight to quarts first, and then from quarts we
can go to gallons. But if you know right from the
get go how many pints there are per gallon, you
could go there. So let's convert
this to quarts. So we have 80 pints, so what
are we going to multiply or divide by to get quarts? Well, one way to think about
it, you're going from a smaller unit, pints, to a larger
unit, so you're going to have less of that
larger unit. So you're going to divide. This number's going
to be smaller when it goes into quarts. And it's going to be smaller by
a factor of 2 because you have 2 pints per quart. You're not going to
multiply by 2. You're not going to
have more quarts. You're going to divide by 2. So you could say, times 1/2. This is the same thing as
dividing by 2, and we'll make sure that the units work out. We have one quart for every 2
pints, or you can view this as 2 pints per quart or 1/2
of a quart per pint. Either way, the units work out,
and you're essentially taking 80 and dividing by 2, or
multiplying by 1/2, and you get 40 quarts. And I want to make sure that
your brain does it both ways. Because when you're just doing
it, you don't have paper, you don't have the units around, you
should just think, hey, 80 pints, there's 2 pints
per quart. I'm going to have half
as many quarts. I'm going to have 40 quarts. But when problems get a little
bit more complicated, it is nice to make sure that the units
cancel out in this way, so that you know, OK,
1 quart is 2 pints. Pints in the denominator, pints
in the numerator, cancel them out, and I'm just left with
quarts, and 80 times 1/2, which is 40. So we have 40 quarts
now, and now we can convert this to gallons. We know that there are 4 quarts
per gallon or that 1 gallon has 4 quarts. And once again, we're going to
go from a smaller unit to a larger unit, to gallons. So we know there's a factor
of 4 difference. Since you're going to a larger
unit, your brain should say, hey, I'm going to divide by 4. I'm going to have a factor 4
fewer gallons because it's a larger unit. And to make sure that units work
out, you just remember, well, we have quarts up here in
the numerator, you're going to want quarts down here
in the denominator. And we care about converting
into gallons, and 1 gallon is 4 quarts. And this will work out. The quarts will cancel out. And notice, you're also
dividing by 4. 40 times 1/4 is the exact same
thing as 40 divided by 4, which makes sense. We're going to a larger unit. So 40 times 1/4 is 10, and the
units left are gallons. So the 80 pints of blood
that the hospital collected is 10 gallons. Their goal was only 8 gallons. So did they meet their goal? Yes, they met their goal! How much more or less
than their goal did the hospital collect? Well, their goal was 8,
they collected 10. They collected 2 extra gallons
than their goal.