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 122

Chapter 1, Problem 122

Identify the property illustrated in each statement. Assume all variables represent real numbers. (38+99) +1 = 38+(99+1)

Verified step by step guidance

Observe the given expression: \( (38 + 99) + 1 = 38 + (99 + 1) \). Notice that the grouping of the numbers changes, but the order of the numbers remains the same.

Recall the properties of addition. The property that allows you to change the grouping of addends without changing the sum is called the Associative Property of Addition.

The Associative Property of Addition states that for any real numbers \(a\), \(b\), and \(c\), the equation \( (a + b) + c = a + (b + c) \) holds true.

In this problem, \(a = 38\), \(b = 99\), and \(c = 1\). The equation matches the form of the Associative Property of Addition exactly.

Therefore, the property illustrated by the statement \( (38 + 99) + 1 = 38 + (99 + 1) \) is the Associative Property of Addition.

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Key Concepts

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

Associative Property of Addition

The associative property of addition states that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. For example, (a + b) + c = a + (b + c). This property allows us to change the grouping of addends without changing the result.

Real Numbers

Real numbers include all rational and irrational numbers and are the set of numbers used in most algebraic operations. Understanding that variables represent real numbers ensures that properties like associativity apply, as these properties hold true within the real number system.

Properties of Equality

Properties of equality allow us to manipulate equations while maintaining equality. Recognizing that both sides of the equation are equal because of a property (like associativity) helps in identifying and justifying algebraic steps in problem solving.

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