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Order of Operations - Problem 1

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

Order of operations, or PEMDAS, is used to simplify or evaluate a basic expression involving more than one operation. First, start by doing the operations inside the parentheses. Next, do the exponents. Next is multiplying and dividing. Even though in PEMDAS, "M" comes before "D", we actually do whichever operation comes first when looking at the expression from left to right. Lastly, we add and subtract. Again, even though "D" is written before "A" in PEMDAS, we do whichever operation comes first when looking at the expression from left to right. Understanding how to simplify expressions is needed to understand how to solve equations.

This is a problem that I want to simplify using the order of operations which is PEMDAS. A lot of people remember it as Please Excuse My Dear Aunt Sally, to help them remember the letters but the most important stuff is that it stands for Parentheses, Exponents, Multiply, Divide from the left to right, and Add, Subtract from the left to right.

So in order to start simplifying the first thing I want to look for is parentheses. There they are so everything is going to stay the same except for what's in that parentheses. 6 minus 4 is grouped together so they get that operation first. That's the P part, parentheses, done.

Exponents don't have any. Sweet okay. Now we need to multiply from left to right. This is the first thing I see that's a division sign, 8 divided by 1/2. Be careful, dividing by fractions is the same as multiplying by the reciprocal so what I'm really doing is 8 times 2. So this piece is going to be 16, everything else stays the same. That was my first multiply divide from left to right.

Next thing I need to do is more multiplying. 16 times 3 is 48, and I still have that +2. Now that I'm done with my multiplying and dividing from left to right I'm ready to add, subtract. You can see your final answer is going to be 50.

When you are working on these problems, please, please, please write everything out step by step by step. Make sure you work vertically instead of horizontally because a lot of times that's where students make their mistakes, when they try to like cram it in or do stuff in their head or whatever. My guess, if you're getting these problems incorrect, it's because you're not writing out things as you go. So this is an example of using the order of operations when we have a whole bunch of mathematical symbols. Just make sure you follow the order of operations which is PEMDAS.

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