- The Commutative Property of Addition
- The Associative Property of Addition
- The Additive Identity
We now consider three simple but very important properties of addition.
Summary: 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.
We now consider three simple but very important properties of addition.
If two whole numbers are added in any order, the sum will not change.
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.
Use the commutative property of addition to find the sum of 12 and 41 in two different ways.
Add the whole numbers
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.
It is a common mathematical practice to use parentheses to show which pair of numbers we wish to combine first.
Add the whole numbers.
Use the associative property of addition to add the following whole numbers two different ways.
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.
Add the whole numbers.
Zero added to 29 does not change the identity of 29.
Add the following whole numbers.
8
5
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.
x
x
17
For the following problems, add the numbers in two ways.
37
45
568
122,323
45
100
556
43,461
For the following problems, show that the pairs of quantities yield the same sum.
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.
The fact that 0 + any number = that particular number is an example of the
property of addition.
Identity
The fact that a first number + a second number = a second number + a first number is an example of the
property of addition.
Use the numbers 15 and 8 to illustrate the commutative property of addition.
Use the numbers 6, 5, and 11 to illustrate the associative property of addition.
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
((Reference)) How many hundreds in 46,581?
((Reference)) Write 2,218 as you would read it.
Two thousand, two hundred eighteen.
((Reference)) Round 506,207 to the nearest thousand.
((Reference)) Find the sum of
550
((Reference)) Find the difference:
"Used as supplemental materials for developmental math courses."