Evaluate variable expressions involving rational numbers

Key notes:

Understanding Variable Expressions

  1. Definition:
    • A variable expression is a mathematical phrase that includes numbers, variables (letters that represent numbers), and operations (addition, subtraction, multiplication, division).
  2. Examples:

Evaluating Variable Expressions

  1. Substitution:
    • To evaluate a variable expression, substitute the values of the variables into the expression and perform the operations according to the order of operations (PEMDAS/BODMAS).
  2. Order of Operations:
    • Parentheses/Brackets: Solve expressions inside parentheses/brackets first.
    • Exponents/Orders: Evaluate exponents or orders (powers and roots).
    • Multiplication and Division: From left to right.
    • Addition and Subtraction: From left to right.

Steps for Evaluation

  1. Substitute Values:
    • Replace each variable in the expression with its given value.
  2. Simplify Inside Parentheses:
    • If the expression contains parentheses, simplify the expression inside them first.
  3. Apply Exponents:
    • If the expression contains exponents, apply them next.
  4. Perform Multiplication and Division:
    • Perform all multiplication and division from left to right.
  5. Perform Addition and Subtraction:
    • Perform all addition and subtraction from left to right.

Examples

  • Simple Variable Expression:
  • Expression with Multiple Variables:
  • Expression with Parentheses:
  • Complex Expression:

Practice Problems

  1. Simple Expressions:
  • Expressions with Multiple Variables:
  • Expressions with Parentheses:
  • Complex Expressions:

Tips for Success

  1. Careful Substitution:
    • Ensure that each variable is correctly substituted with its given value.
  2. Follow Order of Operations:
    • Adhere strictly to the order of operations to avoid mistakes.
  3. Simplify Step-by-Step:
    • Simplify the expression step-by-step to prevent errors.
  4. Check Your Work:
    • After evaluating the expression, double-check each step to ensure accuracy.

Learn with an example

🔮 Evaluate the expression for t = -0.7.

Write your answer as a decimal or whole number.

-15t =_______

Plug in t = -0.7 and simplify.

-15t
-15(-0.7)Plug in t = -0.7
10.5Multiply

🔮 Evaluate the expression for b = 13 and c = 12.

Simplify your answer.

b/b-c =?

Evaluate.

b/b-c

=13/13 âˆ’ 12 Plug-in b = 13 and c = 12
=13/1 Simplify the denominator
=13 Divide

🔮 Evaluate the expression for g = 2 and h = 0.5.

Write your answer as a decimal or whole number.

gh âˆ’ 0.7 = 

Plug in g = 2 and h = 0.5, then simplify.

gh âˆ’ 0.7

2(0.5) âˆ’ 0.7

1 âˆ’ 0.7

0.3

Let’s Practice!