Illustrative Math Alignment: Grade 7 Unit 5
Rational Number Arithmetic
Lesson 9: Multiplying Rational Numbers
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Rational Concepts--Rational Expressions: Example 18 | Math Example--Rational Concepts--Rational Expressions: Example 18TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 19 | Math Example--Rational Concepts--Rational Expressions: Example 19TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 2 | Math Example--Rational Concepts--Rational Expressions: Example 2TopicRational Expressions DescriptionThis 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 |
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Math Example--Rational Concepts--Rational Expressions: Example 20 | Math Example--Rational Concepts--Rational Expressions: Example 20TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 21 | Math Example--Rational Concepts--Rational Expressions: Example 21TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 22 | Math Example--Rational Concepts--Rational Expressions: Example 22TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 23 | Math Example--Rational Concepts--Rational Expressions: Example 23TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 24 | Math Example--Rational Concepts--Rational Expressions: Example 24TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 25 | Math Example--Rational Concepts--Rational Expressions: Example 25TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 26 | Math Example--Rational Concepts--Rational Expressions: Example 26TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 27 | Math Example--Rational Concepts--Rational Expressions: Example 27TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 28 | Math Example--Rational Concepts--Rational Expressions: Example 28TopicRational Expressions |
Rational Expressions |
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Math Example--Rational Concepts--Rational Expressions: Example 3 | Math Example--Rational Concepts--Rational Expressions: Example 3TopicRational Expressions DescriptionThis 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 |
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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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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 01, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 01, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 01, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 01, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 01, Level 3 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 01, Level 3
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 02, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 02, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 02, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 02, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 02, Level 3 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 02, Level 3
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 03, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 03, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 03, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 03, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 03, Level 3 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 03, Level 3
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 04, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 04, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 04, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 04, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 04, Level 3 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 04, Level 3
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 05, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 05, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 05, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 05, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 05, Level 3 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 05, Level 3
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 06, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 06, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 06, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 06, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 06, Level 3 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 06, Level 3
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 07, Level 1 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 07, Level 1
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
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Paper-and-Pencil Quiz: Multiplying Integers, Quiz 07, Level 2 | Paper-and-Pencil Quiz: Multiplying Integers, Quiz 07, Level 2
This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Numerical Expressions |
