# Ch 44: Algebraic Patterns, Equations & Functions

### About This Chapter

## Algebraic Patterns, Equations and Functions - Chapter Summary

Explore the fundamentals of algebraic patterns, equations and functions. When you review the contents of this chapter, you'll expand what you've already learned about these topics. Watch the online video lessons and you could recall how to recognize visual patterns, simplify math expressions, write functions and add variables. The video lessons will define popular terms and demonstrate how they can be used to solve equations. You could also remember how to solve addition and subtraction expressions as you continue your review. Studying these lessons could provide the knowledge necessary to:

- Correctly use variables
- Understand the steps needed to simplify addition expressions
- Identify missing factors with equations
- Write and solve inequalities
- Work with basic math functions
- Use and evaluate algebraic expressions
- Solve equations using the commutative, distributive and associative properties
- Simplify expressions by first combining like terms

This chapter offers a flexible alternative to learning in a classroom. Well-qualified teachers lead the lessons, and they provide answers to your questions about algebraic patterns, equations and functions. The educational video lessons are often less than ten minutes long, and they contain quizzes and worksheets that enhance the study and review process. Have a look at the transcripts, many of which have bold keywords and written examples that you can also learn from.

### 1. Recognizing and Solving Mathematical Patterns

Patterns show up in the world around us on a daily basis. In this lesson, we will define mathematical patterns and look at recognizing and solving these patterns. We will examine examples to solidify our understanding of this process.

### 2. What is a Variable in Algebra?

Did you ever encounter something like a + b = c and wonder how all these letters snuck into a math problem? In this lesson, we'll learn about variables, as well as other parts of equations, constants and coefficients.

### 3. How to Simplify an Addition Expression

Learn how to simplify and combine like terms in any algebraic expression that uses addition with this lesson. Also learn how to follow the order of operations when simplifying your expression.

### 4. What is an Equation in Math? - Definition & Examples

In this lesson, you'll get a refresher on number sentences. You will then learn what equations are and how they can be useful in finding out missing information.

### 5. What is an Inequality?

Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!

### 6. Functions: Identification, Notation & Practice Problems

A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!

### 7. Expressing Relationships as Algebraic Expressions

What do you do when you don't know what a number is but you do know how it relates to something else? You use an algebraic expression. In this lesson, we'll learn how to express relationships as algebraic expressions.

### 8. Evaluating Simple Algebraic Expressions

In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.

### 9. The Commutative and Associative Properties and Algebraic Expressions

The order of operations is important and useful, but a few mathematical properties highlight cases where order doesn't matter. In this lesson, we'll learn about the commutative and associative properties, which may save you time and effort.

### 10. The Distributive Property and Algebraic Expressions

The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.

### 11. Combining Like Terms in Algebraic Expressions

When you have an algebraic expression that's much too long, it would be great if you could simplify it. That's when knowing how to combine like terms comes in. In this lesson, we'll learn the process of combining like terms and practice simplifying expressions.

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