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Which is an example of the identity property of addition?

Published in Mathematics Property 2 mins read

An example of the identity property of addition is 5 + 0 = 5.

Understanding the Identity Property of Addition

The identity property of addition, also known as the additive identity property, states that when any number is added to zero, the sum is the original number. Zero is uniquely referred to as the additive identity because it maintains the "identity" of the number it's added to. This means that adding zero to any number will not change its value.

As provided in the reference, a clear example is:

  • 5 + 0 = 5

In this instance, adding 0 to 5 results in 5, demonstrating that the number's value remains unchanged.

Key Aspects of the Additive Identity

  • Zero's Role: Zero is the only number that acts as the additive identity. No other number possesses this unique characteristic in addition.
  • Preservation of Value: The core principle is the preservation of the original number's value. This property is fundamental in arithmetic and algebra.
  • General Form: The property can be expressed generally as a + 0 = a or 0 + a = a, where 'a' represents any real number.

Practical Examples

Beyond 5 + 0 = 5, the identity property applies universally to all numbers. Consider these examples:

  • Integers:
    • 12 + 0 = 12
    • 0 + (-7) = -7
  • Fractions:
    • 1/2 + 0 = 1/2
  • Decimals:
    • 3.14 + 0 = 3.14
  • Variables:
    • x + 0 = x

Comparing with Other Properties

While focusing on the identity property, it's part of a set of fundamental properties in mathematics that simplify calculations and algebraic manipulations.

Property Name Description Example (Addition)
Identity Property Adding zero to a number leaves it unchanged. a + 0 = a
Commutative Property Changing the order of addends does not change sum. a + b = b + a
Associative Property Grouping of addends does not change sum. (a + b) + c = a + (b + c)

This property is crucial for solving equations and simplifying expressions, providing a foundational rule in mathematics. For more information on fundamental arithmetic properties, you can explore mathematical concepts online.

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