PEMDAS (or “Please Excuse My Dear Aunt Sally”) is an often-used method to remember the “order of operations”. The P stands for Parenthesis. Anything in parentheses needs to be done first.
Now this one may be a little misleading because it’s not only things in parentheses that need to be done first, this counts for all grouping symbols.
It’s about Brackets, Absolute Value, just about anything that’s grouping numbers together.
Before we simplify an expression, knowing what operations need to be performed first is important if there’s more than one operation present in the expression
After Parentheses comes Exponents followed by their inverses that also need to be done next. Following then are Multiplication and Division.
This is actually a bit special since, with multiplication and division, these don’t need to be done one before the other, you just work from left to right with these.
So in this expression, when you look from left to right, you do your multiplication before your division.
Finally, here are Addition and Subtraction. These are working in the same way as before with Multiplication and Division. These also need to be done from left to right. However, they are the last tasks to be done when simplifying or solving an expression.
Let’s see how we put PEMDAS to work when we simplify this expression.
According to PEMDAS, we should begin with the parentheses, the grouping symbols. So 3+9 is where we have to start. This the only thing we need to simplify, so all other things stay the same. 2 plus 5 minus, 3 plus 9 = 12, divided by 2 squared.
So now we’ve done the things in parentheses and grouping symbols and next up are exponents. We’ve got an exponent here at the end, and 2 squared need to be simplified next. So 2 plus 5 minus 12 divided by 2 squared (meaning 2 times itself) which is 4.
Next, we have multiplication and division. We do this from left to right. When I now look from the left to the right, all I need to do is this division operation. So that’s the next thing we need to do: 2 plus 5 minus, and 12 divided by 4 makes 3.
Finally, we come to addition and subtraction. Once again, this worked from the left to the right. So 2 plus 5 makes 7, bring down the minus 3. 7 minus 3 is 4. So simplified, this expression would give us 4.
Now, let’s take a look at what would happen if we would ignore our order of operations. What if we work from left to right. Then, we would be starting with 2 plus 5. This would give you 7, minus 3 plus 9, and then divided by 2 squared.
Thereafter we would do 3 plus 9, so we would have 7 minus 12, and that divided by 2 squared, 7 minus 12 gives us -5 (as we may add the inverse, 7 + -12, makes -5), divided by 2 squared.
This means -5 divided by 4. So, as you see: when we ignore our order of operations, we’ll get a totally different answer and this why it’s so important to ensure that we always go in the correct order. Do this whenever you’re solving or simplifying an expression.