Measurement word problem: blood drive

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 8 gallons of blood from the drive. Did they meet their goal? How much more or less than their goal did 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 8 gallons? So we start with 80 pints. And we can 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 convert this to quarts. So we have 80 pints, so what are we going to multiply or divide by to get quarts? 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. This number's going to be smaller when it goes into quarts. And it's going to be smaller by a factor of 2 because you have 2 pints per quart. You're not going to multiply by 2. You're not going to have more quarts. You're going to divide by 2. So you could say, times 1/2. This is the same thing as dividing by 2, and we'll make sure that the units work out. We have one quart for every 2 pints, or you can view this as 2 pints per quart or 1/2 of a quart per pint. Either way, the units work out, and you're essentially taking 80 and dividing by 2, or multiplying by 1/2, 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, hey, 80 pints, there's 2 pints per quart. I'm going to have half as many quarts. I'm going to have 40 quarts. But when problems get a little bit more complicated, it is nice to make sure that the units cancel out in this way, so that you know, OK, 1 quart is 2 pints. Pints in the denominator, pints in the numerator, cancel them out, and I'm just left with quarts, and 80 times 1/2, which is 40. So we have 40 quarts now, and now we can convert this to gallons. We know that there are 4 quarts per gallon or that 1 gallon has 4 quarts. And once again, we're going to go from a smaller unit to a larger unit, to gallons. So we know there's a factor of 4 difference. Since you're going to a larger unit, your brain should say, hey, I'm going to divide by 4. I'm going to have a factor 4 fewer gallons because it's a larger unit. And to make sure that units work out, you just remember, well, we have quarts up here in the numerator, you're going to want quarts down here in the denominator. And we care about converting into gallons, and 1 gallon is 4 quarts. And this will work out. The quarts will cancel out. And notice, you're also dividing by 4. 40 times 1/4 is the exact same thing as 40 divided by 4, which makes sense. We're going to a larger unit. So 40 times 1/4 is 10, and the units left are gallons. So the 80 pints of blood that the hospital collected is 10 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 goal did the hospital collect? Well, their goal was 8, they collected 10. They collected 2 extra gallons than their goal.