Order of Operations
Please Excuse My Dear Aunt Sally (PEMDAS)
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
The above provides the hierarchy of the operations. Do parenthesis first, then exponents. After that do multiplication and division which are of equal "hierarchy", so do them left to right. And addition and subtraction are equal so do them left to right.
So, lets try some problems where we need to understand order of operations. Just keep in mind the basic rule PEMDAS.
4+3 Start with an easy one, why not?
7 <- Answer
4+3*2 PEMDAS ... therefore, multiply first
4+6
10 <- Answer
(4+3)*2 PEMDAS ... therefore, parenthesis first
7*2=
14 <- Answer
(4^2-10)+3*2 PEMDAS - parenthesis first, but there is an
exponent in the parenthesis,
as indicated by ^ symbol
(16-10)+3*2 PEMDAS - still have a parenthesis
(6)+3*2 PEMDAS - now there is only
one number in that
parenthesis, remove it
6+3*2 PEMDAS - multiplication first
6+6
12 <- Answer
5+10/5 PEMDAS - you might think
this is 3, but divide first
5+2
7 <- Answer
10*10/5 PEMDAS - remember multiplication and
division are of equal precedence,
and merely go left to right.
100/5
20 <- Answer
((4-3-6)^2-(-4)^3)-3*22 PEMDAS - looks like a tough one
... parenthesis first ...
with another exponent ^
((-5)^2-(-4)^3)-3*22 That's progress.
Now what is -5 squared,
oh yes positive 25.
(25-(-4)^3)-3*22 OK, with PEMDAS we have
another exponent.
What is -4 cubed?
Oh yes, -64.
(-4)(-4)(-4)=-64
(25-(-64))-3*22 OK, we have a parenthesis
inside a parenthesis.
What is -(-64)?
Positive 64, of course.
(25+64)-3*22 We still have a parenthesis.
89-3*22 OK, now we have no more parenthesis.
Multiplication first.
89-66
23 <- Answer
Other Sources of Help
Order of Operations - Purplemath
Order of Opns & One Step at a time - Robert Prior