1. Top Ten Common Algebra Mistakes
Presentation by: Valerie Beaman-Hackle
Associate Professor of Mathematics
Macon State College
For the Georgia Tutoring Association (GATA)
10th Annual Conference
Saturday, February 20, 2010
Macon, GA

2. #1 Multiplication before Division?
There are only 4 levels in the order of operations agreement!
On the Multiplication and Division level, we must work left to right.
What’s logical and easy to do mentally may not follow the order of operations agreement.
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3. #2 Inside vs. Outside
There are only 4 levels in the order of operations agreement!
Doing what’s inside the parentheses is on the top level, but there is no “do what’s outside the grouping symbol.”
It may be helpful to write in any understood multiplication symbols.
What’s logical and easy to do mentally may not follow the order of operations agreement.

4. #3 What’s negative?
There are 3 places a negative can be in an exponential expression—hanging out front, part of the base, or part of the exponent.
If the negative is not in parentheses but instead hanging out front of the base, then just bring it down as part of your final answer and proceed to evaluate the exponential expression.
The base is negative only if the negative is inside the parentheses and the exponent is outside the parentheses.
With a negative exponent, the base is moved to the denominator and the exponent becomes positive.

5. #4 Solving equations vs. simplifying expressions
Keep equation balanced!
Order of steps matter
Never combine terms over the equals sign. Think of it like a fence. No jumping over the fence
No sliding =

6. #5 Negative coefficients vs. negative terms
-6 + x is different than ● x
Inverse (reverse) of multiplication is division
Inverse (reverse) of subtraction is addition.
May be helpful to show solution to x – 6 = 30 along side of solution to -6x = 30 to emphasize the difference in the problems

7. #6 Subtracting Polynomials
The first set of parentheses don’t require any special consideration, but the second set does
Think of subtraction rule: change subtraction to addition, take opposite of every term in ( )
Or think of distributing a -1 to each term

8. #7 Squaring a binomial
Squaring a binomial is different that raising a product to a power.
Rewrite in expanded notation and FOIL.
May want to show an example of raising a product to a power to emphasize difference

9. #8 Simplifying Rational Expressions
Differentiate between Factors and Terms
NEVER cancel TERMS.
NEVER cancel parts of terms.
Divide out (cancel) FACTORS!
Only MONOMIALS can be factored using expanded notation

10. #9 Solving Rational Equations
Distribute LCD to all terms (even those that aren’t fractions) before canceling denominators!
Also applies to simplifying complex rational expressions. 2 5

11. #10 Solving Rational Equations
Order of the steps matters!
Isolate radical, THEN square both SIDES (not individual terms)!.
Also remember not to combine terms inside radical with those outside.