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Chapter 1: Problem 11

Determine which property of addition is depicted by the given identity. $$ 28+0=28 $$

Short Answer

Expert verified
This is the identity property of addition.

Step by step solution

01

Understanding the Operation

The operation given in the exercise is addition: \( 28 + 0 = 28 \). Here, the numbers involved are 28 and 0, and they result in 28 after addition.
02

Identifying the Components

Observe that in the expression \( 28 + 0 = 28 \), 28 is a number, and 0 is added to it, yet the sum remains 28. This is key to recognizing which property is illustrated.
03

Recognizing the Property

The identity property of addition states that adding 0 to any number does not change the value of that number. Recognizing that \( 28 + 0 = 28 \) fits this definition precisely means that this is the identity property of addition.

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Key Concepts

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

Addition Properties
Addition properties are fundamental rules that govern how numbers interact when being added. Understanding these properties helps make addition more intuitive and easier.
  • Commutative Property: This property states that the order of numbers does not matter. For instance, if you have two numbers, you can add them in any order: \( a + b = b + a \).
  • Associative Property: This indicates that how you group the numbers when adding does not change the sum. For example, \( (a + b) + c = a + (b + c) \).
  • Identity Property: Adding zero to any number leaves the number unchanged: \( a + 0 = a \).
All these properties work together to provide a consistent and predictable foundation for solving mathematical problems effectively.
Zero in Addition
Zero has a special role in addition as it represents the 'additive identity'. This means that adding zero to any number results in the original number.
  • Doesn't Change Value: Whether you're adding zero to five, twenty-eight, or one million, the number stays the same after addition. For example, \( 5 + 0 = 5 \) and \( 1000000 + 0 = 1000000 \).
  • Foundation in Arithmetic: Recognizing zero's role is fundamental in arithmetic and teaches us consistency and balance in mathematics.
The beauty of zero in addition is that it provides stability and neutrality, ensuring that values remain the same.
Mathematical Identities
Mathematical identities are equations that hold true for all values of their variables. They serve as basic truths or facts in mathematics, which can be particularly useful when solving equations or simplifying expressions.
  • Additive Identity: This states that any number added to zero will always yield the same number. It is a universal truth across all numbers: \( n + 0 = n \).
  • Importance in Algebra: Such identities are crucial in algebra for simplifying expressions and solving equations efficiently.
    • Mathematical identities like the additive identity help mathematicians to articulate and prove more complex concepts, building on these basic truths to explore and solve intricate mathematical challenges.

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