# Ch 1: Working with Real Numbers

### About This Chapter

## Working with Real Numbers - Chapter Summary

In this chapter, our instructors present ways to work with real numbers, including the properties of real numbers and how to solve arithmetic problems with whole numbers. Additionally, you'll review adding, subtracting, multiplying and dividing rational numbers. Topics also include the order of operations with signed numbers and examples of expanded form in math. Once you complete this chapter, you should be ready to:

- Outline the different kinds of number properties
- Give an example of the identity property
- Compare fractions, whole numbers and decimals using the number line
- Define an irrational number and explain how they are graphed on a number line
- Detail the order of operations and exponential expressions
- Provide an example of a radical expression
- Simplify radical expressions with variables
- Explain scientific notation

These learning materials are accessible to you on your mobile phone, tablet or computer 24 hours a day for flexible and convenient studying. Before taking an exam or moving on to other topics, take the short quiz that accompanies each lesson to see how well you've learned. It's easy to go back and review just one portion of a video lesson using the video tabs feature. If you have any questions that you need help with, reach out to one of our instructors through the Dashboard.

### 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. Arithmetic with Whole Numbers

There are four basic mathematical operations: addition, subtraction, multiplication, and division. These four operations are used in a wide range of everyday skills and are the fundamental blocks of arithmetic.

### 3. Adding & Subtracting Rational Numbers

After watching this video lesson, you will be able to add and subtract rational numbers like a pro. Learn what is involved in adding and subtracting these types of numbers.

### 4. Multiplying & Dividing Rational Numbers

After watching this video lesson, you will know how to multiply and divide rational numbers. You will know when you need to flip your number and when you don't.

### 5. Order of Operations With Signed Numbers

In this lesson you'll learn how to calculate mathematical problems when the problem includes addition, subtraction, multiplication, division, parentheses, and exponents. We'll also explain how to calculate these type of problems using negative numbers.

### 6. What is Expanded Form in Math? - Definition & Examples

In this lesson, we'll review place value and find out how it's useful when writing numbers in expanded form. We'll also look at a few examples of numbers written out in expanded form.

### 7. Number Properties: Commutative, Associative & Distributive

We often find ourselves using real number properties when working on math problems. These properties come in a variety of forms, but in this lesson we'll focus on learning about the commutative, associative, and distributive properties.

### 8. Identity Property: Definition & Examples

In this lesson, you will learn the definition of the identity property, discover the four different identity properties and examine examples that clearly illustrate these properties. Following this lesson will be a brief quiz to test your knowledge.

### 9. Using the Number Line to Compare Decimals, Fractions, and Whole Numbers

Watch this video lesson to learn how useful the number line can be when you need to compare two different numbers, be they whole numbers, decimals or even fractions. Learn how to plot these numbers on the number line so you can compare them.

### 10. What are Irrational Numbers? - Definition & Examples

Irrational numbers may not be crazy, but they do sometimes bend our minds a little. Learn about common irrational numbers, like the square root of 2 and pi, as well as a few others that businessmen, artists, and scientists find useful.

### 11. Ordering & Graphing Irrational Numbers on a Number Line

This lesson will help you identify irrational numbers, order irrational numbers, and place the irrational numbers in the correct order on a number line.

### 12. Exponential Expressions & The Order of Operations

When performing mathematical operations, there is a specific order in which the operations should be performed. This includes when to simplify the exponents. This lesson will describe in what order exponents should be solved as you are performing mathematical operations.

### 13. Radical Expression: Definition & Examples

A radical expression is any mathematical expression containing a radical symbol (√). This lesson will go into more detail about the types of radical expressions and give some examples of how to work with them in mathematics. There will be a quiz at the end of the lesson.

### 14. Simplifying Radical Expressions with Variables

What do you think of when you hear the word 'radical'? You may think of something that is extreme or even a person that is a political activist. In this lesson, you will learn what a radical is in math and how to simplify radical expressions.

### 15. Scientific Notation: Definition and Examples

Scientific notation is a special way of writing numbers so they are easier to work with. This lesson will define scientific notations and show some examples of how to convert numbers from standard notation to scientific notation and back.

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### Other Chapters

Other chapters within the GACE Special Education Mathematics & Science (088): Practice & Study Guide course

- Fractions, Decimals, Percents & Ratios
- Understanding Number Theory & Estimation
- Overview of Basic Algebra
- Patterns & Sequences in Algebra
- Characteristics & Relationships of Functions
- Solving Basic Geometric Problems
- Points, Lines, Rays & Angles
- Solving Angle Problems with Triangles & Quadrilaterals
- Geometric Relationships in the Coordinate Plane
- Solving Problems Involving Systems of Measurement
- Displaying & Interpreting Data
- Measures of Central Tendency
- Statistical Models & Processes
- Understanding Probability, Combinations & Permutations
- Scientific Inquiry & Design
- Nature of Scientific Knowledge
- Major Developments & Historical Figures in Science
- Collecting & Evaluating Scientific Data
- Science Laboratory & Field Equipment Safety
- Environmental Effects of Science & Technology
- Energy Production & Natural Resource Management
- Science & Technology in Consumer Products
- Atoms, Energy & Matter
- Concepts & Relationships Between Energy & Matter
- Basics of the Periodic Table
- Chemical Compounds & Reactions
- Acid-Base Chemistry
- Solutions & Solubility
- Concepts of Mechanics Overview
- Electricity & Magnetism Overview
- Waves & Optics Overview
- Structure & Function of Cells & Organelles
- Basic Biochemistry of Life
- Basic Genetics
- Evolution, Natural Selection & Biological Diversity
- Hierarchical Classification of Living Things
- Understanding Plant Structures & Function
- Animal & Human Anatomy & Physiology
- Population Dynamics & Ecology
- Rocks, Minerals & Soil Overview
- Earth's Structure, Shape & Processes
- Historical Geology
- Understanding the Earth's Oceans
- Freshwater Characteristics & Processes
- Atmosphere & Weather
- Climate, Seasons & Geography
- Exploring Features of the Solar System
- Earth-Moon-Sun System
- GACE Special Education Mathematics & Science Flashcards