Textbook Question
State the name of the property illustrated: (6 • 3) • 9 = 6 • (3 • 9)
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 1, Problem 13
State the name of the property illustrated: 3+17 = 17+3
Verified step by step guidance1
Observe the equation given: \(3 + 17 = 17 + 3\).
Notice that the numbers on both sides are the same but their order is switched.
Recall that the property which allows you to change the order of addition without changing the result is called the Commutative Property of Addition.
State that this property means: for any numbers \(a\) and \(b\), \(a + b = b + a\).
Conclude that the equation \(3 + 17 = 17 + 3\) illustrates the Commutative Property of Addition.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Commutative Property of Addition
This property states that changing the order of the numbers in an addition operation does not change the sum. For example, 3 + 17 equals 17 + 3, demonstrating that addition is commutative.
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Change of Base Property
Addition Operation
Addition is a basic arithmetic operation that combines two numbers to get their total or sum. Understanding how addition works is essential to recognize properties like commutativity.
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8:38Performing Row Operations on Matrices
Equality in Equations
Equality means that two expressions represent the same value. In the equation 3 + 17 = 17 + 3, both sides have the same sum, illustrating the concept of equality in algebra.
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06:00Categorizing Linear Equations
Related Practice
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Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27
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Evaluate each exponential expression in Exercises 1–22.
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In Exercises 11–16, factor by grouping. x3−3x2+4x−12
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In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (5x2−7x−8)+(2x2−3x+7)−(x2−4x−3)
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In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). 5(x+2)/(2x-14), for x=10
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