Should I Evaluate or Simplify?

2 Sep

I’ve been doing some searching in textbooks and the internet, and there’s some ambiguity around the mathematical verbs: evaluate and simplify. I wish we could differentiate these better because I think a clearer, more consistent, distinction between the two words would make it easier on the students. They would have a better clue as to the objective of the request.

Many textbooks and teachers only use evaluate when they have an algebraic expression with known variable values.

Ex)  Evaluate  3x + 4 for x = 12

Once the variable is substituted in, then the student is to simplify the numerical expression. And then they use simplify for any other situation regarding expressions.  They use simplify for both numerical and algebraic expressions.

Simplify:  3(12) + 4          or     Simplify : 2(3x + 4) + x

36 + 4                                         6x + 8 + x

40                                               7x + 8

However, other sources define evaluate to mean finding the value of a numerical or algebraic expressions. If a single numerical value is sure to be found for an expression, then evaluate would be appropriate.  Both these examples would use the verb evaluate.

Evaluate:  3x + 4 for x = 12        or   Evaluate:  3(12) + 4

40                                                   40

Then when do you use simplify? Simplify is reserved for algebraic expressions whose variable values are unknown. Algebraic expressions that can potentially be compacted to a smaller number of terms by mathematical operations and/or combining like terms.  So in this case, simplify truly means to make the expression simpler in form even though it may not result in a single numerical value.

Simplify: 2(3x + 4) + x           or       Simplify: 2(3x + 4) – 6x

6x + 8 + x                                      6x + 8 – 6x

7x + 8                                               8

I really like this latter definition.  But mostly I would like the math community to agree on a consistent definition. What do you think?


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