Unit 1 - Section 5: Evaluating Expressions

Article: How to Evaluate Algebraic Expressions

Evaluating expressions means finding the value of an expression when the variable(s) are replaced with specific numbers. This is a fundamental skill in algebra and is often used in real-life applications such as formulas in science, finance, and engineering.

Key Vocabulary

• Variable: A symbol (usually a letter) representing a number.

• Expression: A mathematical phrase with numbers, variables, and operations, but no equals sign.

• Evaluate: To calculate the numerical value of an expression.

Steps to Evaluate an Expression

Step 1: Substitute

Replace each variable in the expression with the given number.

Step 2: Simplify

Follow the order of operations (PEMDAS) to simplify the expression.

Example 1:

Evaluate 3x + 2 when x = 4

• Substitute: 3(4) + 2 = 12 + 2 = 14

Example 2:

Evaluate 2a - 5b when a = 3 and b = 2

• Substitute: 2(3) - 5(2) = 6 - 10 = -4

Example 3:

Evaluate x^2 - 4x + 7 when x = 2

• Substitute: (2)^2 - 4(2) + 7 = 4 - 8 + 7 = 3

Tips and Tricks

• Always use parentheses around substituted values, especially for negative numbers.

• Pay attention to exponents and negative signs.

• Double-check your order of operations.

Real-Life Applications

• Calculating total cost from a pricing formula

• Plugging values into physics or chemistry formulas

• Determining tax, interest, and discounts in business math