Properties of Numbers
As you evaluated the expressions on the previous page, you may have noticed some patterns in the way the numbers behave. There are some specific patterns which are called the properties or laws of numbers. Here is a description of some of the most useful properties.
Commutative Property for AdditionIllustration:When adding a group of 3 soldiers and a group of 5 soldiers, the sum is the same whether 3 is added to 5 or 5 is added to 3.
Commutative Property: If a and b are numbers, then a + b = b + a
Associative Property for Addition
Illustration:When adding groups of missiles, the sum is the same no matter the order in which the groups are added.Associative Property:If a and b and c are numbers, then (a + b) + c = a + (b + c)
Cancellation Property for Addition
Illustration:If the result obtained when group B is added to group A is the same as the result obtained when group C is added to group A, then group B is equal to group C.
Cancellation Property: If a, b and c are numbers, and if a + b = a + c, then b = cCommutative Property for Multiplication
Illustration:
A group of 3 soldiers multiplied by 5, is the same as a group of 5 soldiers multiplied by 3; both results are a group of 15 soldiers.Commutative Property: If a and b are numbers, then a * b = b * a
Associative Property for Multiplication
Illustration:When multiplying groups, the product is the same no matter the order in which the groups are multiplied.
Associative Property: If a and b and c are numbers, then a * (b * c) = (a * b) * c
Cancellation Property for Multiplication
Illustration:If the result obtained when group B is multiplied A is the same as the result obtained when group C is multiplied by A, then group B is equal to group A.
Cancellation Property: If a, b and c are numbers, and if a * b = a * c, then b = c
Distributive Property of Multiplication
Illustration:When multiplying sums of groups of missiles, the product is the same as multiplying each group separately and summing the result.
Distributive Property: If a, b and c are numbers, then a * (b + c) = a * b + a * c
