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

#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. Grits Eaten Daily Makes Students Achieve.

#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.

#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.

#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 =

#5 Negative coefficients vs. negative terms -6 + x is different than -6 ● 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

#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

#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

#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

#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

#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.