Where does PEMDAS come from?

Question

I know what it stands for, but how was the order of operations decided upon?

Answer 1

It was probably decided upon logically if you think of a real world example. If you had 3 bags of apples with 5 apples each and then someone else have you two. That could be represented by 3 x 5 + 2 where you wouldn't add before you multiply because you don't have those extra two apples for every bag but you only have the two additional apples

Answer 2

I would agree that some of it is pure logic.  Also, keep in mind that humans made up the symbols to fit what really already exists.

 

For instance, parenthesis is being used to represent something that has to be done first, i.e. what is outside those parenthesis is applied to the result of whatever is inside the parenthesis.  So that's like saying I'm putting the parenthesis around something because I want that done first, versus I'm doing it first because there's parenthesis around it.  Someone had to come up with a way to show that "this" thing needs done first, regardless of what symbol we use to do it with.  That is, when I hand it to you, you have to know what I mean for you to do, so we both have to know the same rules.

 

For instance, if it's necessary to add 2 numbers together before taking the square of it, there has to be a way to show the adding comes first.  If I write x + y^2, no one would know the adding needs done first unless we make a rule to indicate that.  So what way can I indicate the adding comes first?  (x + y)^2 

 

Somewhere a decision was made that parenthesis would be used to indicate that.  I want the square of the results of x + y, not just the square of y.  This also leaves us with the fact that if I don't use those parenthesis, the square only belongs to the y, and then it means add x to the result of the square of y.

 

These are just examples but hopefully the point comes across.

 

I think it's probably important to keep in mind that in the end this is applied to real life situations where one thing actually needs to be done before another thing, and we need to have an agreed-upon way to show how it's supposed to be.  So if I need a big set of things done, I have to make sure I use the appropriate symbols and using some set of rules, so that you would do it in the same manner.

 

 

Answer 3

Check out http://mathforum.org/library/drmath/view/52582.html.

Answer 4

These are order in which you have to do the operation to simplify expression.

 

   P - p1ranthesis

 

   2 - exponents

   3 - Multiply divide / in

   4 - add 

   5 - Subtraction

 

   You just need to practice and get hang of it. So many of these things are memorized, and causes confusion.

 

Number 3 and for:

 

    30 ÷ 5 * 3 = 6 * 3 = 18

    30 ÷3 *  5  = 10 * 5  = 50

    Here the case that you have to do steps 3 and 4.

    Do the multiplication and division from right to left in order.

 

 

Answer 5

Hi Lana;

PEMDAS is an acronym for...

Parentheses

Exponential

Multiplication

Division

Addition

Subtraction

 

This is the algebraic order-of-operations.

For example...

4x²

You will calculate the exponential before executing the multiplication.

If x=-2

4(-2)²⁼(4)(4)=16....correct result.

If you execute the multiplication first...

-8²=64

This is a different result, which is wrong.

 

The PEMDAS can be remembered as...

Please

Excuse

My 

Dear

Aunt

Sally