體積單位的四則運算 (英)

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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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