Chapter 1: The Language of Algebra

Adapted from Wentworth's Elementary Algebra for MathDoctor.net

1.1 Introduction

In Arithmetic, we deal with specific values like 5, 10, or 25. In Algebra, we use letters to represent numbers. This allows us to create "mathematical blueprints" that work for any situation.

The Basics:

1.2 Mathematical Shorthand

Algebra has its own set of "shortcuts" to make writing long equations faster and cleaner.

Multiplication

We avoid using the × sign because it gets confused with the variable x. Instead, we use juxtaposition (placing items next to each other):

Division

We prefer the fraction bar over the ÷ symbol. In a line of text, it looks like this:

1.3 Modern Practice Problems

Real-World Expressions

Try to write the algebraic expression for these modern scenarios:

Example 1
A streaming service costs $15 per month, plus $4 for every premium movie (m) you rent.
Expression: 15 + 4m

Example 2
A smartphone battery has 100% charge and loses x percent every hour.
Expression: 100 - x

Example 3
You have g gigabytes of data to share equally among 3 family members.
Expression:

g 3

1.4 Terms and Coefficients

When you see an expression like 5x + 3y - 10, it is made up of three Terms.

Term Type Coefficient (The Number Part)
5x Variable Term 5
3y Variable Term 3
-10 Constant Term -10

Chapter 1 Exercises

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Doctor's Recommendation: Master the Language

As you've seen in this chapter, Algebra has its own specific vocabulary. You wouldn't try to learn a new spoken language without flashcards, and the "Language of Algebra" is no different.

Index Cards (3x5) are the perfect low-tech tool for high-tech math. We recommend creating a card for every bolded term in this chapter (like Coefficient, Variable, and Power). Write the term on the front and Wentworth's definition on the back.

View Index Cards on Amazon