Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 124

Chapter 1, Problem 124

Identify the property illustrated in each statement. Assume all variables represent real numbers. 5𝜋 is a real number.

Verified step by step guidance

Understand that the problem asks to identify the algebraic property illustrated by the statement involving 5𝜋, where 𝜋 is a real number.

Recall common algebraic properties such as the Commutative Property, Associative Property, Distributive Property, Identity Property, and Inverse Property, which apply to real numbers.

Analyze the given expression or statement involving 5𝜋 to see which property it demonstrates. For example, if the statement shows multiplication of 5 and 𝜋, it might illustrate the Commutative Property of Multiplication, which states that \$a $\times$ b = b $\times$ a\$.

Check if the statement involves addition or multiplication and whether it rearranges terms or groups them differently, which helps identify the property.

Summarize the property by matching the observed behavior in the statement to the formal definition of the property.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Properties of Real Numbers

Real numbers include all rational and irrational numbers, encompassing integers, fractions, and decimals. Understanding their properties, such as closure, commutativity, associativity, identity, and distributivity, is essential for identifying how numbers behave under various operations.

Closure Property

The closure property states that performing an operation (addition, subtraction, multiplication, or division, except by zero) on any two real numbers results in another real number. For example, multiplying 5 by π (an irrational real number) yields a real number, illustrating closure under multiplication.

Multiplication of Real Numbers

Multiplying real numbers follows specific rules, including the closure property and the existence of multiplicative identity (1). Recognizing that 5π is a product of two real numbers helps confirm it remains within the set of real numbers, reinforcing the concept of multiplication within real numbers.

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Related Practice

Textbook Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. -4a^-2/5+16a^-7/5

Textbook Question

Multiply or divide as indicated. 124.03 ÷ 100

Textbook Question

Perform the indicated operations. Assume all variables represent positive real numbers. (√3 + √8)²

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Textbook Question

Perform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)

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Textbook Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8.

$(3 r + 1)^{- \frac{2}{3}} + (3 r + 1)^{\frac{1}{3}} + (3 r + 1)^{\frac{4}{3}}$

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Textbook Question

Multiply or divide as indicated. 1.62÷10