In mathematics, there are different laws to perform some arithmetic operations. The rules and laws are created in a way that does not affect the outcome of the problem. The existence of the law is to make the calculations simpler. There are many laws that govern the order of operations in arithmetic and in **algebra** problems. The most widely used laws are

- Commutative Law
- Associative Law
- Distributive Law

Let us have a look at these three laws in detail.

## Commutative Law

In commutative law, the rule is “changing or switching the order of numbers”. It is applied only for addition and multiplication. In addition problem, it is referred to as commutative law of addition and in the multiplication problem, it is referred to as commutative law of multiplication.

**Commutative Law of Addition**:

2 + 3 = 3 + 2

5 = 5

**Commutative Law of Multiplication**:

- 3 = 3 . 2

6 = 6

This law is not applicable to subtraction and multiplication operation.

## Associative Law

In associative law, the rule is “shifting the parentheses not the numbers”. As with commutative law, this is also applicable only for addition and multiplication.

**Associative Law of Addition:**

2 + ( 3 + 4) =(2 + 3) + 4

9 = 9

**Associative Law of Multiplication**:

2 . ( 3 . 4) =(2 . 3) . 4

2 . 12 = 6. 4

24 = 24

## Distributive Law

In distributive law, the general rule is “multiply everything inside the parentheses by the outside numbers or variables”.

**Distributive Law:**

- ( 3 + 4) =(2 . 3) + (2. 4)

2 . 7 = 6 + 8

14 = 14

From these examples, it is understood that the laws of mathematics do not affect the solution as it produces the same result. Similarly, there are distinct rules and laws in mathematical concepts like **permutation and combination**, trigonometric laws like the law of sine, cosine and tangents functions etc which helps us to give the accurate result. To know various rules and laws in mathematics, subscribe to BYJU’S YouTube Channel to learn with ease.