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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 5

Rational Number Arithmetic

Lesson 13: Expressions with Rational Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topics
Math Example--Rational Concepts--Rational Expressions: Example 19 Math Example--Rational Concepts--Rational Expressions: Example 19 Math Example--Rational Concepts--Rational Expressions: Example 19

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 2 Math Example--Rational Concepts--Rational Expressions: Example 2 Math Example--Rational Concepts--Rational Expressions: Example 2

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/4 - 1/5. The solution involves finding a common denominator, which is 20, and then subtracting the fractions to get 1/20. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 5/5) - (1 * 4/4) = 5/20 - 4/20. Then, we subtract the numerators while keeping the common denominator: (5 - 4)/20 = 1/20.

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 20 Math Example--Rational Concepts--Rational Expressions: Example 20 Math Example--Rational Concepts--Rational Expressions: Example 20

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 21 Math Example--Rational Concepts--Rational Expressions: Example 21 Math Example--Rational Concepts--Rational Expressions: Example 21

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 22 Math Example--Rational Concepts--Rational Expressions: Example 22 Math Example--Rational Concepts--Rational Expressions: Example 22

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 23 Math Example--Rational Concepts--Rational Expressions: Example 23 Math Example--Rational Concepts--Rational Expressions: Example 23

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 24 Math Example--Rational Concepts--Rational Expressions: Example 24 Math Example--Rational Concepts--Rational Expressions: Example 24

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 25 Math Example--Rational Concepts--Rational Expressions: Example 25 Math Example--Rational Concepts--Rational Expressions: Example 25

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 26 Math Example--Rational Concepts--Rational Expressions: Example 26 Math Example--Rational Concepts--Rational Expressions: Example 26

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 27 Math Example--Rational Concepts--Rational Expressions: Example 27 Math Example--Rational Concepts--Rational Expressions: Example 27

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Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 28 Math Example--Rational Concepts--Rational Expressions: Example 28 Math Example--Rational Concepts--Rational Expressions: Example 28

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 3 Math Example--Rational Concepts--Rational Expressions: Example 3 Math Example--Rational Concepts--Rational Expressions: Example 3

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/x + 1/3. The solution involves finding a common denominator, which is 3x, and then adding the fractions to get (x + 3)/3x. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3/3) + (1 * x/x) = 3/(3x) + x/(3x). Then, we add the numerators while keeping the common denominator: (3 + x)/(3x) = (x + 3)/(3x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 4 Math Example--Rational Concepts--Rational Expressions: Example 4 Math Example--Rational Concepts--Rational Expressions: Example 4

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/x - 1/2. The solution involves finding a common denominator, which is 2x, and then subtracting the fractions to get (x - 2)/2x. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 2/2) - (1 * x/x) = 2/(2x) - x/(2x). Then, we subtract the numerators while keeping the common denominator: (2 - x)/(2x) = (x - 2)/(2x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 5 Math Example--Rational Concepts--Rational Expressions: Example 5 Math Example--Rational Concepts--Rational Expressions: Example 5

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(2x) + 1/5. The solution involves finding a common denominator, which is 10x, and then adding the fractions to get (2x + 5)/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2x)/(5 * 2x) = 5/(10x) + 2x/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2x)/(10x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 6 Math Example--Rational Concepts--Rational Expressions: Example 6 Math Example--Rational Concepts--Rational Expressions: Example 6

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(4x) - 1/7. The solution involves finding a common denominator, which is 28x, and then subtracting the fractions to get (7 - 4x)/(28x), which simplifies to (4x - 7)/(28x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 7)/(4x * 7) - (1 * 4x)/(7 * 4x) = 7/(28x) - 4x/(28x). Then, we subtract the numerators while keeping the common denominator: (7 - 4x)/(28x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 7 Math Example--Rational Concepts--Rational Expressions: Example 7 Math Example--Rational Concepts--Rational Expressions: Example 7

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(8x) + 1/8. The solution involves finding a common denominator, which is 8x, and then adding the fractions to get (x + 1)/(8x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * x)/(8x * x) + (1 * x)/(8 * x) = 1/(8x) + x/(8x). Then, we add the numerators while keeping the common denominator: (1 + x)/(8x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 8 Math Example--Rational Concepts--Rational Expressions: Example 8 Math Example--Rational Concepts--Rational Expressions: Example 8

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(9x) - 1/3. The solution involves finding a common denominator, which is 9x, and then subtracting the fractions to get (1 - 3x)/(9x), which simplifies to (3x - 1)/(9x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * x)/(9x * x) - (3 * x)/(3 * x) = 1/(9x) - 3x/(9x). Then, we subtract the numerators while keeping the common denominator: (1 - 3x)/(9x).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 9 Math Example--Rational Concepts--Rational Expressions: Example 9 Math Example--Rational Concepts--Rational Expressions: Example 9

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(2x) + 1/(5x). The solution involves finding a common denominator, which is 10x, and then adding the fractions to get 7/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2)/(5x * 2) = 5/(10x) + 2/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2)/(10x) = 7/(10x).

