-->
Algebra 1: Identity Property, Additive Inverse, Commutative Property
logo for solving-math-problems.com
leftimage for solving-math-problems.com

Algebra 1: Identity Property, Additive Inverse, Commutative Property

by Cortney Boothe
(Jonesville, LA 71343)







































Properties of Operations – Real Numbers

   • Properties of Numbers

           Identity Property for Addition

           Additive Inverse Property

           Definition of Subtraction

           Commutative Property of Addition

Comments for Algebra 1: Identity Property, Additive Inverse, Commutative Property

Click here to add your own comments

Sep 27, 2012
Properties of Numbers
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.


Additive Inverse Property:

The additive inverse property of any number is the same number with the opposite sign.

When a number and its additive inverse are added to one another, the result is always 0 (zero) - the identity element for addition.

For example:


The additive inverse property of 12 is -12, AND the additive inverse property of -12 is 12.


12 + (-12) = 0

(-12) + 12 = 0


-------------------------------------

Sep 27, 2012
Properties of Numbers
by: Staff


-------------------------------------

Part II

The additive inverse property of 31.99 is -31.99, AND the additive inverse property of -31.99 is 31.99.


31.99 + (-31.99) = 0

(-31.99) + 31.99 = 0



The additive inverse property of ∛5 is -∛5, AND the additive inverse property of -∛5 is ∛5.


∛5 + (-∛5) = 0

(-∛5) + ∛5 = 0


The Additive Inverse Property is an important key which is used to simplify equations .

For example:

Solve for X

X + 20 = 5

To eliminate the +20, the additive inverse property of -20 can be used . . . because +20 - 20 = 0 (the additive identity element).

Add the additive inverse “-20” to each side of the equation.


x + 20 + (-20) = 5 + (-20)

x + 0 = -15

x = -15



Definition of Subtraction:

Subtraction: Finding the difference between two numbers (or two quantities).



Commutative Property of Addition:

Commutative Property of Addition:

Any two addends can be added in either order without changing the results. This is true for all real numbers (including: fractions, decimals, and negative numbers).

For example:


(positive integers)10 + 9 = 9 + 10

(negative numbers)[-52] + 9 = 9 + [-52]

(fractions)¾ + ½ = ½ + ¾

(decimals)1.51 + 0.0055 = 0.0055 + 1.51

(algebraic notation) a + b = b + a




Thanks for writing.

Staff
www.solving-math-problems.com


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2014. All rights reserved. Solving-Math-Problems.com