**Different Types of Number Properties – Associative and Distributive**

In mathematics, we have different types of number properties. These number properties are categorized into four different types which are associative property, commutative property, identity property, and distributive property. These properties are of great significance and come to our aid when we solve complex sums of algebra. Proper understanding of these properties will help you to master math and thus it is very important that you understand these properties nicely. In this article, we will discuss different types of number properties along with some examples so that you can understand these concepts clearly.

**Distributive Property**

It is one of the most important number properties that will come in handy when you solve complex topics of algebra. Distributive property as the name of this property itself signifies that the arithmetic operation of division or distribution will be carried out on a set of numbers. This property tells us that any mathematical expression in the form of M(N + P) can be expanded in the form of M*N + M*P. This is also in the case of the arithmetic operation of subtraction which means that any mathematical expression in the form of M(N – P) can be expanded in the form of M*N – M*P. For example: 15 (10 + 5) can also be written as 15 * 10 + 15 * 5. Both the expressions will fetch the same result. Let us check out one more example with the subtraction. 15 (10 – 5) can also be written as 15 * 10 – 15 * 5. Both the expressions will fetch the same result.

**Commutative Property**

The commutative property works on the arithmetic operation of addition and multiplication. This property tells us that the outcome of the addition or multiplication of two or more numbers is the same irrespective of the order of the numbers in which they are placed. To put it in a mathematical expression: G + H = H + G or G * H = H * G. This property does not apply to the arithmetic operation of division and subtraction. Let us now check out some examples of commutative property: 14 + 15 is the same as 15 + 14 i.e their sum is 19. Also, 12 * 9 is the same as 9 * 12 i.e., their product is 108.

**Associative Property**

The associative property is somewhat similar to the commutative property. An associative property, while carrying out the arithmetic operation of addition and multiplication, the order in which the numbers are grouped using different sets of brackets does not affect their outcome. To put it in a mathematical expression: M + (N + O) = O + (M + N). This property similar to the commutative property does not apply to the arithmetic operation of subtraction and division. Let us now check out some examples of the associative property to understand it more clearly. 14 + (16 + 10) is the same as 16 + (14 + 10) as both the expressions fetch out the same result i.e., 40. Similarly, 5 * (6 * 2) is the same as 2 * (5 * 6) as both the expressions fetch out the same result i.e., 60.

**Identity Property**

The identity property is very simple to understand. According to this property, any number when multiplied with the number 1 retains its identity. This property is not applicable for other arithmetic operations like addition, division and subtraction. Let us now check out some examples of the identity property to understand it more clearly. 77 when multiplied by the number 1 results in the number itself, thereby retaining its identity. Likewise, 56 when multiplied by the number 1 results in the number itself, thereby retaining its identity.

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