# Evaluating Expressions

Student View (Opens in new window) ## Instructor Overview

Students analyze how two different calculators get different values for the same numerical expression. In the process, students recognize the need for following the same conventions when evaluating expressions.

# Key Concepts

• Mathematical expressions express calculations with numbers (numerical expressions) or sometimes with letters representing numbers (algebraic expressions).
• When evaluating expressions that have more than one operation, there are conventions—called the order of operations—that must be followed:
1. Complete all operations inside parentheses first.
2. Evaluate exponents.
3. Then complete all multiplication and division, working from left to right.
4. Then complete all addition and subtraction, working from left to right.
• These conventions allow expressions with more than one operation to be evaluated in the same way by everyone. Because of these conventions, it is important to use parentheses when writing expressions to indicate which operation to do first. If there are nested parentheses, the operations in the innermost parentheses are evaluated first. Understanding the use of parentheses is especially important when interpreting the associative and the distributive properties.

# Goals and Learning Objectives

• Evaluate numerical expressions.
• Use parentheses when writing expressions.
• Use the order of operations conventions.