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a local hospital recently conducted a blood drive where they collected a total of 80 pints of blood from donors the hospital was hoping to collect a total of eight gallons of blood from the drive did they meet their goal how much more or less than their gold at the hospital collect so really they collected 80 pints we just need to figure out how many gallons that is and then say well is that going to be more or less than eight gallons so we have we start with 80 80 pints and we could take it step by step you may or may not know how many pints there are per gallon so let's just go straight to quarts first and then from quarts we can go to gallons but if you know right from the get-go how many pints there are per gallon you could go there so let's do convert this to quarts so we've 80 pints so what are we going to multiply or divided by to get the courts well one way to think about it you're going from a smaller unit pints to a larger unit so you're going to have less of that larger unit so you're going to divide you're going to this number is going to be smaller when it goes into quarts and it's going to be smaller than by a factor of two because you have two pints per quart so you're going to have you're not going to multiply by two you're not gonna have more courts you can divide by two so you could say times 1/2 this is the same thing as dividing by two and we'll make sure that the units work out we have one quart one quart for every two pints or you could view this as two pints per quart or one half of a quart per pint either way the units work out and you're essentially taking 80 and dividing by two or multiplying by one half and you get 40 quarts and I want to make sure that your brain does it both ways because when you're just doing it you don't have paper you don't have the units around you should just think you know hey 80 pints there's two pints per quart I'm gonna have half as many quarts I'm gonna have 40 quarts but when problems get a little more complicated it is nice to make sure that the unit's cancel out in this way so that you know okay one quart is two pints pints in the denominator pints in the numerator cancel them out I just left with quarts and eighty times 1/2 which is 40 so we have 40 quarts now 40 quarts and now we can convert this to gallons we know that there are 4 quarts per gallon or that one gallon has 4 quarts and once again we're going to go from smaller unit to a larger unit to gallons so it's we know there's a factor for difference since you're going to a larger unit your brain should say hey I'm gonna divide by four I'm gonna have I'm going to have a factor of four fewer gallons because the larger unit and to make sure the units work out you just remember well we have a quartz up here in the numerator you're gonna want two quarts down here in the denominator and you have any what we care about converting into gallons and one gallon is four quarts and this will work out the courts will cancel out and notice you're also dividing by four forty times one half of sorry forty times one fourth is the exact same thing as 40 divided by four which makes sense we're going into a larger unit so 40 times one fourth is 10 and the units left are gallons so the 80 pints of blood of blood that the hospital collected is 10 gallons their goal was only 8 gallons their goal was only 8 gallons so did they meet their goal yes they met their goal how much more or less than their gold at the hospital collect well their goal was 8 they collected 10 they collected two two extra gallons two extra gallons then their goal