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Common Algebra II Mistakes - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Some of the most common algebra mistakes come from misunderstanding the order of operations or what is commonly known as PEMDAS. We must keep in mind that the multiplication and division are done at the same time in the order of operations, as are addition and subtraction. The most important way to help not make these common algebra mistakes is by practicing and being aware of pitfalls.

Now I'm going to talk about some common mistakes that Algebra 2 students make. The first and foremost that I want to talk about is PEMDAS your golden order of operations thing from Algebra 1 and then I'm going to break [IB] a little bit is not actually true okay and why it is not true is students tend to take this literally and that you have powers then exponents then multiplication then division then addition and subtraction. But what you really have to remember is that multiplication and division as well as addition and subtraction are really just the same operation and so you actually just do them left to right no matter what the order is.
Okay so for here we have 12 divided by 3 times 2 PEMDAS will tell us to multiply before dividing so what we would do is we multiply our 3 times 2 get 6, 12 divided by 6 is 2. So if you use PEMDAS you will get 2, however what you need to remember is that dividing by 3 is the same thing as multiplying by one third. Okay so by just re-writing this as multiplication what we've done is 12 times one third times 2 what we got in this case is 12 divided by 3 is 4 times 2 is 8. Okay so 8 is actually the right answer for this problem, you plug it into your calculator just as this 8 will come out and the reason being is that division and multiplication are on the same level.
Okay so if you have a problem without parenthesis or exponents or anything like that just multiplication and division all you do is you go left to right you hit the division sign first that's fine, you hit multiplication sign first that's fine as well. Okay but you just go left or right, the same thing for addition or subtraction, you don't necessary do addition first you just look for the addition, subtraction and you go left or right and just follow the flow as opposed to looking for the sign first. Okay so first red flag PEMDAS isn't true okay multiplication, division are the same, addition, subtraction are the same.

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