Evaluating Algebraic Expression

How to Evaluate Algebraic Expressions

Hi, this is Wyatt, and today we're going to be talking about how to evaluate algebraic expressions. This is usually taught in seventh-grade algebra, so let's get right to it!

PEMDAS

Before we begin, remember the order of operations:

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction
  • A common way to remember this is: Please Excuse My Dear Aunt Sally.

    Example 1

    Evaluate: (2x)2 - 3 × 2 when x = 2.

    Replace x with 2:

    (2 × 2)2 - 3 × 2

    Parentheses:

    42 - 3 × 2

    Exponents:

    16 - 3 × 2

    Multiplication:

    16 - 6

    Subtraction:

    10

    Answer: 10

    Example 2

    Evaluate: (4xy2)/2 - 3/2 when x = 1 and y = 2.

    (4 × 1 × 22)/2 - 3/2

    Exponents:

    (4 × 1 × 4)/2 - 3/2

    Multiplication:

    16/2 - 3/2

    Subtraction:

    (16 - 3)/2 = 13/2

    Answer: 13/2

    Example 3

    Evaluate: 4x-2 + yz when x = 1, y = 2, and z = 3.

    Negative exponents mean:

    x-2 = 1/x2

    4/(12) + (2 × 3)

    4/1 + 6

    4 + 6 = 10

    Answer: 10

    Challenge Problem

    Evaluate: y3/2/3 + (z/3)2 - 2/3

    when y = 4 and z = 1.

    First, evaluate:

    43/2

    A power of 3/2 means:

    (√4)3

    23 = 8

    Rewrite the expression:

    8/3 + 1/9 - 2/3

    Convert to ninths:

    24/9 + 1/9 - 6/9

    25/9 - 6/9 = 19/9

    As a mixed number:

    2 1/9

    Answer: 19/9 or 2 1/9

    Conclusion

    And that's how you evaluate algebraic expressions using substitution and PEMDAS. Thanks for watching, and bye for now!