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?

### Like this:

Like Loading...

*Related*

Tags: evaluate, math vocabulary, simplify

## Leave a Reply