This document discusses properties of whole numbers in addition and multiplication. It covers the closure or uniqueness property, commutative property, associative property, identity properties in addition and multiplication, zero property in multiplication, and distributive property of multiplication. For example, the closure property states that the sum or product of two whole numbers is also a whole number. The commutative property means the order of numbers does not change the sum or product.

1. PROPERTIES OF WHOLE
NUMBERS IN ADDITION
AND MULTIPLICATION

2. A. Closure or Uniqueness Property
Each pair of whole numbers has a unique (only and
only one) sum or product which is also a whole
number.
Example:
8 + 12 = 20
7 + 5 = 15
6 x 3 = 18
6 x 7 = 42

3. B. Commutative Property
The sum/product of two numbers will not change
even if the positions are interchanged.
Example:
If 13 + 5 = 18 and 5 + 13 = 18, then
13+5 = 5+13.
If 6x2 = 12, and 2x6 = 12, then
6 x 2 = 2 x 6

4. C. Associative Property
Changing the groupings of the numbers will not
affect the sum/product.
Example:
(4 + 5) + 7 = 4 + (5+7)
2 x (8 x 3) = (2 x 8) x 3

5. D. Identity Property In Addition
It states that when a whole number is added
to zero, the sum is itself.
Example:
6 + 0 = 6
0 + 13 = 13
0 + 7 = 7

6. E. Identity Property In Multiplication
It states that when a whole number is multiplied
to 1, the product is itself.
Example:
13 x 1 = 13
1 x 17 = 17
1 x 3 = 3

7. F. Zero Property In Multiplication
It states that when a whole number is multiplied
to 0, the product is 0.
Example:
8 x 0 = 0
0 X 16 = 0
0 X 5 = 0

8. G. Distributive Property of Multiplication
a x (b+c) = (axb) + (axc)
a x (b-c) = (axb) – (a-c)