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**Kristin****Member**- Registered: 2005-09-30
- Posts: 1

I am trying to learn how to do Orders of Operations and I am having a hard time understanding how to do them properly and get the correct answer.

Here's one of my problems :

21 divided by 7 + 4 x 3

And then there are problems like

5 ( 3+6 ) -3 to the 2 power. I know with the 3 to the second power you times 3 twice. However, that does - before 3 mean? Does this mean - subtracted?

Could someone explain it to me so I can understand it. The directions I have I am having a hard time understanding. Here's what they are :

Step 1 : Do Operations within the Parentheses

Step 2 : Do Operations with Powers and Roos ( What is that ) ?

Step 3 : Do all multiplication and subtraction operations from left to right

Step 4 : Do all addition and subtraction operations from left to right

It's pretty much explanitory to some, however I don't think so. How do you get the answers to the problems?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,050

Step 1 : Do Operations within the Parentheses

3 - (6 + 8) x 3 = 3 - 14 x 3 = 3 - 42 = -39

The first operation to be done is always the one within the Parantheses.

Step 2 : Do Operations with Powers and Roots

3 + 2^5 = 3 + 32 = 35 (Here ^ represents powers)

3 + √ 16 = 3 ± 4 = 7 or -1.

Step 3 : Do all multiplication and division operations from left to right

Step 4 : Do all addition and subtraction operations from left to right

50 ÷ 10 ÷ 2 = (50 ÷ 10 ) ÷ 2 = 5 ÷ 2 = 2.5

If it is done from the other direction, you get a different (and wrong) answer.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Andrew****Guest**

B - Brackets

E - Exponentials (powers)

M - Multiplication

D - Division

A - Addition

S - Subtraction

Roots, etc, count as Exponents (root 2 = 2^(1/2)).

Just remenber the word BEMDAS.

**Andrew****Guest**

Example you gave:

5 ( 3+6 ) -3 to the 2 power

Let's rewrite that as 5(3 + 6) - 3^2

^ = power symbol as someone already mentioned (I'm assuming here that you only power the 3, not the entire line)

First thing you do is parenthises (brackets), so let's do what's in the brackets.

3 + 6 = 9

So now the original line looks like:

5(9) - 3^2

Next thing to do is the power. 3^2 = 9 (3^2 means 3 squared.. in other words, 3 x 3.)

So now you have..

5(9) - 9

Next is multiplication

5(9) is another way of writing 5x9, which = 45

Now you have:

45 - 9

Now there's only one thing left to do..

45 - 9 = 36

..if that makes any sense.

Just follow that sort of order for everything you get, and it should work.

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

Great answer, Andrew!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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