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

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Vocabulary[edit]

Variable
Term
Operation
Expression
Evaluate
Substitute

Lesson[edit]

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 6x and 5, 6x 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 two 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[edit]

Evaluate 5 \times x when x is 2.

Substitute 2 for x to get 5 \times 2.

Evaluate 5 \times 2 to get the answer 10.


Evaluate \frac{x}{3} + y when x is 9 and y is 4.

Substitute 9 for x and substitute 4 for y is to get \frac{9}{3} + 4.

Evaluate \frac{9}{3} + 4 to get the answer 7.

Practice Games[edit]

Practice Problems[edit]

Evaluate each expression if a = 1, b = 2, c = 3, and d = 5. remember order of operations

  1. 5 \times b=
  2. 9 \times c=
  3. c-2=
  4. d-5=
  5. \frac{b}{2}=
  6. \frac{36}{c}=
  7. b \times c + 2=
  8. b \times c \times d - 5=

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

  1. x+y=
  2. 2z=
  3. xz=
  4. x+y+z=
  5. xy+z=
  6. yz-x=
  7. \frac{6}{y}+z=
  8. \frac{2x}{2+y}=

More harder questions:

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

  1. (2+x) \times y=
  2. \frac {3y-9}{5}=
  3. \frac {27}{x+4} - (y-5)=
  4. \frac {z+12}{2x-3} + y=
  5. (\frac {6x}{2+y} - z)+(x- \frac{z}{3})=
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Order of Operations Working With Negative Numbers