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體積單位的四則運算 (英): 體積單位的四則運算
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- 16 fluid ounces plus 3 pints plus 4 quarts is equal to how
- many gallons?
- Now the one unfamiliar thing here that we haven't seen
- before is this 16 fluid ounces.
- We've seen ounces before, but not fluid ounces.
- And to make things confusing, they're actually very
- different things.
- Fluid ounces are a measure of a volume.
- Fluid ounces measure volume, just like cups and pints and
- quarts and gallons do.
- While ounces measure weight.
- And this might make it kind of confusing,
- or maybe less confusing.
- But it also happens that a fluid ounce of water, at
- standard temperature and pressure, is going to weigh a
- little bit more than an actual ounce.
- So that's why they're kind of close.
- A fluid ounce of water is not that different in weight than
- an ounce, but they're two
- fundamentally different things.
- This is volume.
- This is weight.
- Now a fluid ounce, there's many ways you
- could think of this.
- One is that you have 8-- let me write it here-- you have 8
- fluid ounces per cup.
- Or, since there are 2 cups per pint, you also have 16 fluid
- ounces per pint.
- You could view it either way.
- Or you could say that you have 32 fluid ounces per quart.
- Or you can multiply that times 4, and that's how many fluid
- ounces you have per gallon.
- Ounces, which is a unit of weight, you have
- 16 ounces per pound.
- And since I told you that a fluid ounce is a little bit
- more that an ounce, you can kind of figure out that, hey,
- a pint of water, at standard temperature and pressure and
- all of that, will weigh a little bit more.
- Almost a pound, or actually a little bit more than a pound,
- but roughly equal to a pound.
- So that's something that might make things
- simpler, or more difficult.
- Now let's actually tackle the problem.
- So we have 16 fluid ounces.
- I just told you that there are 16 fluid ounces per pint.
- So 16 fluid ounces, let me write over here.
- So 16 fluid ounces times-- now we want the fluid ounces to
- cancel out, so we want fluid ounces in the denominator
- times fluid ounces.
- Now how many fluid ounces are there per pint?
- We want a pint in the numerator so that this and
- this cancel out.
- We just saw it, there are 16 fluid ounces per pint, or that
- 1/16 of a pint per fluid ounce.
- Either way.
- But we see this and this will cancel out.
- And so 16 over 16, because 16 times 1, divided by 16, 1
- equal to 1 pint.
- And we know that.
- 16 fluid ounces equal a pint.
- If we have 16 fluid ounces right over here, this is 1
- pint right over there.
- So we have 1 pint plus another 3 pints, so if we were to add
- all of this part right here together, 1 pint plus 3 pints
- is 4 pints.
- Now we have 4 pints, let's convert to quarts.
- Now we know that there are 2 pints per quart.
- Or we can view it this way, we want the pints to cancel out,
- or 1 quart is 2 pints, or 1/2 quart per pint.
- And we wrote it this way instead of 2 over 1 because we
- wanted the quarts in the numerator, and the pints in
- the denominator, so that that, and that, cancel out.
- And it makes sense.
- If you're converting a smaller unit to a larger unit you're
- going to have fewer of them.
- So you're essentially dividing by 2.
- So 4 times 1/2, or 4 divided by 2, is equal to 2 quarts.
- So this whole piece right here, these 4 pints, are equal
- to 2 quarts.
- That's 2 quarts.
- And you could visualize it.
- 2 of these combined make 1 quart, so 4 of them is going
- to be 2 quarts.
- So you have 2 quarts here, plus another 4 quarts.
- So this entire quantity of 2 quarts plus this 4 quarts are
- going to be 6 quarts.
- So the entire quantity is 6 quarts.
- And we have to convert that to gallons.
- So let me write it right here.
- We have 6 quarts and we want to convert to gallons.
- So we want gallons and the numerator, and we want quarts
- in the denominator, so that it cancels out with this quarts
- when we multiply them.
- And how many quarts are there in a gallon?
- Or 1 gallon is 4 quarts.
- Or 1/4 of a gallon per quart.
- Now we can multiply.
- The quarts cancel out.
- You have 6 times 1/4, which is 6/4 gallons.
- And now we can simplify this.
- We can divide the numerator and the denominator by 2.
- This is the same thing as 3/2 gallons.
- So 3/2 would be an acceptable answer right here.
- This would be 3/2 gallons.
- If you want to write it as a mixed number, 3 divided by 2
- is 1 with the remainder 1.
- So it's 1 and 1/2 gallons.
- Either one would be an acceptable answer.
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