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Order of Operations - Problem 2
Order of operations, or PEMDAS, is used to simplify or evaluate an expression involving a fraction with more than one operation in both the numerator and the denominator. Although "P" stands for parentheses, it refers to grouping symbols in general. Grouping symbols include parentheses, brackets, braces, radicals, and fraction lines. Since a fraction line is considered a grouping symbol, think of everything in the numerator as being in one set of parentheses and everything in the denominator as being in another set of parentheses. Then continue to simplify by using the correct order of operations. Knowing how to simplify or evaluate expressions will be useful when solving equations.
For a lot of students Algebra class is the first time they see a funky fraction like this. It's kind of weird because not only is it like a fraction but you have Math on the top or the numerator, you also have Math to do in the denominator. So when you're simplifying a fraction like this be really careful to follow the order of operations.
First thing you need to do is take care of any groupings which are what the P stands for parentheses. So the first thing I'm going to do is on top there that 3 plus 2 is going to become 5, -8 I haven't dealt with, everything else is going to stay the same, because there is no other simplifying groupings or parentheses, P done.
Next thing I need to do is take care of e which stands for exponents. So you can see I have this -3 squared in the bottom of the fraction. The top will stay the same but the bottom -3 times -3 is +9 and then plus 1, exponents done.
Next thing I need to do is multiplying and dividing moving from left to right. So on top I have some multiplying 5 times -8 is -40. Bottom stays the same, multiplying and dividing done.
The last step is this adding subtracting. I'm going to move up here, pardon me. So I have -40 divided by 9 plus 1 is 10 and then I'm going to simplify that fraction -40 divided 10 is equal -4.
It's kind of confusing because those of you who know a lot about fractions know that what I did here was actually a division step but division happened earlier in my PEMDAS ordering. That's one of the tricks with PEMDAS or with order of operations is you need to simplify different groups before you simplify the entire problem. So when you come to problems like this that are big scary fractions simplify the top and bottom using PEMDAS and then reduce your final answer.