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.