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we have negative three-fourths minus seven six minus three sixths and there's many ways to do this but it immediately jumps out at me that these last two numbers have a six in the denominator so I'm going to worry about these first I'm going to view this as negative 7 6 minus 3 6 so if we have negative 7 6 minus 3 6 that's going to be the same thing as negative 7 minus 3 over 6 and of course we have this negative three-fourths out front that we're going to add to whatever we get over here so this is these two terms that I'm adding together negative 7 minus 3 is negative 10 so it's negative 10 over 6 and then I'm going to have to add that to negative three-fourths to negative I'm using a negative three-fourths and now I have to worry about finding a common denominator let me write that so they look a little bit they have a similar size negative three-fourths so now I have to worry about finding a common denominator what is the smallest number that is a multiple of both 4 & 6 well it might jump out of you that it's 12 you can literally just go through the multiples of 4 or you can look at the prime factorization of both of these numbers and what's the smallest number that has all of the prime factors of both of these so you need two twos and you need a 2 and a 3 so if you have two 2s and a 3 that's 4 times 3 is 12 so let's rewrite this as as something over 12 plus plus something over 12 plus something over 12 well to get your denominator from 4 to 12 you have to multiply by 3 so let's multiply our numerator by 3 as well so if you multiply negative 3 times 3 you're going to have negative 9 and to get your denominator from 6 to 12 you have to multiply by 2 so let's multiply our numerator by 2 as well so that we don't change the value of the fraction so that's going to be negative 20 and now we are ready to add our common denominator is 12 and so this is going to be negative 9 negative 9 plus negative 20 or even write that as minus 20 over 12 which is equal to and we deserve a drum roll now this is negative twenty nine over twelve and twenty nine is a prime number so it's not going to share any common factors other than one with twelve so we also have this in the in the most simplified form