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體積單位的應用題 (英) : U06_L1_T3_we3 Solving application problems involving units of volume
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- 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.
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