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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 7

Rational Numbers

Lesson 5: Using Negative Numbers to Make Sense of Contexts

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Examples Math Examples Collection: Graphs of Rational Functions

Overview

This collection of 28 math examples focuses on the topic of Graphs of Rational Functions, offering a comprehensive resource for students and educators alike. The examples cover a wide range of skills and concepts related to rational functions, progressively increasing in complexity to challenge learners at various levels of understanding.

Rational Functions and Equations
Math Videos Math Video Collection: Texas Instruments Tutorial Videos

Overview

This collection aggregates all the math videos and resources in this series: Texas Instruments Tutorial Videos. There are a total of 266 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Rational Expressions, Sequences, Series, Polynomial Functions and Equations, Graphs of Quadratic Functions, Quadratic Equations and Functions, Solving Systems of Equations, Trig Expressions and Identities, Probability, Geometric Constructions with Triangles, Composite Functions, Geometric Constructions with Angles and Planes, Distance Formula, Data Analysis, Slope, Special Functions, Trigonometric Functions, Graphs of Exponential and Logarithmic Functions, Radical Functions and Equations, Rational Functions and Equations, Slope-Intercept Form, Coordinate Systems, Graphs of Linear Functions, Inequalities, Matrix Operations and Midpoint Formula
Desmos Resource Desmos Algebra Activities

Overview

This is a collection of graphing calculator activities, videos, and tutorials that cover a wide range of algebra topics. Some of these activities include companion worksheets. 

 

 

 

Special Functions, Slope-Intercept Form, Quadratic Equations and Functions, Graphs of Linear Functions, Radical Functions and Equations, Trigonometric Functions, Standard Form, Applications of Linear Functions, Point-Slope Form, Applications of Exponential and Logarithmic Functions, Graphs of Exponential and Logarithmic Functions, Graphs of Quadratic Functions, Rational Functions and Equations, Slope and Proportions
Rationals and Radicals Collection Math Definitions Collection: Rationals and Radicals

Overview

The collection of definitions on Rationals and Radicals from Media4Math is an invaluable resource for students and educators alike. This comprehensive glossary includes key terms such as rational numbers, radicals, simplifying radicals, rationalizing the denominator, and irrational numbers. These terms are essential for understanding the foundational concepts in algebra and higher-level mathematics.

Rational Functions and Equations, Radical Expressions, Radical Functions and Equations and Rational Expressions
Google Earth Google Earth Voyager Collection

Overview

The Google Earth Voyager Story Collection offers an engaging set of lessons focused on geometric models, leveraging the immersive capabilities of Google Earth. This collection enables students to explore a variety of geometric concepts through real-world applications, enhancing their understanding of geometry, architecture, and culture. Each lesson is designed to develop geometric skills such as understanding shapes, symmetry, scale, and spatial reasoning.

Perpendicular Lines, Parallel Lines, Applications of Points and Lines, Applications of Circles, Cylinders, Applications of Angles and Planes, Applications of Polygons, Pyramids, Triangular Prisms, Rectangular Prisms, 3-Dimensional Figures, Applications of Surface Area and Volume, Rational Functions and Equations, Surface Area, Volume, Applications of Triangles and Applications of Quadrilaterals
Math Examples Math Examples Collection: Graphical Solutions to Rational Equations

Overview

This collection aggregates a set of math examples on the topic of Graphical Solutions to Rational Equations. There are 10 examples.

 

Rational Functions and Equations
Rationals and Radicals Collection Math Video Definitions Collection: Rationals and Radicals

Overview

This collection aggregates all the video definitions around the topic of Rationals and Radicals. There are a total of 47 videos. This collection of resources is made up of downloadable MP4 files that you can easily incorporate into a presentation.

 

 

 

Rational Functions and Equations, Radical Expressions, Radical Functions and Equations and Rational Expressions
Rationals and Radicals Collection Math Video Definitions Collection: Rationals and Radicals (Spanish)

Overview

This collection aggregates all the video definitions around the topic of Rationals and Radicals with Spanish audio. There are a total of 47 videos. This collection of resources is made up of downloadable MP4 files that you can easily incorporate into a presentation.

