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 $y$
• $2÷s$ 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:

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

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

Examples of evaluating expressions:

• $3+4$ evaluates to 7.
• $18÷3$ 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 $3+4$.
• $18÷x$ is $18÷3$.
• $4\times 5-x$ 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.

Practice Games

• Evaluating expressions
• Advanced Expression Evaluator

Practice Problems

remember order of operations

<quiz display=simple points="1/1"> {Evaluate each expression if $a$ = 1, $b$ = 2, $c$ = 3, and $d$ = 5.}

{ |type="{}"} $5\times b=${ 10_2 }

{ |type="{}"} $9\times c=${ 27_2 }

{ |type="{}"} $c-2=${ 1_2 }

{ |type="{}"} $d-5=${ 0_2 }

{ |type="{}"} $\frac{b}{2}=${ 1_2 }

{ |type="{}"} $\frac{36}{c}=${ 12_2 }

{ |type="{}"} $b\times c+2=${ 8_2 }

{ |type="{}"} $b\times c\times d-5=${ 25_2 }

{Evaluate each expression if $x$ = 4, $y$ = 2, and $z$ = 3.}

{ |type="{}"} $x+y=${ 6_2 }

{ |type="{}"} $2z=${ 6_2 }

{ |type="{}"} $xz=${ 12_2 }

{ |type="{}"} $x+y+z=${ 9_2 }

{ |type="{}"} $xy+z=${ 11_2 }

{ |type="{}"} $yz-x=${ 2_2 }

{ |type="{}"} $\frac{6}{y}+z=${ 6_2 }

{ |type="{}"} $\frac{2x}{2+y}=${ 2_2 }

{More harder questions:

Evaluate each expression if $x$ = 5, $y$ = 8, and $z$ = 9.}

{ |type="{}" coef="2"} $(2+x)\times y=${ 56_2 }

{ |type="{}" coef="2"} $\frac{3y-9}{5}=${ 3_2 }

{ |type="{}" coef="2"} $\frac{27}{x+4}-(y-5)=${ 0_2 }

{ |type="{}" coef="2"} $\frac{z+12}{2x-3}+y=${ 11_2 }

{ |type="{}" coef="2"} $(\frac{6x}{2+y}-z)+(x-\frac{z}{3})=${ -4_2 } </quiz>