Order of Operations Tutorial
Creator of Tutorial: TheSmartOne

Question

Tutorials · Answer

$\Huge\bf Order~of~Operations:$

We memorize $\Large\bf PEMDAS$ so that we know which order to follow.

$\bf\Large P: Parenthesis$

$\bf\Large E: Exponents$

$\bf\Large M: Multiplication$

$\bf\Large D: Division$

$\bf\Large A: Addition$

$\bf\Large S: Subtraction$

We follow it in order from left to right.

One way to remember PEMDAS is by this sentence

$\Large\bf Please~Excuse~My~Dear~Aunt~Sally$

or by this sentence

$\Large\bf Pink~Elephants~Make~Dandy~Apple~Sauce$

So here is a practice problem

$\Large\bf (13-3)^2 -5 \times 4 +6 -9 + 4^2 \div 2$

First we would solve any parenthesis from left to right.

$\Large\bf \color{green}{(10)}^2  -5 \times 4 +6 -9 + 4^2 \div 2$

Next we solve any exponents from left to right.

$\Large\bf \color{red}{100} -5 \times 4 +6 -9 + \color{red}{16}\div 2$

Now we do any multiplications from left to right.

$\Large\bf 100 - \color{blue}{20} +6 -9 + 16 \div 2$

Now we have to do any division from left to right.

$\Large\bf 100 - 20 +6 -9 + \color{orange}{8}$

Now we can do addition from right to left.

$\Large\bf 100 - \color{purple}{14} -\color{purple}{1}$

Now we can subtract from left to right.

$\Large\bf \color{pink}{86} -1$

$\Large\bf \color{pink}{85}$

$\Large\bf So~the~answer~is~\color{gold}{85}$

$\Huge\bf Note:$

20+6=26 but there is a – sign in front of the 20 that you have to account for. So it is actually -20+6=-14

The same goes for -9+8=-1. We have to account for that – sign, because otherwise we would get a different answer.

$\Huge\bf Tips:$

You can just start doing both addition and subtraction from left to right. For example when you have:

$\normalsize 100-20+6-9+8$

You can do whatever comes first addition or subtraction and ove from left to right.

$\normalsize \color{teal}{80}+6-9+8$

And continue just like this.

$\normalsize \color{lime}{86}-9+8$

$\normalsize \color{brown }{77}+8$

$\normalsize \color{violet }{85}$

Ashely · Answer

thanks