 

 

 

Rational Functions and Equations, Radical Expressions, Radical Functions and Equations and Rational Expressions
Math Examples Math Examples Collection: Extraneous or No Solutions

Overview

This collection of examples focuses on solving equations with extraneous or no solutions, providing students with a comprehensive set of problems to enhance their understanding of these challenging concepts. The examples progress in complexity, covering a range of skills including algebraic manipulation, graphing, and critical thinking.

Radical Functions and Equations and Rational Functions and Equations
Math Examples Math Examples Collection: Rational Functions in Tabular and Graph Form

Overview

The Media4Math collection on Rational Functions offers a comprehensive set of examples that explore this fundamental algebraic concept. This resource provides students with a diverse range of problems, progressively increasing in complexity, to develop and reinforce their understanding of rational functions. The examples cover various skills, including graphing, analyzing asymptotes, and solving equations involving rational expressions.

Rational Functions and Equations
Math Clip Art Math Clip Art Collection: Graphs of Functions and Relations

Overview

This collection aggregates all the math clip art around the topic of Graphs of Functions and Relations. There are a total of 19 images. This collection of resources is made up of downloadable PNG files that you can easily incorporate into a presentation.

 

Coordinate Systems, Trigonometric Functions, Polynomial Functions and Equations, Conic Sections, Graphs of Exponential and Logarithmic Functions, Applications of Points and Lines, Exponential and Logarithmic Functions and Equations, Graphs of Quadratic Functions, Rational Functions and Equations and Applications of Coordinate Geometry
Math Videos Math Video Collection: Algebra Applications Video Series: Rational Functions

Overview

This collection aggregates all the math videos and resources in this series: Algebra Applications Video Series: Rational Functions. There are a total of 23 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Rational Expressions and Rational Functions and Equations
VIDEO: Algebra Applications: Rational Functions VIDEO: Algebra Applications: Rational Functions VIDEO: Algebra Applications: Rational Functions

In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models.

This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Applications: Rational Functions Closed Captioned Video: Algebra Applications: Rational Functions Closed Captioned Video: Algebra Applications: Rational Functions

In this episode of Algebra Applications, students explore various scenarios that can be explained through the use of rational functions. Such disparate phenomena as submarines, photography, and the appearance of certain organisms can be explained through rational function models.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Applications: Rational Functions, Segment 1: Submarines Closed Captioned Video: Algebra Applications: Rational Functions, 1 Closed Captioned Video: Algebra Applications: Rational Functions, Segment 1: Submarines

In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Applications: Rational Functions, Segment 2: Biology Closed Captioned Video: Algebra Applications: Rational Functions, 2 Closed Captioned Video: Algebra Applications: Rational Functions, Segment 2: Biology

All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Applications: Rational Functions, Segment 3: Hubble Telescope Closed Captioned Video: Algebra Applications: Rational Functions, 3 Closed Captioned Video: Algebra Applications: Rational Functions, Segment 3: Hubble Telescope

The Hubble Telescope has transformed how we view the universe. We learn about the lens formula and how it is used in the construction of telescopes.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Nspirations: Rational Functions and Expressions Closed Captioned Video: Algebra Nspirations: Rational Functions Closed Captioned Video: Algebra Nspirations: Rational Functions and Expressions

After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Nspirations: Rational Functions and Expressions, Segment 1 Closed Captioned Video: Algebra Nspirations: Rational Functions, 1 Closed Captioned Video: Algebra Nspirations: Rational Functions and Expressions, Segment 1

In this Investigation we look at an application of rational functions: Boyle's Law. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 1 and 2 are grouped together.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Nspirations: Rational Functions and Expressions, Segment 3 Closed Captioned Video: Algebra Nspirations: Rational Functions, 3 Closed Captioned Video: Algebra Nspirations: Rational Functions and Expressions, Segment 3

