Basic Algebra/Introduction to Basic Algebra Ideas/Variables and Expressions

Vocabulary

Variable
Term
Operation
Expression
Evaluate
Substitute

Lesson

A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are $a$ , $x$ , $y$ , $\theta$ and $\lambda$ . The letters x and y are commonly used, but remember that any other symbols would work just as well.

Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.

Some examples of variables in use:

$3x$ -- three times of $x$ .
$5-y$ -- five minus $y$
$2\div s$ or ${\frac {2}{s}}$ -- 2 divided by $s$

A term is a number or a variable or a cluster of numbers and variables multiplied and or divided separated by addition and subtraction.

Examples of terms:

$3+5$ The terms are 3 and 5.
${\frac {6}{x}}$ The term is $6/x$ , 6 over $x$ is one term, because the operation is division.
$6x+5$ The terms are 6 $x$ and 5, 6 $x$ and 5 are separate terms because they are separated by a addition or subtraction.

An operation is a thing you do to numbers, like add, subtract, multiply, or divide. You use signs like +, –, *, or / for operations.

An expression is one or more terms, with operations between all terms.

Examples of expressions:

$3\div 6$
$8\times x$
$x\times 6+y$
$a\times b\times c\times d$

To evaluate an expression, you do the operations to the terms of an expression.

Examples of evaluating expressions:

$3+4$ evaluates to 7.
$18\div 3$ evaluates to 6.
$4\times 5-3$ evaluates to 17.

To evaluate an expression with variables, you substitute (put a thing in the place of an other thing) numbers for the variables.

Examples of substituting: (Substitute 3 for x in these examples.)

$x+4$ is $3+4$ .
$18\div x$ is $18\div 3$ .
$4\times 5-x$ is $4\times 5-3$ .

Example Problems

Evaluate the following expressions

$5\times x$	When $x=2$
$5\times 2$	Substitute 2 for $x$ .
$10$	Evaluate $5\times 2$ to get the answer.

${\frac {x}{3}}+y$	When $x=9$ and $y=4$
${\frac {9}{3}}+4$	Substitute 9 for $x$ and substitute 4 for $y$ .
$7$	Evaluate ${\frac {9}{3}}+4$ to get the answer.