Algebra: Evaluating Statements

Equations like the ones we wrote in the precipitation scenario are part of a larger group of mathematical objects called mathematical expressions. Mathematical expressions are mathematical statements made up of numbers, variables, symbols that represent mathematical actions- actions like addition, subtraction- and symbols that represent relationships like equality and so on.

Some mathematical expressions are

3 - 2                writen as "Three minus two"

5 + 4               written as "Five plus four"

You'll notice that these two expressions don't have an equal sign. Instead, they just have a mathematical symbol representing the mathematical action addition (mathematical actions are also called mathematical operations).

When we perform all of the actions in the expression, this larger action (or collection of mathematical actions) is called "evaluating the expression".

In this case, the expression 3 - 2 evaluates to 1, and the expression 5 + 4 evaluates to 9.

Question: What does 4 + 3 evaluate to? (Answer 1)
Question: What does 2 * 3 evaluate to? (Answer 2)
Question: What does 10 - 9 evaluate to? (Answer 3)

You'll notice that, in the above questions, I used the word 'evalute' rather than 'equal'. Similarly, when discussing the expression 3 - 2, above, I avoided saying

"three minus two equals one"
(in symbols, 3 - 2 = 1).

That's because writing "3 - 2 = 1" changes the situation. "3 - 2 = 1" is an equation that evaluates to the values TRUE or FALSE, whereas "3 - 2" by itself is an expression, that evaluates to the number 1.

These two expressions:

3 - 2
and
3 - 2 = 1

are very closely related, but they aren't exactly the same. One evaluates to a number, and one evaluates to TRUE or FALSE.

Question: What does 5 - 2 evaluate to?
Question: What does 5 - 2 = 3 evaluate to?
Question: What does 5 - 2 = 6 evaluate to?