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CCSS.Math:

so we have blank plus 1/16 is equal to three-halves so encourage you to pause the video and figure out what blank is what plus 1/16 is equal to three-halves all right now let's work through this together well one thing that might make it a little bit simpler for our brains is if we were to express 1/16 and three-halves with a common denominator well when we think about a common denominator we would look at a common multiple of the denominators here and lucky for us 16 is already divisible by 2 it's divisible by 16 as well so it is the common multiple or it is the least common multiple of 16 and do there are other common multiples but the smallest one is going to be 16 times 1 which is also divisible by 2 so let's write both of these let's write both of these fractions let's rewrite this equation where both of these fractions have 16 as their denominators this one obviously already has it so let's write that so we're going to have we're going to have blank plus 1/16 1/16 is equal to is equal to you'll see let's write three-halves as something over 16 well to get our denominator from 2 to 16 we have to multiply by 8 so we have to multiply the numerator by 8 as well so 3 times 8 is going to be 24 now at this point you might be able to do it in your head you'll say okay blank plus 1/16 is equal to 24 16 we could say okay this could this is good we could view this as a certain number of 16 so how many 16 plus 1/16 is going to be 24 16 well 23 16 out of 23 sixteenths and I add one more sixteenth I'm going to have 24 16 another way that you could have thought about it when we actually could even thought about it when from the first step is you could say look if blank plus 1/16 is equal to three-halves then you could say that blank you could say that blank is going to be equal to three-halves three-halves minus 1/16 minus 1 sixteenth this is another way that you could have tackled it if blank plus 1/16 is three has then blank is going to be equal to three-halves minus 1/16 and we know that this is going to be equal to three-halves we already know is the same thing as 24 sixteen so 24 over 16 minus 1/16 minus one sixteenth which we figured out is 23 16 which is equal to I'll just rewrite it again 23 over 16 let's do another example so here this is a little bit different i have blank minus three-fourths is equal to two-thirds and there's a couple of ways to think about it if blank minus three-fourths is equal to two-thirds that one way to think about it you could say well blank that means that blank is going to be the same thing as two-thirds plus three-fourths two-thirds plus three-fourths plus three-fourths and what is this going to be well once again I could rewrite both of these fractions so they have a common denominator well what's the least common multiple of three and four well we could look at the multiples of four and and keep and keep increasing them until we find one that's perfectly divisible by three four isn't divisible by three eight isn't divisible by three 12 is divisible by three in fact it's three times four is 12 so we can rewrite both of these as something over 12 so this is going to be the same thing as so to go from three to 12 we multiply by four so you have to multiply the numerator by four as well so two times four is eight two thirds is the same thing as eight twelfths so this is going to be equal to eight twelve plus and then three fourths is the same thing as what over twelve well to go from four to 12 you have to multiply by three so if to multiply the numerator by three as well three times three is nine and what's that going to be equal to so it's equal to this which is equal to eight 12 plus nine 12 is going to be eight plus nine 9 is 17 17 12 so we get 17 12 minus 3/4 is equal to 2/3 now another way that you could have done it is you could have just kept it the same you could have said okay let me just rewrite let me just rewrite this but I'm going to rewrite the fraction so that they have a common denominator we already said well our common denominator we'd want to use is 12 at least this is one we use it could used 24 or something larger than that but this would have been the least common multiple so this keeps things a little bit simpler and 3/4 we could have rewritten as 9 12 9 over 12 is equal to and 2/3 you could rewrite it as 8 over 12 and you could assume that this is going to be a certain number of twelfths so blank 12 minus 9 12 is equal to 8 12 so if i have blank of something minus 9 of something and i'm left with the eighth of that something well that means that i had 17 of that something to begin with 17 12 minus 9 12 is equal to 8 12 but either way you get 17 12 for our blank