SOLUTION: I am having issues understanding how and when to "reorder the operations". It appears when the reorder of operations is done that all expressions with a letter get moved to the ri

Question 439478: I am having issues understanding how and when to "reorder the operations". It appears when the reorder of operations is done that all expressions with a letter get moved to the right and all subtraction problems get changed to additions problems. What are the rules of this?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
first something about the OF OPERATIONS RULES
When performing more than one operation on an algebraic expression, work out the operations and signs in the following order:
calculate powers and roots.
perform all multiplication and division.
Finally, with addition and subtraction.
of operations are a of that mathematicians have to to avoid mass when mathematical expressions or equations.

easier way to remember the ORDER OF OPERATIONS RULES
For those of you that remember best with acronyms:

()
Please ...=>...Parentheses
Escuse...=>...Exponents
My ...=>...Multiplication
Dear ...=>...Division
Aunt ...=>...Addition
Sally ...=>...Subtraction
now, about the OF OPERATIONS RULES
the Property, the property, and the property-three basic properties of numbers- allow you to

, , all affecting the result

the Associative Property-Use the associative property to change the grouping in an algebraic expression to make the work tidier or more convenient.

The commutative property makes working with algebraic expressions easier. The commutative property changes the order of some numbers in an operation to make the work tidier or more convenient � all without affecting the result.
Addition:
Example: and , so
the numbers affect the result.

Multiplication:
Subtraction: is not equal to (except in a few special cases)
Example: (�5) � (+2) = (�7) and (+2) � (�5) = +7, so (�5) � (+2) is not equal to (+2) � (�5)
Here, you see how follow the commutative property.
Exception: If and are the same number, then the subtraction appears to be commutative because switching the order doesn�t change the answer.
Example: 2 �2 = 0 and �2 + 2 = 0, so 2 �2 = �2 + 2

Division: (except in a few special cases)
Example: and , so is not equal to
Division also follow the commutative property.
Exception: If a and b are opposites, then you get �1 no matter which order you divide them in.
Example: 2 : �2 = �1 and �2:2 = �1, so 2:�2 = �2 :2

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