In this Investigation we look at graphs of rational functions. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Rational Functions and Expressions. Segments 3 and 4 are grouped together.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: TI-Nspire Mini-Tutorial: Exploring Rational Function Graphs with Sliders Closed Captioned Video: Exp Rational Functions Closed Captioned Video: Exp Rational Functions

In this TI Nspire tutorial, the Graph window is used to create a slider-based graph of a rational function. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Rational Functions and Equations
Closed Captioned Video: Rational Numbers: Adding Rational Numbers Closed Captioned Video: Rational Numbers: Adding Rational Numbers Closed Captioned Video: Rational Numbers: Adding Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Comparing and Ordering Rational Numbers Closed Captioned Video: Rational Numbers: Comparing and Ordering Rational Numbers Closed Captioned Video: Rational Numbers: Comparing and Ordering Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Dividing Rational Numbers Closed Captioned Video: Rational Numbers: Dividing Rational Numbers Closed Captioned Video: Rational Numbers: Dividing Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Multiplying Rational Numbers Closed Captioned Video: Rational Numbers: Multiplying Rational Numbers Closed Captioned Video: Rational Numbers: Multiplying Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Numerical Expressions with Rational Numbers Closed Captioned Video: Rational Numbers: Numerical Expressions with Rational Numbers Closed Captioned Video: Rational Numbers: Numerical Expressions with Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Rational Numbers and Absolute Value Closed Captioned Video: Rational Numbers: Rational Numbers and Absolute Value Closed Captioned Video: Rational Numbers: Rational Numbers and Absolute Value

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Rational Numbers and Exponents Closed Captioned Video: Rational Numbers: Rational Numbers and Exponents Closed Captioned Video: Rational Numbers: Rational Numbers and Exponents

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Rational Numbers and Irrational Numbers Closed Captioned Video: Rational Numbers: Rational Numbers and Irrational Numbers Closed Captioned Video: Rational Numbers: Rational Numbers and Irrational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Rational Numbers on a Number Line Closed Captioned Video: Rational Numbers: Rational Numbers on a Number Line Closed Captioned Video: Rational Numbers: Rational Numbers on a Number Line

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Rational Numbers on the Cartesian Coordinate System Closed Captioned Video: Rational Numbers: Rational Numbers on the Cartesian Coordinate System Closed Captioned Video: Rational Numbers: Rational Numbers on the Cartesian Coordinate System

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Subtracting Rational Numbers Closed Captioned Video: Rational Numbers: Subtracting Rational Numbers Closed Captioned Video: Rational Numbers: Subtracting Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: Variable Expressions with Rational Numbers Closed Captioned Video: Rational Numbers: Variable Expressions with Rational Numbers Closed Captioned Video: Rational Numbers: Variable Expressions with Rational Numbers

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Closed Captioned Video: Rational Numbers: What Are Rational Numbers? Closed Captioned Video: Rational Numbers: What Are Rational Numbers? Closed Captioned Video: Rational Numbers: What Are Rational Numbers?

This is part of a collection of video tutorials on the topic of Rational Numbers. This includes defining rational numbers, rational number operations, comparing and ordering rational numbers, and applications of rational numbers.

—PRESS PREVIEW TO SEE THE VIDEO TUTORIAL— To see the complete collection of these videos on fractions, click on this link.

The following section includes background information on rational numbers. Refer to this section as you view the videos, or as review material afterward.

Rational Expressions
Definition--Rationals and Radicals--Asymptotes for a Rational Function Definition--Rationals and Radicals--Asymptotes for a Rational Function Asymptotes for a Rational Function

Topic

Rationals and Radicals

Definition

An asymptote is a line that a graph approaches but never touches.

Description

Asymptotes are significant in the study of Rational Numbers, Expressions, Equations, and Functions. They help in understanding the behavior of graphs of rational functions, particularly as the values of the variables approach certain limits. Horizontal asymptotes indicate the value that the function approaches as the input grows infinitely large or small. Vertical asymptotes show the values that the function cannot take because they cause division by zero.

