## Multiplication Without Parentheses (MWP)

The discussion here necessarily must begin with an appeal
to the **order of algebraic operations** (**OO**).
These are rules
of hierarchy as to which operations to perform 1st, 2nd, etc.
when an algebraic expression requires more than one operation
be performed. There are three levels of hierarchy:

- powers,
- multiplication and division, and
- addition and subtraction.

When faced with an expression like the one below that has both
an addition and a multiplication in it, the order of operations
dictates that the multiplication be performed first:

The levels above do not give the whole story, however. For
instance, what if an expression has both an addition and a
subtraction, operations which appear at the same level? The answer
here is that operations appearing on the same level are always
performed left-to-right:

Also, one may use parentheses to override these rules. Things
in parentheses are performed before things outside of those
parentheses, starting from the inside and working out. So

while

and

These order of operations apply to expressions involving
variables as well. Thus

In this light, acceptable notation for the product of two
expressions like and is

*not, as so many students write,*

Top Algebra Errors Made by Calculus Students
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Thomas L. Scofield
2003-09-04