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

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Back to Table of Contents Algebra I

Vocabulary

Variable

Term

Operation

Expression

Evaluate

Substitute

Lesson

A variable is a letter or sign that takes place of a number. You use letters like a, x, y, θ, or λ. People often use the letter x for a variable.

Examples of using a variable:

  • Do not say 3 + 5. Say 3 + x. In this example the variable x takes the place of the number 5.
  • Do not say 4 * 8. Say 4 * x or x * 8. In this example the variable x takes the place of the number 8 or 4.

A term is a number or a variable.

Examples of terms:

  • 3 + 5 The terms are 3 and 5.
  • 6 / x The terms are 6 and x.

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 / 4
  • 8 * x
  • x * 6 + y
  • a * b * c * 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 * 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 * 5 - x is 4 * 5 - 3.

Example Problems

Evaluate 5*x when x is 2.

Substitute 2 for x to get 5*2.

Evaluate 5*2 to get the answer 10.

Evaluate x / 3 + y when x is 9 and y is 4.

Substitute 9 for x and substitute 4 for y is to get 9 / 3 + 4.

Evaluate 9 / 3 + 4 to get the answer 7.

Practice Games

http://www.quia.com/cm/29771.html (evaluating expressions) 4(a-1)

Practice Problems

(Note: put answer in parentheses after each problem you write)

Evaluate each expression when a = 1, b = 2, c = 3, and d = 5.

  1. 5*b (10)
  2. 9*c (27)
  3. c-2 (1)
  4. d-5 (0)
  5. b/2 (1)
  6. 36/c (12)
  7. b*c + 2 (8)
  8. b*c*d - 5 (25)

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

  1. x+y (6)
  2. 2*z (6)
  3. x*z (12)
  4. x+y+z (9)
  5. x*y+z (11)
  6. y*z-x (2)