Pre-Algebra Notes on Evaluating Algebraic Expressions

Pre-Algebra Study Notes

Chapter 6: Evaluating Algebraic Expressions

Section 6.4: Introduction

  • Focus on simplifying algebraic expressions using the correct order of operations.

Simplification Examples

  1. Prepare to Simplify Values:

    • Expression: 2 + 32 imes 4 - 5

  2. Brackets in Expressions:

    • Expression: (2 + 32)4 - 5

  3. Parentheses for Clarity:

    • Expression: 2 + 32(4 - 5)

Lesson Opener: Initial Evaluations

  • Evaluations to complete: 3, 3, -7 (included as placeholders for specific calculations).

Example Evaluations Using Variables

  • Variable Assignments: Evaluate expressions by substituting given values.
  1. For x = -2 and y = 3:
    1. Evaluate: 2x^2y
    2. Evaluate: 2y - x + 4
    3. Evaluate: x^2 - y^2
    • Calculated results: 24, 12, -5 (numbers are results of respective calculations).

Detailed Example Evaluations

Example 1: Evaluating a Simple Expression
  • Expression: 2xy
  • Values: Let x = 3, y = 1.
  • Calculation: 2 imes 3 imes 1 = 6
Example 2: Complex Evaluation
  • Expression: rac{y}{x} + z
  • Given values: x = -3, y = 4, z = 7.
  • Calculation Steps:
    • Evaluate: rac{4}{-3} + 7
    • Step 1: Approximate $ rac{4}{-3} o - rac{4}{3}$
    • Step 2: Add z = 7 (convert to fraction for easier addition): - rac{4}{3} + rac{21}{3} = rac{17}{3}
Example 3: Evaluate with Decimals
  • Expression: 5x - 12y
  • Values: Let x = 0.4, y = -2.05.
  • Calculation:
    • Step 1: 5 imes 0.4 = 2
    • Step 2: 12 imes -2.05 = -24.6
    • Result: 2 + 24.6 = 26.6

Skill Check Exercises

  • Evaluate the following expressions based on provided inputs:
    1. f + e when e = 15 and f = 9 → Result: 24
    2. ab + 8 when a = 9 and b = -18 → Result: -166

Additional Evaluations for Practice

  1. Evaluate: 5x - 7y when x = 3 and y = -3.
  2. Evaluate: 12a + 3b when a = 2 and b = -5.
    • Resulting evaluations: 9, 65.

Follow-up Examples

Example 4: Evaluation with Powers
  • Expression: 4x^2y
  • Values: Let x = 3, y = -1.
  • Calculation Sequence:
    • Step 1: Calculate 4(3^2)(-1)
    • Step 2: (3^2 = 9) o 4 imes 9 imes -1 = -36
Example 5: Multi-term Expression
  • Expression: -3x - 2xy + 9y
  • Values: x = 2, y = 1.
  • Calculation:
    • Step 1: Substitute: -3(2) - 2(2)(1) + 9(1)
    • Results calculated: 70.5
Example 6: Complex Expression Handling
  • Expression: -(4y - 3x)
  • Values: x = 6, y = 2.
  • Sequence:
    • Step 1: Substitute values: -(4(2) - 3(6))
    • Evaluate: - (8 - 18) = -(-10) = 10

Final Evaluations with Multiple Variables

  • Evaluate the following when x = -3, y = 1, z = 3.7, and w = 0.05:
    1. Evaluate: x^2 + y^2
    2. Evaluate: rac{w}{z} + 4y
    3. Evaluate: 5z - 0.1w
    • Skill check results shown as application of evaluations.

Continuing Exercises

  • Skills check for different variable combinations to solidify understanding of evaluating algebraic expressions.

Assignment

  • Additional evaluations and exercises to reinforce learning concepts.