Lesson 1: Expressions

Property

A variable is a letter that represents a number whose value may change.
A constant is a number whose value always stays the same.

Examples 1

• In the formula for the area of a square, $A = s^2$, the area $A$ and side length $s$ are variables, as they can change depending on the square.
• If a taxi charges 3 dollars per mile, the cost per mile is a constant. The total fare and the distance traveled are variables.
• The number of days in January, 31, is a constant. The number of sunny days in January, $d$, is a variable.

Example 2

• If a taxi charges 3 dollars per mile, the cost per mile is a constant. The total fare and the distance traveled are variables.
• The number of days in January, 31, is a constant. The number of sunny days in January, $d$, is a variable.

Property

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Examples

• To evaluate $8y - 5$ when $y=-3$, substitute $-3$ for $y$: $8(-3) - 5 = -24 - 5 = -29$.

• To evaluate $a^2 + 5$ when $a=-4$, substitute $-4$ for $a$: $(-4)^2 + 5 = 16 + 5 = 21$.