# Ch 1: NY Regents - Number Theory & Basic Arithmetic: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other NY Regents integrated algebra prep work.
- Identify the number theory and basic arithmetic concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our NY Regents integrated algebra tutoring solution will benefit any student who is trying to learn number theory and basic arithmetic to prepare for the exam. This resource can help students including those who:

- Struggle with understanding types of numbers, the order of operations in math, or any other number theory and basic arithmetic topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves struggling to prepare for the NY Regents integrated algebra test
- Cope with ADD or ADHD
- Want to get ahead in preparing for the NY Regents integrated algebra test
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning number theory and basic arithmetic simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live algebra tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn number theory and basic arithmetic on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Describe the different types of numbers.
- Understand what a number line is.
- Be able to graph rational numbers on a number line.
- Take a look at notation for rational numbers, decimals and fractions.
- Learn how to work with inequalities.
- Determine the absolute value of a real number.
- Discuss binary and non-binary operations.
- Perform arithmetic calculations with signed numbers.
- Become familiar with the commutative property, associative property and multiplication property of zero.
- Explain how to find the greatest common factor and least common multiple.
- Understand the rules for using parentheses in math.
- Take a look at algebra vocabulary terms.
- Learn how to use the order of operations.

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

There are different types or families of numbers. Learn how to identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

### 2. What Is a Number Line?

A number line is a visual representation, or picture, of real numbers on a straight line. Learn how to identify points on a number line and then solve addition and subtraction problems using a number line.

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

Graphing rational numbers on a number line is a method of representing a set of numbers by placing a dot at the correct values on a number line. Learn how to draw a number line and graph rational numbers.

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

A rational number can be expressed as a fraction and converted to a decimal, which can be converted to a fraction as well. Learn what rational numbers are, and explore the notation of and relationship between rational numbers, fractions, and decimals.

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

An inequality is an operation that describes how one number can be compared to another. Explore symbols for less than and greater than, how to use inequalities, and the order of real numbers.

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

The distance from zero on the number line is referred to as the absolute value of a number. Explore the absolute value and real numbers and discover how to find the absolute value of a real number through a series of examples.

### 7. Binary and Non-Binary Operations

A mathematical operation is a non-binary or binary operation depending on whether it involves one or two numbers, respectively. Learn the definition of an operation, and explore binary and non-binary operations with a few examples of each.

### 8. Arithmetic Calculations with Signed Numbers

Signed numbers are integers that are often used with mathematical operation signs to solve arithmetic calculations. Learn how to add, subtract, multiply, and divide integers in arithmetic calculations through a series of examples.

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

The commutative property in mathematics asserts that terms in an equation can be swapped, and still have the same answer. Learn the implications of this principle, and how to use it in examples problems.

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

The associative property is a principle in mathematics which states that in addition or multiplication problems, terms grouped in different ways produce the same answer. Study the definition and examples of this principle, and it's importance.

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

In multiplication, the number zero has a special effect on other numbers. Explore how zero plays by its own rules and learn about the multiplication property of zero.

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

To find the greatest common factor, look at all the factors of two numbers and see which factor is the largest that they have in common. Learn what a factor is and study examples of how to find the greatest common factor.

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

The smallest number that can be evenly divided by two numbers is the least common multiple of those two numbers. Learn about the least common multiple, why it is important, and how to find it. Understand what a multiple is, and recognize that sometimes, the least common multiple of two numbers is one of the original numbers.

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

Parentheses are used two different ways in math: to multiply and to tell what numbers to work first. Learn about parentheses, their rules, and examples of their use in multiplication and order of operations.

### 15. Algebra Vocabulary Terms

Basic algebra vocabulary terms provide the necessary foundation to comprehend algebraic concepts and rules. Learn about equations, variables, coefficients, terms, and constants.

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

The order of operations in mathematics is the sequence in which a problem is solved. Explore the definition and examples of the order of operations in math, discover the steps involved, and learn the shortcut for remembering the steps defined by the acronym PEMDAS.

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Tutoring Solution course

- NY Regents - Problems with Decimals and Fractions: Tutoring Solution
- NY Regents - Problems with Percents: Tutoring Solution
- NY Regents - Problems with Exponents: Tutoring Solution
- NY Regents - Problems with Exponential Expressions: Tutoring Solution
- NY Regents - Problems with Radical Expressions & Equations: Tutoring Solution
- NY Regents - Problems with Algebraic Expressions and Equations: Tutoring Solution
- NY Regents - Distributing Terms in Algebra: Tutoring Solution
- NY Regents - Algebraic Linear Equations & Inequalities: Tutoring Solution
- NY Regents - Matrices and Absolute Value: Tutoring Solution
- NY Regents - Overview of Functions: Tutoring Solution
- NY Regents - Factoring with Variables: Tutoring Solution
- NY Regents - Quadratics & Polynomials: Tutoring Solution
- NY Regents - Rational Expressions: Tutoring Solution
- NY Regents - Graphing Functions: Tutoring Solution
- NY Regents - Calculations with Ratios, Percent & Proportions: Tutoring Solution
- NY Regents - Sets: Tutoring Solution
- NY Regents - Probability and Statistics: Tutoring Solution
- NY Regents - Probability Mechanics: Tutoring Solution
- NY Regents - Working with Data: Tutoring Solution
- NY Regents - Well-Known Equations: Tutoring Solution
- NY Regents - Intro to Trigonometry: Tutoring Solution
- NY Regents - Measurement for Algebra Students: Tutoring Solution
- NY Regents - Geometry for Algebra Students: Tutoring Solution