Rational Functions and Equations
Definition--Rationals and Radicals--Conjugate of a Radical Definition--Rationals and Radicals--Conjugate of a Radical Conjugate of a Radical

Topic

Rationals and Radicals

Definition

The conjugate of a radical expression is obtained by changing the sign between two terms in a binomial.

Description

In the context of Radical Numbers, Expressions, Equations, and Functions, the concept of conjugates is essential for simplifying expressions. When dealing with radicals, particularly in the denominator, multiplying by the conjugate can help to rationalize the expression. This process eliminates the radical from the denominator, making the expression easier to work with.

Radical Expressions
Definition--Rationals and Radicals--Cube Root Definition--Rationals and Radicals--Cube Root Cube Root

Topic

Rationals and Radicals

Definition

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Description

The cube root is a fundamental concept in Radical Numbers, Expressions, Equations, and Functions. It is the inverse operation of raising a number to the power of three. Understanding cube roots is crucial for solving equations involving cubic terms and for simplifying radical expressions.

Cube roots also appear in various real-world applications, such as calculating volumes and in certain physics equations. They are an integral part of higher-level mathematics, including algebra and calculus.

Radical Expressions
Definition--Rationals and Radicals--Extraneous Solution Definition--Rationals and Radicals--Extraneous Solution Extraneous Solution

Topic

Rationals and Radicals

Definition

An extraneous solution is a solution derived from an equation that is not a valid solution to the original equation.

Description

Extraneous solutions often arise in the context of Rational and Radical Equations. They are solutions that appear during the process of solving an equation but do not satisfy the original equation. This can happen when both sides of an equation are squared or when other operations introduce additional solutions.

Rational Functions and Equations
Definition--Rationals and Radicals--Factoring a Radical Definition--Rationals and Radicals--Factoring a Radical Factoring a Radical

Topic

Rationals and Radicals

Definition

Factoring a radical involves expressing it as a product of simpler expressions.

Description

Factoring radicals is a key technique in the study of Radical Numbers, Expressions, Equations, and Functions. It simplifies complex radical expressions, making them easier to work with. This process is essential for solving equations and for performing algebraic manipulations involving radicals.

Understanding how to factor radicals is also important for simplifying expressions in calculus and higher-level mathematics. It helps in breaking down complex problems into more manageable parts.

Radical Functions and Equations
Definition--Rationals and Radicals--Fourth Root Definition--Rationals and Radicals--Fourth Root Fourth Root

Topic

Rationals and Radicals

Definition

The fourth root of a number is a value that, when raised to the power of four, gives the original number.

Description

The fourth root is an important concept in Radical Numbers, Expressions, Equations, and Functions. It is the inverse operation of raising a number to the power of four. Understanding fourth roots is crucial for solving higher-degree equations and for simplifying radical expressions.

Fourth roots are also relevant in various scientific and engineering applications where higher-degree roots are required. They are a part of advanced mathematical studies, including algebra and calculus.

Radical Expressions
Definition--Rationals and Radicals--Geometric Mean Definition--Rationals and Radicals--Geometric Mean Geometric Mean

Topic

Rationals and Radicals

Definition

The geometric mean of two numbers is the square root of their product.

Description

The geometric mean is an example of using radical expressions to solve a problem. It provides a measure of central tendency that is particularly useful in situations where the numbers are multiplied together rather than added.

In geometry, the geometric mean appears in various theorems and constructions. It is also used in finance and statistics to calculate average growth rates and to compare different sets of data.

Radical Expressions
Definition--Rationals and Radicals--Graphs of Radical Functions Definition--Rationals and Radicals--Graphs of Radical Functions Graphs of Radical Functions

Topic

Rationals and Radicals

Definition

Graphs of radical functions are visual representations of equations involving radicals.

