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your car gets 25 miles per gallon per gallon and you want to go on a 400 mile road trip right now gas costs three dollars 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 for 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 three dollars per gallon so I can multiply the number of gallons by three dollars so to figure out the number of gallons what I want to what I want to multiply 400 miles what I want to multiply that times the miles per gallon which is 25 or what I want to multiply by the gallons per mile well if I multiply by the gallons per mile then I would get 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 so I want to multiply times I'll write the unit's first the gallons the gallons per mile the gallons per mile and what are the gallons per mile well we have 25 miles per gallon we have 25 miles for every one gallon or you could say we have one gallon for every 25 miles so I really just took the reciprocal of 25 miles per gallon and made it one over 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 were going to use well we see that our miles cancel out miles cancel out with miles and then I have 400 times 1 over 25 gallons which is the same thing as 400 divided by 25 gallons so this is equal to 400 over 25 gallons which is the same thing as water 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 make sense that 16 is a much lower we're number than 400 well sure it does and actually if you have any experience filling up a car you would sense that okay well that's about the size you know on around 16 gallons you a car tends to go 300 or 400 miles if it if it gets pretty good fuel mileage so that just makes sense from experience and also makes sense based on how it's stated you get 25 miles per gallon so you're going to need fewer gallons then 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 figure out how much fuel we're going to use so that we could take our 16 gallons 16 gallons and to figure out the dollar cost so we're 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 unit's will will cancel out and it also makes sense if I whatever number of dollars per gallon I multiplied 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 three dollars per gallon I'm going to fill up 16 gallons a 3 times 16 so let's do that so it's three dollars per gallon we see the gallons cancel out and we are left with 16 times three dollars 16 times three dollars which is the same thing as 48 dollars and we are done