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?

(Answer 3)

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

(Answer
4)

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

(Answer 5)

Answers

Answer 1:
7

Answer 2:
6

Answer 3:
1

Answer 4:
3

Answer 5: TRUE, because it's TRUE that 5 - 2 is 3

Answer 6: FALSE, because 5 - 2 is not 6

Copyright Jen Schellinck, 2006