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Identity Properties of Addition and Multiplication

by Caleigh
(Lumberton, NC )











































Identity Property

Are there problems any one can show me which will help my child on her project?

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Nov 17, 2012
Identity Property
by: Staff




Answer

Part I


Identity Property for Addition:

There is a difference between the identity property and the identity element.


An identity property only applies to a group of numbers as a whole.


The group of numbers is a set, such as the set of all real numbers, ℝ. The identity property does not apply to individual numbers within the set.

When you consider the set of all real numbers (ℝ), there is one number which has a particularly unique quality: the number zero (0).


The number zero (0) is called an identity element (or the neutral element). Every real number remains unchanged whenever zero (0) is added to it.


For example:


12 + 0 = 12

31.99 + 0 = 31.99

∛5 + 0 = ∛5


Because the number zero (0) has this unique quality, the set of all real numbers possesses an Identity Property of addition.




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Nov 17, 2012
Identity Property
by: Staff


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Part II

Identity Property for Multiplication:

A multiplicative identity is a number that can be multiplied by any number without changing the value of the other number.


As before, a multiplicative identity only applies to a group of numbers as a whole.


When you consider the set of all real numbers (ℝ), there is one number which has a particularly unique quality: the number zero (1).


The number one (1) is the multiplicative identity (the neutral element). Every real number remains unchanged whenever it is multiplied by one (1).


For example:


12 * 1 = 12

31.99 * 1 = 31.99

∛5 * 1 = ∛5


Because the number one (1) has this unique quality, the set of all real numbers possesses an Identity Property of multiplication.






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Staff
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