Order of Operations
It's a classic stumper on the internet: a math problem with multiple operations and people arguing about what order to do the steps to get the right answer.
No matter what your Facebook friends may say, there is only one correct way to do these problems, by following the standard order of operations. A common mnemonic device for this is PEMDAS or "Please Excuse My Dear Aunt Sally."
For the first step, "P" stands for "Parentheses." Any operation inside parentheses or other grouping symbols should come first. If there's more than one operation inside, go through the PEMDAS steps inside the grouping symbols first!
A couple important notes:First: Sometimes parentheses are placed next to each other to represent multiplication, but that falls under step 3. The "P" step only includes doing whatever's inside the parentheses or grouping symbols.
Second: "Grouping symbols" includes more than just parentheses and brackets. Square root symbols and fraction bars* also qualify as part of this step. But remember, this only means to do the steps inside the square root or the top or bottom of the fraction first; it doesn't mean to actually do the square root or simplify the fraction yet.
Step 2: "E" stands for "Exponents." Evaluate any powers and roots within the problem.
Step 3: "MD" for "Multiplication and Division." Evaluate any multiplication and division steps, working from left to right. (This is one place where those Facebook memes tend to dissolve into arguments - people often remember the PEMDAS mnemonic and forget that the "MD" part is a single step.)
Step 4: "AS" for "Addition and Subtraction." Once again, these two operations are part of the same step and should be evaluated from left to right.
*SPECIAL NOTE: Fraction bars are the other place where those Facebook meme problems tend to fall into debate! If the fraction is written vertically with a clear top and bottom, then the fraction bar qualifies as a grouping symbol, so simplify the top and simplify the bottom as part of step 1. However, if the fraction is typed out linearly, then the fraction bar qualifies as a division symbol and falls under step 2. That means the division of the terms on either side of the fraction bar comes before any addition and subtraction, and before any multiplication to the right of it.
If a linear fraction is meant to have operations within it, then there need to be parentheses to clearly denote what's on top and what's on the bottom.
