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Order of Operations

When presented with a math problem containing various operations, in order to arrive at the proper answer, these operations must be performed in a particular order.  One of the most popular mnemonics for remembering the order of operations in mathematics is

Please Excuse My Dear Aunt Sally. 

The proper order of operations is Parentheses, exponents, multiplication, division, addition and subtraction.

Consider the following expression  (4)²-3 +4 x 9 =

Lets first work it out doing operations left to right 16-3+4 x 9=

Now we have 13 + 4 x 9 =

An now 17 x 9 = 153

The correct Order of Operations yields a different answer

(4)²-3 + 4 x 9 =

Now doing parentheses and exponents first we have 16 -3 + 4 x 9 =

Moving onto multiplication we have 16-3 + 36

On now to addition and subtraction we have 13 + 36 = 49

What do you suppose would happen if mathematicians didn't agree on the proper order in which to do things? 

Exercises

1. (2 + 3)²+ 3 - (4 x 2) =

2. 4 x 6(2) - 4^{2 =}

Variables and Algebraic Expressions

Exercises

6. x minus 17 plus 4

Evaluate each express for x=4, b=2 and y=9

1. x + b-7=                               

2. y-4=

3. y-x=

4. b+x+y=