Commutative properties
Definition of Commutative Property
• Commutative Property of Addition: It says that changing the order of addends
(the numbers you add together) does not change the sum.
• Commutative Property of Multiplication: It says that changing the order of factors
does not change the product.
Examples of Commutative Property
• 2 + 3 = 3 + 2. Whether you add 3 to 2 or you add 2 to 3, you get 5 both ways.
• 4 × 7 = 7 × 4, Whether you multiply 4 by 7 or you multiply 7 by 4, the product is
the same, 28.
Associative Properties
Definition of Associative Property
• Associative property states that the change in grouping of three or more addends
or factors doesn’t change their sum or product.
Examples of Associative Property
• Addition
(2 + 3) + 5 = 2 + (3 + 5)
Whether you add 2 & 3 first or 3 & 5 first doesn’t matter as you get the same sum
(10) both ways.
• Multiplication
(4 . 5) . 10 = 4 . (5 . 10)
Whether you multiply 4 & 5 first or 5 & 10 first does not matter as you get the same
product (200) both ways.
Identity Properties
Definition of Identity Properties
• Identity property of addition states that the sum of zero and any number or
variable is the number or variable itself.
For example, 4 + 0 = 4, - 11 + 0 = - 11, y + 0 = y are few examples illustrating the
identity property of addition.
• Identity property of multiplication states that the product of 1 and any number or
variable is the number or variable itself.
For example, 4 × 1 = 4, - 11 × 1 = - 11, y × 1 = y are few examples illustrating the
identity property of multiplication.
Distributive Property
Definition of Distributive Property
• Distributive property states that the product of a number and a sum is equal to
the sum of the individual products of addends and the number.
Examples of Distributive Property
• 5(3 + 1) = 5 × 3 + 5 × 1
Like This: 5(3 + 1) = 5(4) = 20
Or This: 5 × 3 + 5 × 1 = 15 + 5 = 20
Equality Property
Definition of The Property of Equality
• Addition Property of Equality :
If the same number is added to both sides of an equation, the two sides remain
equal.
Examples of Addition Property of Equality
a) 3 = 3
Add the same number to both sides,
3+2=3+2
The same goes for subtraction, multiplication, and division.
Inverse Properties
Definition of Inverse Properties
• Inverse Properties state that when a number is combined with its inverse, it is
equal to
• There are two types of inverses of a number: Additive Inverse and Multiplicative
Inverse.
• - a is the additive inverse of `a` if a + (- a) = 0.
• 1/a is said to be multiplicative Inverse of a if a * 1/a = 1 .
Example of Inverse Properties
• The additive inverse of 54 is – 54 because if a is a real number, then the additive
inverse of a is - a so that a + (- a) = 0.