# Ch 1: Explorations in Core Math Algebra 1 Chapter 1: Equations

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Equations chapter of your textbook.
- Watch fun videos that cover the equations you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- How to use, translate and evaluate algebraic equations
- Addition, subtraction, and multiplication properties
- Associative, distributive, multiplicative and identity properties
- Solving equations with two or more steps
- How to collect like terms and rewrite literal equations
- Working with absolute value, ratios, rates and proportions
- Understanding similarity transformations
- Measurements, unit conversion, dimensional analysis and uncertainty

*Explorations in Core Math Algebra 1 is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. 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.

### 2. 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.

### 3. Translating Words to Algebraic Expressions

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

### 4. Addition Property of Equality: Definition & Example

After watching this video lesson, you should be able to use the addition property of equality to help you solve problems. In addition, you can learn the formula for this property.

### 5. Subtraction Property of Equality: Definition & Example

In this video lesson, we look at the subtraction property of equality. Learn how it helps you to solve problems and how it keeps equations the same. Learn what you must do to both sides of an equation.

### 6. The Associative Property: Definition and Examples

There are three basic number properties that help to form the backbone of algebra. One of those properties is the associative property. This lesson will define the associative property and give some examples of how it works.

### 7. Multiplication Property of Equality: Definition & Example

After watching this video lesson, you will learn to use the multiplication property of equality to help you solve problems in math. You will also learn the formula for this property.

### 8. Distributive Property: Definition, Use & Examples

After completing this lesson, you will be able to state the distributive property and apply it to various types of problems. You will also be able to accurately perform the mathematical operations that are involved with the distributive property.

### 9. Multiplicative Inverse: Definition, Property & Examples

In this lesson, we will cover the definition of the multiplicative inverse, as well as its property. We will review some examples of the property so that we can gain a better understanding of the material. Following the lesson will be a brief quiz.

### 10. Identity Property of Multiplication: Definition & Example

This lesson will give you the definition of the identity property of multiplication, examples of this property and an explanation of why this property always works. Following the lesson will be a brief quiz to test your knowledge of the material.

### 11. Associative Property of Multiplication: Definition & Example

There are all kinds of rules that govern our basic operations. In this lesson, you will learn about one of these rules, the associative property of multiplication, and how re-grouping the numbers we multiply first in a problem can help us simplify our calculations.

### 12. Two-Step Equation: Definition & Examples

Solving problems that just have two steps can sometimes trip people up. Read on to find out what two-step equations are and see some examples. Meet our friend Ramon as he learns about this mathematical concept.

### 13. How to Solve Equations with Multiple Steps

In algebra, when you want to solve an equation for a particular variable, you will need to perform multiple steps that include adding, subtracting, multiplying, and dividing. Watch this video lesson to learn the order you need to do these steps.

### 14. Collecting Like Terms On One Side of an Equation

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

### 15. How to Rewrite Literal Equations

In this lesson, we will define literal equations and learn how to rewrite them to solve for different variables. We will review different examples including some commonly used formulas.

### 16. How to Solve an Absolute Value Equation

Once you get familiar with any new operation, the next step in any algebra class is to learn how to solve equations with that operation in them. Absolute values are no different. Solve absolute value equations here!

### 17. Solving a System of Absolute Value Equations by Graphing

A system of absolute value equations is two more equations that contain absolute value symbols. To solve these systems you will need to find a point (x,y) or points that will work for both equations. This lesson explains how to solve these systems by graphing.

### 18. Calculations with Ratios and Proportions

Even if only 99 out of 100 people need to know how to work with ratios, the odds that they'll be useful to you are very high. In this lesson, we'll practice performing calculations with ratios and proportions.

### 19. Solving Problems Using Rates

In this video lesson, learn how to set up rate problems so you can easily solve them. You will become familiar with the rate formula and you will see how easy it is to use.

### 20. Similarity Transformations in Corresponding Figures

Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.

### 21. Unit Conversion and Dimensional Analysis

How is solving a chemistry problem like playing dominoes? Watch this lesson to find out how you can use your domino skills to solve almost any chemistry problem.

### 22. Measurements & Uncertainty in Science

In this lesson, you will discover the importance of precision and accuracy in science while learning to make measurements. Also, you will understand how to perform calculations with measurements that conserve precision and limit uncertainty.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 1: Online Textbook Help course

- Explorations in Core Math Algebra 1 Chapter 2: Inequalities
- Explorations in Core Math Algebra 1 Chapter 3: Functions
- Explorations in Core Math Algebra 1 Chapter 4: Linear Functions
- Explorations in Core Math Algebra 1 Chapter 5: Systems of Equations and Inequalities
- Explorations in Core Math Algebra 1 Chapter 6: Exponents and Polynomials
- Explorations in Core Math Algebra 1 Chapter 7: Factoring Polynomials
- Explorations in Core Math Algebra 1 Chapter 8: Quadratic Functions and Equations
- Explorations in Core Math Algebra 1 Chapter 9: Exponential Functions
- Explorations in Core Math Algebra 1 Chapter 10: Data Analysis