# Ch 37: Fractions, Ratios & Integers

### About This Chapter

## Measurement, Data & Statistics - Chapter Summary

In this chapter, our professional instructors will help you study the processes used to solve problems with integers, fractions, percents, ratios and proportions. When you've completed this part of our study guide you should have a better understanding of:

- The definitions of integers and fractions
- Definition and properties of exponents
- How to use number lines to graph numbers
- Addition, subtraction, multiplication and division of fractions and decimals
- How to use fraction strips and other visual representations to model fractions
- The process of simplifying word problems with fractions
- Definitions and examples of ratios and proportions
- Solving word problems with ratios

In addition to the lesson videos, use the lesson transcripts to review the material covered in them and the key terms and figures of the chapter. Use the lesson quizzes to assess your knowledge. When you discover a topic you don't understand, use the video tags to return to that part of a video lesson or ask our instructors for assistance via the 'teacher' tabs of the lessons.

### 1. What are Integers? - Definition & Examples

Integers are numbers that have no fractional or decimal components. Learn the definitions of integers and non-integers and how to differentiate between them, plus find examples of numbers that contain both.

### 2. What is a Fraction? - Definition and Types

A fraction represents part of a whole expressed through a numerator and a denominator. Learn about the definition of fractions and explore different types of fractions such as proper and improper fractions, like and unlike fractions, and mixed numbers.

### 3. Exponent: Definition & Properties

An exponent denotes the number of times a given number should be multiplied by itself. Learn about the definition of an exponent, discover the four types of exponents -- positive, negative, zero, and rational exponents -- as well as equations with exponents, and check out some examples of exponents.

### 4. 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.

### 5. How to Add and Subtract Unlike Fractions and Mixed Numbers

Some of the most commonly seen forms of fractions are unlike fractions and mixed numbers. Learn to add and subtract unlike fractions and mixed numbers by reviewing how fractions are handled then explore these processes using real-life examples.

### 6. Multiplying Fractions and Mixed Numbers

Fractions can be multiplied, even when presented as mixed numbers, where an integer accompanies a fraction. Demonstrate understanding through solving examples in dollars, and practicing multiplying fractions and mixed numbers.

### 7. Dividing Fractions and Mixed Numbers

Fractions can be divided even when presented as mixed numbers, which is where an integer accompanies a fraction. Practice the division of fractions and mixed numbers in a series of practical scenarios.

### 8. Addition, Subtraction, Multiplication, and Division with Decimal Notation

The syntax rules in expressing decimals are known collectively as decimal notation and allow for consistency in calculations. Explore the notation in addition and subtraction and learn the rules for multiplication and division as well.

### 9. Calculating & Converting Percentages, Fractions & Decimals

Conversions can be a time saver and an extreme help when solving complex problems. Discover how to convert (or change) percentages, fractions, and decimals.

### 10. How to Model Fraction Equivalents with Fraction Strips

Fraction strips can be used to model fraction equivalents and can help students to understand fractions. Learn how to describe fraction strips, how to prepare the strips, and how to use them for like components and unlike components.

### 11. How to Simplify Word Problems with Fractions Using Whole Numbers

Simplifying word problems with fractions using whole numbers first requires labeling all of the important pieces provided. Learn more about equations that use fractions in word problems and how to multiply by the least common denominator to remove the fractions and solve the equation using whole numbers.

### 12. Visual Representations of Fractions

Abstract concepts such as fractions can be visualized in different ways to deepen understanding. Learn how this appears through three models of fractions: linear models, area models, and set models.

### 13. Ratios and Proportions: Definition and Examples

Proportions are ratios, or value comparisons, that are equal to one another. Learn more about proportions and ratios, how to use them, and real world examples.

### 14. How to Solve Ratio Word Problems

Ratios are everywhere. They are just a way to compare two numbers. Learn what ratios are, how they can be used to create a proportion, and how to use them to solve a word problem.

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### Other Chapters

Other chapters within the FTCE Elementary Education K-6 (060): Practice & Study Guide course

- About the FTCE Elementary Education K-6 Test
- Understanding Emergent Literacy
- The Reading Process & Comprehension Strategies
- Representations of Information in the Classroom
- Literary Analysis & Genres
- Understanding & Teaching the Writing Process
- Literacy Instruction & Assessment
- Classroom Organization & Grouping
- Communication & Media Literacy
- Social Science Instruction & Comprehension
- Cultural Contributions & Technological Developments in History
- World Civilizations & Historical Timelines
- Age of Exploration, Settlement & Growth
- Florida & U.S. History
- History's Impact on World Institutions
- Fundamental Geography Concepts
- Regional Divides & Connections
- Fundamental Government & Civics Concepts
- Fundamental Economics Concepts
- Strategies for Science Instruction
- Tools & Resources for Science Instruction
- Understanding the Nature of Science
- Scientific Data Interpretation & Analysis
- Interdisciplinary Nature of Science
- Basics of Physical Science
- Basics of Earth Science
- Basics of Space Science
- Cells & Organ Systems
- Life Science Classification & Life Cycles
- Interactions Among Living Things
- Basics of Plant Biology
- Mathematics Instructional Practices
- Interpreting Numbers, Data & Expressions
- Properties of Equality & Operations
- Solving Arithmetic & Word Problems
- Number Theory Concepts
- Measurement, Data & Statistics
- Geometric Concepts
- Studying for FTCE Elementary Education
- FTCE Elementary Education K-6 Flashcards