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.

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

Learn with an example

🎯 Evaluate the expression for x = 0.1 and y = 8.8.

Write your answer as a decimal or whole number.

xy = 

Plug in x = 0.1 and y = 8.8, then simplify.

xy

0.1(8.8)

0.88

🎯 Evaluate the expression for y = -12 and z = –4.

Simplify your answer.

y/z =

Evaluate.

y/z

= -12/-4 Plug in y = -12 and z = -4

= 3 Divide

🎯 Evaluate the expression for n = -9.

Simplify your answer.

n/3 =

Evaluate.

n/3

= -9/3 Plug in n = -9

= -3 Divide

Let’s Practice!