Description

Graphs of radical functions are crucial in the study of Radical Numbers, Expressions, Equations, and Functions. They provide a visual understanding of how these functions behave, including their domains, ranges, and key features such as intercepts and asymptotes.

Radical Functions and Equations
Definition--Rationals and Radicals--Graphs of Rational Functions Definition--Rationals and Radicals--Graphs of Rational Functions Graphs of Rational Functions

Topic

Rationals and Radicals

Definition

Graphs of rational functions are visual representations of equations involving rational expressions.

Description

Graphs of rational functions are fundamental in the study of Rational Numbers, Expressions, Equations, and Functions. They help in understanding the behavior of these functions, including their asymptotes, intercepts, and regions of increase and decrease.

Rational Functions and Equations
Definition--Rationals and Radicals--Horizontal Asymptote Definition--Rationals and Radicals--Horizontal Asymptote Horizontal Asymptote

Topic

Rationals and Radicals

Definition

A horizontal asymptote is a horizontal line that a rational function graph approaches as the input values become very large or very small.

Description

Horizontal asymptotes are an important concept in the study of Rational Numbers, Expressions, Equations, and Functions. They indicate the value that a function approaches as the input grows infinitely large or small. Understanding horizontal asymptotes is crucial for graphing rational functions accurately and for analyzing their long-term behavior.

Rational Functions and Equations
Definition--Rationals and Radicals--Inverse Variation Definition--Rationals and Radicals--Inverse Variation Inverse Variation

Topic

Rationals and Radicals

Definition

Inverse variation describes a relationship between two variables in which the product is a constant. When one variable increases, the other decreases proportionally.

Rational Functions and Equations
Definition--Rationals and Radicals--Irrational Number Definition--Rationals and Radicals--Irrational Number Irrational Number

Topic

Rationals and Radicals

Definition

An irrational number is a number that cannot be expressed as a ratio of two integers. Its decimal form is non-repeating and non-terminating.

Rational Expressions
Definition--Rationals and Radicals--Irrational Number 2 Definition--Rationals and Radicals--Irrational Number 2 Irrational Number 2

Topic

Rationals and Radicals

Definition

An irrational number is a number that cannot be expressed as a ratio of two integers. Its decimal form is non-repeating and non-terminating.

Rational Expressions
Definition--Rationals and Radicals--Laws of Rational Exponents Definition--Rationals and Radicals--Laws of Rational Exponents Laws of Rational Exponents

Topic

Rationals and Radicals

Definition

The laws of rational exponents describe how to handle exponents that are fractions, including rules for multiplication, division, and raising a power to a power.

Description

The Laws of Rational Exponents are vital in the study of Rational Numbers, Expressions, Equations, and Functions. These laws provide a framework for simplifying expressions involving exponents that are fractions. For example, the law

 $$a^{m/n} = \sqrt[n]{a^m}$$ 

Rational Expressions
Definition--Rationals and Radicals--nth Root Definition--Rationals and Radicals--nth Root nth Root

Topic

Rationals and Radicals

Definition

The nth root of a number is a value that, when raised to the power of n, gives the original number. It is denoted as $$\sqrt[n]{a}$$

Description

The nth Root is a fundamental concept in the study of Radical Numbers, Expressions, Equations, and Functions. It generalizes the idea of square roots and cube roots to any positive integer n. For example, the cube root of 8 is 2 because 

$$2^3 = 8$$

Radical Expressions
Definition--Rationals and Radicals--Oblique Asymptote Definition--Rationals and Radicals--Oblique Asymptote Oblique Asymptote

Topic

Rationals and Radicals

Definition

An oblique asymptote is a diagonal line that the graph of a function approaches as the input values become very large or very small.

Description

Oblique Asymptotes are important in the study of Rational Numbers, Expressions, Equations, and Functions. They occur in rational functions where the degree of the numerator is one more than the degree of the denominator. For example, the function 

$$f(x) = \frac{x^2 + 1}{x}$$

Rational Functions and Equations