Evaluating Expressions
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn how to evaluate algebraic expressions by replacing variables with given numbers and following the order of operations.
The Concept
Section titled “The Concept”Evaluating an expression means plugging in a specific value for each variable and computing the result, just like following a recipe with exact amounts.
Steps:
- Replace every instance of the variable with the given number (use parentheses if needed to avoid confusion).
- Follow order of operations: Parentheses → Exponents → Multiply/Divide (left to right) → Add/Subtract (left to right).
Example: Evaluate when and
Another: when
Worked Examples
Section titled “Worked Examples”Evaluate when and
- Substitute:
- Multiply first:
- Add/subtract left to right:
Final result:
Real-World Applications
Section titled “Real-World Applications”Evaluating expressions helps calculate costs or totals when you know the values. Example: Monthly phone bill = 30 dollars base + 0.05 dollars per text. If you send 400 texts: dollars. Or fuel cost = 3.50 dollars per gallon × g gallons. Plug in g = 12 for 42 dollars.