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 1 Math Example--Rational Concepts--Rational vs Irrational--Example 1 Math Example--Rational Concepts--Rational vs Irrational--Example 1

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 10 Math Example--Rational Concepts--Rational vs Irrational--Example 10 Math Example--Rational Concepts--Rational vs Irrational--Example 10

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 2 Math Example--Rational Concepts--Rational vs Irrational--Example 2 Math Example--Rational Concepts--Rational vs Irrational--Example 2

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 3 Math Example--Rational Concepts--Rational vs Irrational--Example 3 Math Example--Rational Concepts--Rational vs Irrational--Example 3

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 4 Math Example--Rational Concepts--Rational vs Irrational--Example 4 Math Example--Rational Concepts--Rational vs Irrational--Example 4

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 5 Math Example--Rational Concepts--Rational vs Irrational--Example 5 Math Example--Rational Concepts--Rational vs Irrational--Example 5

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 6 Math Example--Rational Concepts--Rational vs Irrational--Example 6 Math Example--Rational Concepts--Rational vs Irrational--Example 6

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 7 Math Example--Rational Concepts--Rational vs Irrational--Example 7 Math Example--Rational Concepts--Rational vs Irrational--Example 7

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 8 Math Example--Rational Concepts--Rational vs Irrational--Example 8 Math Example--Rational Concepts--Rational vs Irrational--Example 8

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
Math Example--Rational Concepts--Rational vs Irrational--Example 9 Math Example--Rational Concepts--Rational vs Irrational--Example 9 Math Example--Rational Concepts--Rational vs Irrational--Example 9

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Rational Expressions
MATH EXAMPLES--Teacher's Guide: Rational Expressions MATH EXAMPLES--Teacher's Guide: Rational Expressions MATH EXAMPLES--Teacher's Guide: Rational Expressions

This Teacher's Guide provides an overview of the 28 worked-out examples that show how to simplify a variety of rational expressions.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Rational Expressions and Rational Functions and Equations
Quizlet Flash Cards: Adding Rational Numbers, Set 01 Quizlet Flash Cards: Adding Rational Numbers, Set 01 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 02 Quizlet Flash Cards: Adding Rational Numbers, Set 02 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 03 Quizlet Flash Cards: Adding Rational Numbers, Set 03 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 04 Quizlet Flash Cards: Adding Rational Numbers, Set 04 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 05 Quizlet Flash Cards: Adding Rational Numbers, Set 05 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 06 Quizlet Flash Cards: Adding Rational Numbers, Set 06 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 07 Quizlet Flash Cards: Adding Rational Numbers, Set 07 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 08 Quizlet Flash Cards: Adding Rational Numbers, Set 08 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 09 Quizlet Flash Cards: Adding Rational Numbers, Set 09 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 10 Quizlet Flash Cards: Adding Rational Numbers, Set 10 Description

Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see other resources related to this topic, click on the Resources tab above.

Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

Numerical Expressions
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 01

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 02

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 03

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 04

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 05

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 06

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 07

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 08

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 09

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
QuizletFlashCards.jpg Quizlet Flash Cards: Subtracting Rational Numbers, Set 10

Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

Related Resources

To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq
Subtract Multiple-Digit Numbers
Video Definition 1--Rationals and Radicals--Addition of Rational Expressions Video Definition 1--Rationals and Radicals--Addition of Rational Expressions Video Definition 1--Rationals and Radicals--Addition of Rational Expressions

Topic

Rationals and Radicals

Description

Addition of rational expressions involves combining rational expressions to create a new rational expression, often requiring a common denominator. Examples include 1 / x + 1 / 2x = 3 / 2x and 1 / (x + 1) + 1 / (x - 1) = 2x / (x2 - 1). This term introduces the concept of combining rational expressions, which is fundamental to operations involving fractions with polynomial expressions.

Rational Functions and Equations