Lesson Order of Operations

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Order of Operations can be your friend. They help make your mathmatical life easier and your answers correct. It's relatively easy to master and you never forget it once you do. It's like a scar on your brain that never goes away. But it's a good scar, you know, one of those that you like to show your buddies, tell elaborate stories about how you got it, and it makes you feel tough and all that jazz. Well, the only difference is that Order of Operations doesn't exactly make you feel tough and you can't really tell very elaborate stories about how you learned about it sitting in a boring Algebra class with the teacher who spoke in a monotone voice for an hour, said the word "uh" at least twice in every sentence, and who's breath smells like cat pee no matter how many mints he ate that morning.

Ok, stop with the memories and get back on topic. Order of Operations are commonly used in numeric equations. When a student uses the Order of Operations correctly, they get the right answer. The Order of Operations goes in this order:

P - arenthesis
E - xponents
M - ultiplication
D - ivision
A - ddition
S - ubtraction

The best way to remember these six Ops is to address like it is one word. "PEMDAS".

Or, you could use acronyms. The one I find most common is "Please Excuse My Dear Aunt Sally." But, my classmates sort of played around with it and came up with "Please Embalm My Dead Aunt Sally." (My apologies to those of you out there with an Aunt Sally who just died. May she rest in peace.)

Alright, so now you've got this ingrained in your brain and you're ready to begin. Let's start with something simple...

{{{(8(9))6+4}}}

Ok, so we've got some parenthesis in here. Work them out FIRST!

{{{(72)6+4}}}

Now we still have the parenthesis, but there's not an expression inside, just an answer. Still, the parenthesis are just another way of saying "multiply me!" It looks a lot better than a little dot or an X that can be easily confused with the variable "x" in Algebra.

So, because we don't have any exponents to deal with, what we're doing now is multiplying the 72 by the 6. This one takes a little brain power.

{{{72(6)=432}}}

Ah, that's nice. Ok, plug in the 432 in the expression. The next Operation that we could do in the PEMDAS list would be Addition, so....

{{{432+4}}}

And you get 436.

Let's take it a step further. I'm gonna throw a little bit of division and subtraction.

{{{(8(9))6+4-4/2}}}

PEMDAS. Get rid of the parenthesis expression first.

{{{(8(9))=72}}}

{{{(72)6+4-4/2}}}

Now, we don't have any exponents so we skip to the Multiplying part of the expression.

{{{432+4-4/2}}}

Ok, I know you're tempted to go ahead and work the whole problem left to right, but DON'T! You will screw the whole thing up if you do that! You MUST follow the Order of Operations! You will use the next Operation in line...Division. Get rid of that 4/2. You'll get 2 because 4/2 is 2. Now plug the 2 in there.

{{{432+4-2}}}

NOW you can work the problem left to right because Addition and Subtraction come last.

{{{432+4=436}}}

{{{436-2=434}}}

Alright, back up to the 432 + 4 - 2. Let's try something different and switch it around.

{{{2 - 4 + 432}}}

Ok, we have a dilemna. The Order of Operations says to Add first, then Subtract. BUT in our expression, subtraction is written before addition. So, just like before, DON'T work it left to right because it will be wrong. Do the addition first.

{{{4+432=436}}}

Now, plug the 436 in the expression and NOW you can work it across.

{{{2-436=-434}}}

Yes, the answer is different than before, but remember, we switched the expression around, forming a totally new equation. The answer is going to different because it's not the same expression as before.

Now, we're going to go a little more in-depth with the Parenthesis, Multiplication/Division, and Addition/Subtraction. Hows about we leave the exponents for last, eh? I don't know about you, but I'm all for it.

So, what we're going to do is work out an expression with more than one parenthesis, multiplication/division expressions, and addition/subtraction expressions.

{{{(8(9))6+4-4/2+3(5(6))-7}}}

So, we're gonna take care of the parenthesis first. DO BOTH PARENTHESIS AT THE SAME TIME.

{{{(72)6+4-4/2+3(30)-7}}}

Now, next in line is the multiplication, due to the fact that there are no exponents in the expression. Remember this: when there is more than one of the same operation in the same equation, you work them left to right. So, we'll multiply 72 and 6 first, then we'll take care of 3 and 30.

{{{432+4-4/2+90-7}}}

Ok, now just like before, next in line is division...

{{{432+4-2+90-7}}}

Work the addition problems left to right, just like the multiplication expressions.

{{{436-92-7}}}

And now work the subtraction left to right and you'll get your answer.

{{{436-92=344}}}

{{{344-7=337}}}

And your answer is 337.

Lastly, I'm going to throw in an exponent. Let's not make this harder than we have to, shall we?

{{{(8(9))6+4-4/2+9^2}}}

PEMDAS. Get rid of the parenthesis first.

{{{(72)6+4-4/2+9^2}}}

Ok, NOW we have an exponent in there. According to PEMDAS, we do these next. 9^2 = 9(9) = 81

{{{(72)6+4-4/2+81}}}

The exponents are gone, so we now do the mulitplication.

{{{432+4-4/2+81}}}

The division has got to go! 4/2 = 2

{{{432+4-2+81}}}

Next is the addition. We have more than one addition expression, so work those left to right. Leave the subtraction for last.

{{{436-83}}}

Do the math and you have your answer.

{{{436-83=353}}}

Now, let's summarize the two key points we went over in this lesson...

2 - PEMDAS. Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction. You must use the Order of Operations when solving a numeric equation. If you don't, you will fail...in solving the equation, anyway. PEMDAS can best be remembered by either using it as one word or using an acronym.

1 - When you run into an equation with more than one of an operation, always work them from left to right. It makes solving the equation a lot easier.

And there you have it, the Order of Operations. Well, it's the basics, anyway. The more advanced stuff is another lesson. But for now, enjoy the new scar in your mind, because it's not going away anytime soon.