Order of Operations
Before simplifying expressions, it is important to know which operations to perform first if more than one operation is present in the expression.
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“Please Excuse My Dear Aunt Sally”, or PEMDAS, is often used for remembering the order of operations.
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The following transcript is provided for your convenience.
P is for Parenthesis, anything in parenthesis should be done first. This one’s a little misleading, though, because it’s not just parenthesis that should be done first, it’s all grouping symbols. Brackets, absolute value, anything that groups numbers together. Followed by Exponents, and then their inverses, roots, should be done next. Following that is Multiplication and Division, and this is special, because of multiplication and division, it’s not that one needs to be done before the other, these are just worked from left to right. So, in your expression, when you’re looking from left to right, you’ll do all your multiplication before you do your division. Finally, Addition and Subtraction work the same way as Multiplication and Division. So, these will also be done from left to right, but these will be the last things done when simplifying an expression.
Let’s put PEMDAS to work. We’re going to simplify this expression.
So, according to PEMDAS, we need to start with our parenthesis or our grouping symbols. 3+9 then is where we need to start. That’s the only thing we’re going to simplify, so everything else stays the same. 2 plus 5 minus, 3 plus 9 is 12, divided by 2 squared.
We’re done with our parenthesis or grouping symbols, so next up is exponents, and we have an exponent right here at the end, so 2 squared will be the next thing we simplify.
2 plus 5 minus 12 divided by 2 squared means 2 times itself, 2 times, which is 4.
Then we have our multiplication and division from left to right. So, as we look from left to right, all we have is this one division operation to perform, so that’ll be the next thing we do.
2 plus 5 minus, 12 divided by 4 is 3.
Finally, we get to our addition and subtraction. Again, these are worked from left to right. So, 2 plus 5 is 7, bring down our minus 3, and 7 minus 3 is 4.
So, this expression simplified would give you 4.
Now, let’s see what happens if we ignore the order of operations, and just work from left to right. If we were just working from left to right, we would start with 2 plus 5, which would give us 7, minus 3 plus 9, divided by 2 squared. Then we would do our 3 plus 9, so we’d have 7 minus 12 divided by 2 squared, 7 minus 12 would give -5, since we can add the inverse, 7 + -12, -5, divided by 2 square.
So, as you can see, if we ignore the order of operations, we get a completely different answer, which is why it’s very important to make sure you’re always going in the correct order whenever you solve or simplify an expression.
This lesson is a part of the Math Basic chapter and is included in our practice tests.