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

Practice Games

 * Evaluating expressions
 * Advanced Expression Evaluator

Practice Problems
remember order of operations

 {Evaluate each expression if $$a$$ = 1, $$b$$ = 2, $$c$$ = 3, and $$d$$ = 5.}

{ $$5 \times b=$${ 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 }
 * type="{}"}

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

{ $$x+y=$${ 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 }
 * type="{}"}

{More harder questions:

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

{ $$(2+x) \times y=$${ 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"}

{ $$\left(\frac {6x}{2+y} - z\right)+\left(x- \frac{z}{3}\right)=$${ -4_2 }
 * type="{}" coef="2"}