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okay and now heres where it all comes together factoring plus the symbols game equals fraction mastery if you can factor things and you understand the symbols game you have our master of fractions for example suppose that we want to reduce oh I dont know 16 40th step one factor sixteen is four times four which is two times two times two times two and down below 40 is 4 times 10 4 is 2 times 2 and 10 is 2 times 5 ok thats the factoring wheres the symbols game you got the same thing above and below you can get rid of them same thing above and below you can get rid of the same thing above and below get rid of them theres nothing left this is the takeaway as much as you can game you are left with two fits that is 16 40th reduced what else can we do we can find equivalent fractions find three fractions equivalent to I dont know whats your favorite fraction 47 okay four sevens what is that you put a 4 up top you put a 7 down below you put anything else you want in this is one of those