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Order of Operations - Problem 3

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

Use Order of operations (PEMDAS) to evaluate or simplify expressions with more than one set of parentheses. Start by simplifying the inside, or inner most, set of parentheses first. Within that group, use the correct order of operations (PEMDAS) to simplify. Next, use order of operations to simplify the next set of parentheses. After all the parentheses are simplified, move onto the next step in the order of operations -- [E] exponents, then [M] multiplication and [D] division (from left to right), and [A] addition and [S] subtraction (from left to right). The same skills will be used when solving equations

This expression is kind of tricky because I have 2 sets of parentheses going on. A lot of times out of our classes the first time you see this like parentheses inside more parentheses. In order to simplify it make sure you follow the order of operations which is PEMDAS, Parentheses, Exponent, Multiply, Divide, almost forgot it and then Add, Subtract from left to right. Make sure you follow that as you go along.

So the first thing I'm going to do is do my inside parentheses first then I'm going to work with the rest of these parentheses, the square parentheses before I multiply by 3 or take care of that 10 stuff. So here we go. I'm going to have 3, these big parentheses are staying. First thing I'm going to deal with is 4 plus 1 which is 5. That's tricky because I did some addition and addition doesn't officially come till back here in the order of operations but what I'm really doing is I'm still on step one, I'm still simplifying the grouping, the parentheses.

Now I have these square parentheses to deal with, I need to simplify what's in there. So let's see. 2 times 5² is the same thing as 25. I'm still not done with these square parentheses. I still have some simplifying to do, 2 times 25 is 50. All of that stuff was this first grouping, the first set of parentheses.

Now I'm ready to continue with multiplying and dividing and adding subtracting using the exponents now that I've taken care of my parentheses. So let's see, parentheses done, I'm ready to do exponents so 10², 10 times itself is 100. 3 times 50 take away 100 is where I'm at, 3 times 50 is equal to 150, so my final answer is going to be 50.

Please be careful when you're doing order of operations that you do all the parentheses groupings first. This one you can see had like a double parentheses that I had to work with in addition to the exponents and that's what makes it a really challenging problem. If you don't understand this whole problem hopefully you understand it from about here down because this is kind of like the basic level. If you understand all of this stuff you're like an A+ student so way to go. So when you come to problems like this in your homework, again I just want to say follow the order of operations, be really careful with the groupings and you guys will have a lot of success.

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