Your car gets 25
miles per gallon, and you want to go on
a 400-mile road trip. Right now, gas
costs \$3 per gallon. How much will the gas
for your road trip cost? So let’s see. They tell us they’re going
on a 400-mile road trip. 400 miles. So the first thing that I’d
want to think about is, well, how many gallons am I using? And then once I know how
many gallons I’m using, I know it’s \$3 per
gallon, so I can multiply the number
of gallons by \$3. So to figure out the
number of gallons, would I want to
multiply 400 miles– would I want to multiply that
times the miles per gallon, which is 25, or would I want
to multiply by the gallons per mile? Well, if I multiply by
the gallons per mile, and I multiply that
times 400, then I would get the number of gallons. So let’s just think about that. I want to multiply
that times– and I’ll write the units first–
the gallons per mile. And what are the
gallons per mile? Well, we have 25
miles per gallon. We have 25 miles
for every 1 gallon. Or you could say we have 1
gallon for every 25 miles. So I really just
took the reciprocal of 25 miles per gallon and
made it 1/25 gallons per mile. Now what do we get when we
multiply these two things? The whole purpose
was to figure out how many gallons
we’re going to use. Well, we see that
our miles cancel out. Miles cancel out with miles. And then I have 400
times 1/25 gallons, which is the same thing as
400 divided by 25 gallons. So this is equal to
400/25 gallons, which is the same thing as 400 divided
by 25 is equal to 16 gallons. Now it’s always important
to do a reality check here, not just to try to
blindly cancel out units. Does this actually
makes sense that 16 is a much lower number than 400? Well, sure it does. And actually, if you have any
experience filling up a car, you would sense that, OK,
well, that’s about the size. On around 16
gallons, a car tends to go 300 or 400 miles if it
gets pretty good fuel mileage. So that just makes
sense from experience. And it also make sense
based on how it’s stated. You get 25 miles per gallon. So you’re going to
need fewer gallons than you’re going to need miles. So this all seems to
make sense so far. But we haven’t answered
their question. They want to know, how
much will my trip cost? Right now, we’ve just
figured out how much fuel we’re going to use. So then we could
take our 16 gallons. And to figure out
the dollar cost, are we going to multiply
it by dollars per gallon or gallons per dollar? Well, if we’re thinking
just about unit conversion, we want to multiply times
the dollars per gallon. So I could write it like this. I could write it like
dollars per gallon. Actually, let me just write
out the word “dollar.” Dollars per gallon. The units will cancel out. And it also makes sense. Whatever number of
dollars per gallon, I multiply it times
the number of gallons, and that’s going to tell me
how much it’s going to cost. This happens at the
fuel pump every day. Hey, it’s \$3 per gallon. I’m going to fill up 16 gallons. Hey, 3 times 16. So let’s do that. So it’s \$3 per gallon. We see the gallons cancel out. And we are left
with 16 times \$3, which is the same thing as \$48. And we are done.