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Chapter 0: Problem 22

The _____ property of addition indicates that \(a+(b+c)=(a+b)+c\).

Short Answer

Expert verified
Associative Property

Step by step solution

01

Identify the property

Determine which property of addition is described by the equation given.
02

Recall the properties of addition

List the properties of addition you have learned. These include the Commutative Property, Associative Property, and Identity Property.
03

Match the property to the description

Compare the given equation to the properties identified in step 2. The equation given is of the form \(a + (b + c) = (a + b) + c\), which matches the Associative Property of addition.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Associative Property
The Associative Property of Addition is an essential concept in basic algebra. It tells us that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. This property is formally expressed as \(a + (b + c) = (a + b) + c\).
This means that whether you group the numbers as \(b + c\) or as \(a + b\), the result will be the same.
This is particularly useful in simplifying complex algebraic expressions and solving problems efficiently.
Understanding this property helps in building a solid foundation for more advanced mathematical concepts.
Properties of Addition
In addition to the Associative Property, there are other fundamental properties that govern addition:
  • Commutative Property: This property states that the order in which two numbers are added does not change the sum. It can be written as \(a + b = b + a\).
  • Identity Property: This property asserts that adding zero to any number does not change the value of that number. It can be expressed as \(a + 0 = a\).

Each of these properties plays a crucial role in simplifying mathematical computations and proofs.
They enable students to recognize patterns and develop a deeper understanding of algebra.
Basic Algebra
Basic Algebra is the foundation of higher-level mathematics and involves the study of variables, expressions, equations, and their properties.
One of the key skills in basic algebra is understanding how different properties, like the Associative and Commutative properties, apply to operations such as addition and multiplication.
By mastering these basic principles, students can tackle more complex algebraic problems with confidence.
Remember, the goal of algebra is to develop the ability to think logically, to solve equations, and to understand the relationships between variables.

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