There are different types of number properties that we study in mathematics. These properties are very useful because they facilitate the process of solving advanced sums of algebra in our higher classes and make complex problem-solving easy.
Basically, there are four categories of number properties, namely, associative property, commutative property, identity property, and distributive property.
In this article, we will discuss in detail two types of number properties – commutative property and distributive property.
We will also solve some examples related to both the properties so that this concept becomes clearer to you.
What Do You Mean by Distributive Property?
The distributive property is one of the properties that will be used most frequently while solving complex sums of algebra.
It is also commonly referred to as distributive law. It states that any mathematical expression given in the form of X (Y + Z) can be expanded in the form of XY + XZ.
This is also true in the case of subtraction which means that X (Y – Z) can be expanded in the form of XY – XZ.
Let us discuss in detail the distributive property over addition and the distributive property over subtraction with the help of examples:
- Distributive Property Over Addition: When any number is multiplied by the sum of two numbers, the distributive law of multiplication over addition is applied. To put it in a more understandable manner: X (Y + Z) = XY + XZ
Let us check out some examples of the distributive law of multiplication over addition.
- 5 (6 + 4) = 5 * 6 + 5 * 4 = 30 + 20 = 50
- 10 (8 + 2) = 10 * 8 + 10 * 2 = 80 + 20 = 100
- 3 (2 + 3) = 3 * 2 + 3 * 3 = 6 + 9 = 15.
- Distributive Property Over Subtraction: When any number is multiplied by the difference of two numbers, the distributive law of multiplication over subtraction is applied. To put it in a more understandable manner: X (Y – Z) = XY – XZ.
Let us check out some examples of the distributive law of multiplication over subtraction.
- 5 (6 – 4) = 5 * 6 – 5 * 4 = 30 – 20 = 10.
- 10 (8 – 2) = 10 * 8 – 10 * 2 = 80 – 20 = 60.
- 3 (3 – 2) = 3 * 3 – 3 * 2 = 9 – 6 = 3.
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What Do You Mean by Commutative Property?
Commutative property basically tells us that the end result of a sum or a multiplication of two or more numbers results in the same even when the change in the order or the position of the numbers is in consideration.
This property does not hold true for the arithmetic operation of subtraction.
The Commutative property is categorized into two parts namely, the commutative property in case of addition and the commutative property in case of multiplication.
Let us discuss the types of commutative property in detail:
- In case of Addition: The total of the addition of two or more numbers is the same, irrespective of the position or the order in which the numbers are placed. To put it in a more understandable manner, we can say that X + Y = Y + X. Example: 16 + 14 = 20 or 14 + 16 = 20; 26 + 24 = 50 or 24 + 26 = 50. Let us take examples of 3 numbers: 4 + 5 + 1 = 10 or 1 + 5 + 4 = 10.
- In case of Multiplication : The product of the multiplication of two or more numbers is the same irrespective of the position or the order in which the numbers are placed. To put it in a more understandable manner, we can say that X * Y = Y * X. Example: 10 * 100 = 1000 or 100 * 10 = 1000; 8 * 6 = 48 or 6 * 8 = 48. Let us take example of 3 numbers: 4 * 5 * 2 * = 40 or 2 * 5 * 4 = 40.
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