# Ch 4: Explorations in Core Math Grade 6 - Chapter 4: Number Theory & Fractions

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Number Theory & Fractions chapter of your textbook.
- Watch fun videos that cover the fractions and number theory concepts 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 math topics covered in the textbook chapter, including:

- Explanation and illustrations of factoring
- Finding prime factorization and greatest common factor
- Polynomial functions vocabulary
- Understanding fraction notation, equivalent expressions and equivalent fractions
- Distributive, commutative and associative properties in algebra
- Changing decimals and repeating decimals into fractions, etc.
- Conversions between mixed numbers and improper fractions
- How to order and compare fractions

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

### 1. What is Factoring in Algebra? - Definition & Example

Factoring with ordinary numbers involves knowing that 6 is the product of 2 and 3. But what about factoring in algebra? In this lesson, we'll learn the essential elements of algebra factoring.

### 2. How to Find the Prime Factorization of a Number

The prime factorization of a number involves breaking that number down to its smallest parts. This lesson will show you two different ways to discover the prime factorization of any number.

### 3. 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!

### 4. Terminology of Polynomial Functions

After watching this video lesson, you will be able to understand and use the words associated with polynomial functions like a pro. You will see words, such as leading coefficient, and you will immediately know what it is referring to.

### 5. How to Find the Greatest Common Factor of a Polynomial

When working algebra problems, you'll constantly find yourself simplifying equations and solving for unknowns. This often involves finding the greatest common factor of a polynomial, which you'll learn how to do here.

### 6. Equivalent Expressions and Fraction Notation

Did you know that two fractions can look completely different, but actually be the same? In this lesson, we'll learn about equivalent fractions. We'll also learn to simplify fraction notation.

### 7. The Commutative and Associative Properties and Algebraic Expressions

The order of operations is important and useful, but a few mathematical properties highlight cases where order doesn't matter. In this lesson, we'll learn about the commutative and associative properties, which may save you time and effort.

### 8. The Distributive Property and Algebraic Expressions

The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.

### 9. Changing Between Decimals and Fractions

In this video lesson, you will learn about the usefulness of knowing how to change quickly between decimals and fractions. You will also learn how changing from a decimal to a fraction is different than changing from a fraction to a decimal.

### 10. Converting Repeating Decimals into Fractions

After watching this video lesson, you will be able to convert any repeating decimal that you come across into a fraction. Learn how to write the two equations that are needed for the conversion.

### 11. What are Equivalent Fractions? - Definition & Examples

In this lesson, you'll review some fraction terminology and then learn what equivalent fractions are. Afterward, you can test your new knowledge with a brief quiz.

### 12. Changing Between Improper Fraction and Mixed Number Form

Improper fractions and mixed numbers are two different types of fractions. They both have different purposes when using fractions in a problem. In this lesson, you will learn how to convert between these two different forms.

### 13. Comparing and Ordering Fractions

Comparing and ordering fractions is way to examine fractions that contain different-sized sets. In order to compare these fractions, you must find a common denominator and make equivalent fractions.

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### Other Chapters

Other chapters within the Explorations in Core Math - Grade 6: Online Textbook Help course

- Explorations in Core Math Grade 6 - Chapter 1: Operations & Properties
- Explorations in Core Math Grade 6 - Chapter 2: Introduction to Algebra
- Explorations in Core Math Grade 6 - Chapter 3: Decimals
- Explorations in Core Math Grade 6 - Chapter 5: Fraction Operations
- Explorations in Core Math Grade 6 - Chapter 6: Data Collection & Analysis
- Explorations in Core Math Grade 6 - Chapter 7: Proportional Relationships
- Explorations in Core Math Grade 6 - Chapter 8: Measurement & Geometry
- Explorations in Core Math Grade 6 - Chapter 9: Integers & Coordinate Plane
- Explorations in Core Math Grade 6 - Chapter 10: Functions