Variables and Algebraic Expressions
Define a variable as a symbol representing an unknown or changing quantity. Identify parts of an expression (term, coefficient, constant, factor) and translate verbal phrases into algebraic form.
A lesson of Pre-Algebra, in Expressions & Equations, about 10 minutes.
By the end of this lesson, you will be able to write algebraic expressions from verbal descriptions, identify terms and coefficients, and evaluate expressions.
Key Vocabulary
Variable: a letter representing an unknown or changing value ($x$, $n$, $t$).
Constant: a fixed number that doesn't change.
Term: a single number, variable, or product of numbers and variables. Terms are separated by + or −.
Coefficient: the number multiplied by a variable ($3x$ → coefficient is 3; $-7y$ → coefficient is −7).
Expression: a combination of terms (no equal sign). Example: $4x - 3y + 7$
Writing Expressions from Words
| Words | Expression |
|---|---|
| A number plus 8 | $n + 8$ |
| 5 less than $x$ | $x - 5$ |
| 3 times a number | $3n$ |
| A number divided by 6 | $n \div 6$ or $n/6$ |
| Twice a number, increased by 4 | $2n + 4$ |
| The square of a number minus 1 | $n^2 - 1$ |
Watch: "5 less than $x$" = $x - 5$ (not $5 - x$)
Evaluating Expressions
Substitute the given value for the variable, then simplify using order of operations.
Evaluate $3x^2 - 2x + 1$ when $x = 4$:
$3(4)^2 - 2(4) + 1 = 3(16) - 8 + 1 = 48 - 8 + 1 = 41$
Summary
Term → coefficient × variable. $5x$ has coefficient 5.
Expression: no equal sign; write from verbal descriptions.
Evaluate: substitute the value, then follow PEMDAS.