Recall the Order of Operations (it is the same as before)



Goals: To refine our understanding of the order of operations and how it applies to examples with fractions Recall the Order of Operations (it is still the same as before)Learn how we treat the operations including division, exponents, and absolute values involving complex fractions and fractions operations where multiple operations are present at onceRecall the Order of Operations (it is the same as before)Parenthesis or grouping symbolsExponentsMultiplication AND Division in order of appearance from L→RAddition AND Subtraction in order of appearance from L→RNote: division or fraction bars, absolute value bars, and square root symbols act as a grouping symbols.Lets recall what exponents mean.am=a?a???am times am literally means “a times a times a times a…etc and you do it for the same number of times equal to the number m.Example a4=a?a?a?a timesSo if a happens to be a fraction, then so be it, we are just multiplying a bunch of fractions, which means…We are just multiplying a bunch of numerators by themselves divided by a bunch of denominators by themselves.Example: If we let a=23 from the previous example we would have a4=234=23?23?23?234 times=2?2?2?23?3?3?3=2434=1681Try some:Bonus Question353=144= 325=if a=12 find a3What if the fraction is negative? Just treat it like a problem with two parts, one is the fraction, the other is the negative! (Why can we do this? Can you think of a justification for how this is a correct way of simplifying?)-432=-233=-142=Negatives and exponents: be mindful of when a number is your base and when it is just the opposite.Examples:-24=-(2)4=If you want to include it (negative symbol), put it in a grouping symbol!! So let’s just put a bunch of operations together with fractions.Examples-3423-9529= 232--2315=-12-57+27-32= 342--34212=-223+12-4÷212= 232--23215=-12+98?23= 5313-232=Now What if we have to divide some fractions that are being added? This might end up being just a really complex fraction.Example: Rewrite this problem using only one fraction bar 12-23÷12+1236379152540if true, find the answer, if false find the correct expression00if true, find the answer, if false find the correct expressionExample: T or F 13-23÷12+12=13-2312+12 Examples:12-3214+14= 78+1989-16=-58-65-54-38=-78+19-89+16= 37-2929-37=52+1869-23=Optional/Bonus Page:If a rectangular room is 712 by 912 feet. What is the area and perimeter of the room?Crazy (fun) Bonus Problems252-252+7327÷412?32-32= 234-1212= 425÷5?5-552+232= ................
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