THE LAWS OF ADDITION: application exercises

The Laws of Addition are mathematical principles that describe the properties of the addition of numbers or quantities. Below are some of the most important laws:

Laws of Addition
1. *Comutative Law*: The sum of two numbers is independent of the order in which they are added.
a + b = b + a

2. *Associative Law*: The sum of three numbers is independent of the order in which they are added.
(a + b) + c = a + (b + c)

3. *Law of Identity*: The sum of a number and zero is equal to the number itself.
a + 0 = a

4. *Law of Inverse*: The sum of a number and its inverse is equal to zero.
a + (-a) = 0

5. *Law of Monotony*: If two quantities that vary monotonically in the same direction are added, the sum will also vary monotonically in that direction.

Applications
The Laws of Addition apply in various areas, such as:

1. Arithmetic and algebra
2. Mathematical analysis
3. Statistics and probability
4. Physics and engineering
5. Economy and finance

Examples
1. 2 + 3 = 3 + 2 (Commutative Law)
2. (2 + 3) + 4 = 2 + (3 + 4) (Associative Law)
3. 5 + 0 = 5 (Law of Identity)
4. 5 + (-5) = 0 (Inverse Law)