# Ch 1: Number Theory & Basic Arithmetic

### About This Chapter

## Number Theory and Basic Arithmetic - Chapter Summary

Use this chapter to study number theory and basic arithmetic. Learn about several different mathematical properties and how to apply them to number problems. Instructors cover the following topics in this chapter:

- Graphing and noting rational numbers
- Finding the absolute value of a real number
- Comparing and contrasting binary and non-binary operations
- Adding and subtracting signed numbers
- Using the commutative and associative properties
- Explaining how to use the multiplication property of zero
- Finding the greatest common factor and least common multiple
- Mastering common algebra terms
- Solving math problems using the order of operations

The short and interactive video lessons can help you prepare for the Integrated Algebra Regents exam. Knowledgeable instructors explain the material in easy-to-understand terms, and self-assessment quizzes are provided to test your learning. You can also view lesson transcripts if you have questions about any of the material.

### Number Theory and Basic Arithmetic Objectives

To receive a Regents Diploma in the state of New York, you must pass a series of five tests, including the Integrated Algebra Regents exam. The integrated algebra section is composed of four parts, with approximately 39 questions in all. You'll have three hours to complete the exam. Much of the test is multiple choice, but some questions require you to write your answers in spaces provided. You may also need to produce mathematical diagrams, graphs and charts. Students need to score a 65 or above to pass this test.

### 1. 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.

### 2. What Is a Number Line?

A number line is a visual representation of all real numbers. In this lesson, we'll learn how to identify points on a number line. We'll also practice addition and subtraction, letting the number line do all the hard work.

### 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. Finding the Absolute Value of a Real Number

You can find the absolute value of any real number. This lesson will define absolute value, explain what real numbers are and give the steps to finding the absolute value of any real number.

### 7. Binary and Non-Binary Operations

Binary and non-binary are two terms that might really scare you, much like an operation may scare you. But don't worry, this lesson is super fun and super easy. You'll learn the definitions of these terms and see examples of each.

### 8. Arithmetic Calculations with Signed Numbers

Signed numbers are often referred to as integers. Integers include both positive and negative numbers. In this lesson, you will learn how to add, subtract, multiply, and divide integers.

### 9. The Commutative Property: Definition and Examples

There are three major properties that deal with the addition and multiplication of numbers. One of those properties is the commutative property. This lesson will define and give examples of the commutative property and how it works.

### 10. 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.

### 11. The Multiplication Property of Zero: Definition & Examples

The number zero has different rules than other numbers; it behaves according to it's own unique properties. This lesson will define the multiplication property of zero and give some examples of how it works.

### 12. How to Find the Greatest Common Factor

If the factors of a number are the different numbers that you can multiply together to get that original number, then the greatest common factor of two numbers is just the biggest one that both have in common. See some examples of what I'm talking about here!

### 13. How to Find the Least Common Multiple

The least common multiple of two numbers is the smallest number that can be divided evenly by your two original numbers. See some examples of what I'm talking about here!

### 14. Parentheses in Math: Rules & Examples

Watch this video lesson to learn how parentheses are used in math. Learn how to read them as multiplication and how they let you know which numbers to work with first.

### 15. Algebra Vocabulary Terms

Watch this video lesson to learn about some basic vocabulary words that you will come across again and again in the course of your studies in algebra. After you finish this video, you should know and be able to identify each term.

### 16. What Is The Order of Operations in Math? - Definition & Examples

The order of operations is the steps used to simplify any mathematical expression. In this video, learn how to solve problems using these steps and easy tricks to remember them.

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course

- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards