# Ch 4: Honors Algebra 1: Properties of Real Numbers

### About This Chapter

## Honors Algebra 1: Properties of Real Numbers - Chapter Summary and Learning Objectives

In this chapter, review how mathematicians differentiate between the different types of numbers, how to order and solve inequities with real numbers and how to complete arithmetic operations with negative numbers in them. Each lesson video is taught by one of our professional instructors so that you may have access to an effective way to study:

- Different categories of numbers and their properties
- How to graph and order real/rational numbers
- Fractional and decimal notations of rational numbers
- Addition, subtraction, multiplication and division with negative numbers

Video | Objective |
---|---|

What are Real Numbers? - Definition & Properties | Understand the properties of real numbers. |

What are the Different Types of Numbers? | Learn the classifications of real numbers. |

Graphing Rational Numbers on a Number Line | Use number lines to solve problems. |

Notation for Rational Numbers, Fractions & Decimals | Review the properties of fractions and decimals. |

The Order of Real Numbers: Inequalities | Utilize inequalities to compare two numbers. |

How to Rationalize the Denominator with a Radical Expression | Simplify fractions with radicals in the denominator. |

Algebraic Numbers and Transcendental Numbers | Differentiate between algebraic and transcendental numbers. |

Understanding Numbers That Are Pythagorean Triples | Learn about Pythagorean Triples and how they are formed. |

Adding & Subtracting Negative Numbers | Review how to complete addition and subtractions with negative numbers. |

Multiplying & Dividing Negative Numbers | Complete multiplication and division problems with negative numbers. |

### 1. What are Real Numbers? - Definition & Properties

There are many definitions of real numbers, but they all lead to the same conclusion. Real numbers are numbers that have a measurable value. Learn more about real numbers with some examples and a quiz to test your knowledge.

### 2. What are the Different Types of Numbers?

Learn all of the different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. This video lesson teaches you how to classify any numbers you come across.

### 3. Graphing Rational Numbers on a Number Line

Number lines have many uses both in mathematics and everyday life. This lesson will teach you how to graph numbers on a number line and give real-world examples of how to use number lines.

### 4. Notation for Rational Numbers, Fractions & Decimals

How do fractions become decimals? And how do decimals become fractions? In this lesson, we'll learn about the notation of rational numbers, fractions and decimals and learn how they're related.

### 5. The Order of Real Numbers: Inequalities

An inequality is an operation describing how one number can be compared to another. This lesson will describe and define inequalities and the symbols used to represent them. It will also give some examples on how to work with inequalities.

### 6. How to Rationalize the Denominator with a Radical Expression

Watch this video lesson to learn what you can do to simplify your expression when you have a radical in the denominator. Learn what the single step solution to your problem is.

### 7. Algebraic Numbers and Transcendental Numbers

Math is all about numbers. In this lesson, you'll learn about the two different categories of numbers, called algebraic and transcendental. You'll learn the definition of each type and find out how common each of them is.

### 8. Understanding Numbers That Are Pythagorean Triples

In this video lesson, you will learn about numbers that form Pythagorean Triples. Learn why these are special numbers and what they have to do with triangles.

### 9. Adding & Subtracting Negative Numbers

After watching this video lesson, you will be able to add and subtract negative numbers with ease. Learn what you need to watch for and what will make your job easier.

### 10. Multiplying & Dividing Negative Numbers

After watching this video lesson, you will be able to multiply and divide negative numbers with ease. Learn what to watch for and how to handle the negative signs so that you get the right answer every time.

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### Other Chapters

Other chapters within the Honors Algebra 1 Textbook course

- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Solving Algebraic Expressions & Equations
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- Honors Algebra 1: Matrices in Linear Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Probability & Statistics
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Similar Polygons
- Honors Algebra 1: Pre-Calculus Geometry
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math