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- Properties of addition
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses properties of addition. By the end of the module students should be able to understand the commutative and associative properties of addition and understand why 0 is the additive identity.
Section overview
- The Commutative Property of Addition
- The Associative Property of Addition
- The Additive Identity
We now consider three simple but very important properties of addition.
The commutative property of addition
Commutative property of addition
If two whole numbers are added in any order, the sum will not change.
Sample set a
Add the whole numbers
The numbers 8 and 5 can be added in any order. Regardless of the order they are added, the sum is 13.
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Practice set a
Use the commutative property of addition to find the sum of 12 and 41 in two different ways.
and
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The associative property of addition
Associative property of addition
If three whole numbers are to be added, the sum will be the same if the first two are added first, then that sum is added to the third, or, the second two are added first, and that sum is added to the first.
Using parentheses
It is a common mathematical practice to
use parentheses to show which pair of numbers we wish to combine first.
Sample set b
Practice set b
Use the associative property of addition to add the following whole numbers two different ways.
and
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The additive identity
0 is the additive identity
The whole number 0 is called the
additive identity , since when it is added to any whole number, the sum is identical to that whole number.
Sample set c
Practice set c
Add the following whole numbers.
Suppose we let the letter x represent a choice for some whole number. For the first two problems, find the sums. For the third problem, find the sum provided we now know that x represents the whole number 17.
Exercises
For the following problems, add the numbers in two ways.
For the following problems, show that the pairs of quantities yield the same sum.
and
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and
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The fact that (a first number + a second number) + third number = a first number + (a second number + a third number) is an example of the
property of addition.
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The number zero is called the additive identity. Why is the term identity so appropriate?
…because its partner in addition remains identically the same after that addition
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Exercises for review
Questions & Answers
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Source:
OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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