Building a Conceptual Understanding of Expressions Overview

Introduction

When you ask a question like, "How much should I add to 5 to make a total of 8?" you are talking out loud using an algebraic equation. We use algebra all the time in everyday life. When you ask your parents for money for an ice cream at lunch and they say how much do you need? You are using algebra to figure out the amount of money needed to buy an ice cream based on how much money you already have in your lunch account. In this unit, you will learn how to write and solve algebraic equations.

Essential Questions

How do I choose and interpret units of measure?
What does each part of an expression represent in the context of the problem?
How are polynomial operations related to operations in the real number system?
How can polynomials be used to express realistic situations?
How do I simplify radical expressions?
What type of number will result from the addition or multiplication of two rational numbers, one rational and one irrational number, or two irrational numbers?

Key Terms

The following key terms will help you understand the content in this module.

Algebraic Expression: An expression involving at least one variable and sometimes numbers and operation symbols.
Associative Property of Addition: The sum of a set of numbers is the same no matter how the numbers are grouped. a + (b + c) = (a + b) + c
Associative Property of Multiplication: The product of a set of numbers is the same no matter how the numbers are grouped. a(bc)=(ab)c
Coefficient: A number multiplied by a variable in an algebraic expression.
Commutative Property of Addition: The sum of a group of numbers is the same regardless of the order in which the numbers are arranged. a + b = b + a
Commutative Property of Multiplication: The product of a group of numbers is the same regardless of the order in which the numbers are arranged. ab = ba
Constant: A quantity that does not change its value.
Distributive Property: If you multiply a sum by a number, you will get the same result if you multiply each addend by that number and add the products. a(b+c)=ab+bc
Exponent: The number of times a number or expression (called the base) is used as a factor of repeated multiplication. Also called the power.
Term: A number, a variable, or a product of numbers and variables.
Like Terms: Terms in an algebraic expression that have the same variable raised to the same power. Only the coefficients of like terms are different.
Order of Operations: The rules to be followed when simplifying expressions.
Variable: A letter or symbol used to represent a number or quantities that vary.

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