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.
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Math Example--Rational Concepts--Rational Expressions: Example 4 | Math Example--Rational Concepts--Rational Expressions: Example 4TopicRational Expressions DescriptionThis 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 |
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Math Example--Rational Concepts--Rational Expressions: Example 5 | Math Example--Rational Concepts--Rational Expressions: Example 5TopicRational Expressions DescriptionThis 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 |
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Math Example--Rational Concepts--Rational Expressions: Example 6 | Math Example--Rational Concepts--Rational Expressions: Example 6TopicRational Expressions DescriptionThis 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 |
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Math Example--Rational Concepts--Rational Expressions: Example 7 | Math Example--Rational Concepts--Rational Expressions: Example 7TopicRational Expressions DescriptionThis 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 |
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Math Example--Rational Concepts--Rational Expressions: Example 8 | Math Example--Rational Concepts--Rational Expressions: Example 8TopicRational Expressions DescriptionThis 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 |
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Math Example--Rational Concepts--Rational Expressions: Example 9 | Math Example--Rational Concepts--Rational Expressions: Example 9TopicRational Expressions DescriptionThis 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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Rational Expressions and Rational Functions and Equations |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see other resources related to this topic, click on the Resources tab above. Quizlet LibraryTo see the complete Quizlet Flash Card Library, click on this Link to see the collection. |
Numerical Expressions |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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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 ResourcesTo see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq |
Subtract Multiple-Digit Numbers |
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Video Definition 1--Rationals and Radicals--Addition of Rational Expressions | Video Definition 1--Rationals and Radicals--Addition of Rational Expressions
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
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Video Definition 1--Rationals and Radicals--Addition of Rational Expressions (Spanish Audio) | Video Definition 1--Rationals and Radicals--Addition of Rational Expressions (Spanish Audio)
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
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Video Definition 10--Rationals and Radicals--Geometric Mean | Video Definition 10--Rationals and Radicals--Geometric Mean
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Radical Expressions |
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Video Definition 10--Rationals and Radicals--Geometric Mean (Spanish Audio) | Video Definition 10--Rationals and Radicals--Geometric Mean (Spanish Audio)
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Radical Expressions |
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Video Definition 11--Rationals and Radicals--Graphs of Radical Functions | Video Definition 11--Rationals and Radicals--Graphs of Radical Functions
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Radical Functions and Equations |
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Video Definition 11--Rationals and Radicals--Graphs of Radical Functions (Spanish Audio) | Video Definition 11--Rationals and Radicals--Graphs of Radical Functions (Spanish Audio)
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Radical Functions and Equations |
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Video Definition 12--Rationals and Radicals--Graphs of Rational Functions | Video Definition 12--Rationals and Radicals--Graphs of Rational Functions
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
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Video Definition 12--Rationals and Radicals--Graphs of Rational Functions (Spanish Audio) | Video Definition 12--Rationals and Radicals--Graphs of Rational Functions (Spanish Audio)
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
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Video Definition 13--Rationals and Radicals--Horizontal Asymptote | Video Definition 13--Rationals and Radicals--Horizontal Asymptote
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
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Video Definition 13--Rationals and Radicals--Horizontal Asymptote (Spanish Audio) | Video Definition 13--Rationals and Radicals--Horizontal Asymptote (Spanish Audio)
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
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Video Definition 14--Rationals and Radicals--Index | Video Definition 14--Rationals and Radicals--Index
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Radical Expressions |
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Video Definition 14--Rationals and Radicals--Index (Spanish Audio) | Video Definition 14--Rationals and Radicals--Index (Spanish Audio)
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Radical Expressions |
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Video Definition 15--Rationals and Radicals--Integer | Video Definition 15--Rationals and Radicals--Integer
This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video. |
Rational Functions and Equations |
