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CCSS.Math:

how many cups are in three and a half gallons so before even addressing this question let's just think about how large a cup is and actually I'll give you a little bit of overview of how many cups there are in a pint how many pints in a quart and how many quarts in a gallon so let me just draw a little let me draw a cube here and let's imagine that this is a gallon let's imagine this is a gallon the most common time we see a gallon is when you see a gallon of milk so let's say that that whole thing is a gallon you can imagine if it had a handle it'd be kind of a big gallon of milk now there are four quarts per gallon there are let me write this over here there are four there are four quarts four quarts per gallon so if I were to draw the quartz here I could divide this gallon into four quarts and then each of these sections would be a quart so you have four quotes four quarts so this right here that I've just drawn in blue would be exactly that would be one one quart and obviously there's four of them in this entire gallon now you can divide the courts into pints you have two two pints two pints per quart two pints per quart so this court that I drew here I can divide it into two I can divide it into two like that and this little section that I'm highlighting in magenta is a pint that is a pint right over there and then finally there are two cups per pint there are two two cups two cups per pint so this pint right here I can divide it into two and each of these will be a cup so this section right here right here will be a cup now we could go straight and figure out exactly how many cups there are per gallon actually that might be an interesting way to think about it if you have four quarts rayless let's multiply it right here so you have four quarts per gallon so you have four quarts four quarts per gallon times two pints per quart times two pints two pints per quart what does this give you this gives you four times two is equal to eight and then the quartz cancel out and you have eight pints eight pints per gallon eight pints per gallon and that makes complete sense because we had four quarts in this gallon and then each of those quartz have two pints in them so four times two so eight pints per gallon and then we can multiply that times two cups per pint which I could just copy and paste this right here so let me just copy and paste this copy and paste actually I should have cut and paste so let me select it again I want to do that so I get that real estate back so edit cut edit paste there you go so now you multiply this times two cups per pint and the reason why this will work is because you have a pints in the numerator cancels out with a pints in the denominator and you will be left with you will be left with I'll go back to the yellow eight times two is sixteen in the numerator we have cups cups per gallon now we just figured how many cups per hour per gallon that makes sense this section right here is about is exactly 1/16 of this entire cube this entire gallon but we haven't even answered our question we want to figure out how many cups there are in three and a half gallons so let's write it over here so we're concerned with 3 and 1/2 gallons I don't like working with mixed numbers I like to turn them into improper fractions three and a half is the same thing as 2 times 3 is 6 plus 1 is 7 this is the same thing as 7 over 2 if you divided 7 by 2 you would get 3 with a remainder of 1 or this would be 3 and a half so this is the exact same thing so we want to know how many cups are in 7 halves gallons so what we want to do is end up with cups and we want the gallons to cancel out so we have a gallons in the numerator right here or it's definitely not in the denominator and so we want to divide by gallons we want to divide by gallons and then we're going to have a numerator we have cups in the numerator and how many cups are there per gallon well we just figure that out there are 16 16 cups per gallon when you multiply these two quantities the gallons will cancel out and you'll just be left with cups and that's what we wanted so it's going to be seven halves times 16 so this is going to be 7 times 16 over 2 cups cups and then 16 divided by 2 or you could divide 16 by 2 and get 8 2 divided by 2 is 1 so just become 7 times 8 divided by 1 or just 7 times 8 which is 56 so this is equal to 56 cups and this should make sense this should be a much larger number because cups are much a smaller unit so if you have three and a half gallons you will have many many many more cups in that three and a half gallon so this makes sense