PROPERTIES OF WHOLE NUMBERS IN ADDITION AND MULTIPLICATION

A. Closure or Uniqueness PropertyEach pair of whole numbers has a unique (only and

only one) sum or product which is also a whole number.

Example:8 + 12 = 207 + 5 = 156 x 3 = 186 x 7 = 42

B. Commutative PropertyThe 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, then6 x 2 = 2 x 6

C. Associative PropertyChanging 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

D. Identity Property In AdditionIt states that when a whole number is

added to zero, the sum is itself.

Example:6 + 0 = 60 + 13 = 130 + 7 = 7

E. Identity Property In MultiplicationIt states that when a whole number is

multiplied to 1, the product is itself.

Example:13 x 1 = 131 x 17 = 171 x 3 = 3

F. Zero Property In MultiplicationIt states that when a whole number is

multiplied to 0, the product is 0.

Example:8 x 0 = 00 X 16 = 00 X 5 = 0

G. Distributive Property of Multiplication

a x (b+c) = (axb) + (axc)

a x (b-c) = (axb) – (a-c)