Properties of Real Numbers Rules
Catagory | Definition | Example |
Natural Numbers | Contain all counting numbers which start from 1. N = {1, 2, 3, 4,……} | All numbers such as 1, 2, 3, 4, 5, 6,…..… |
Whole Numbers | Collection of zero and natural numbers. W = {0, 1, 2, 3,…..} | All numbers including 0 such as 0, 1, 2, 3, 4, 5, 6,…..… |
Integers | The collective result of whole numbers and negative of all natural numbers. | Includes: -infinity (-∞),……..-4, -3, -2, -1, 0, 1, 2, 3, 4, ……+infinity (+∞) |
Rational Numbers | Numbers that can be written in the form of p/q, where q≠0. | Examples of rational numbers are ½, 5/4 and 12/6 etc. |
Irrational Numbers | The numbers which are not rational and cannot be written in the form of p/q. | Irrational numbers are non-terminating and non-repeating in nature like √2. |
Commutative Property
If m and n are the numbers, then the general form will be m + n = n + m for addition and m.n = n.m for multiplication.
Addition: m + n = n + m. For example, 5 + 3 = 3 + 5, 2 + 4 = 4 + 2.
Multiplication: m × n = n × m. For example, 5 × 3 = 3 × 5, 2 × 4 = 4 × 2.
Associative Property
If m, n and r are the numbers. The general form will be m + (n + r) = (m + n) + r for addition(mn) r = m (nr) for multiplication.
Addition: The general form will be m + (n + r) = (m + n) + r. An example of additive associative property is 10 + (3 + 2) = (10 + 3) + 2.
Multiplication: (mn) r = m (nr). An example of a multiplicative associative property is (2 × 3) 4 = 2 (3 × 4).
Distributive Property
For three numbers m, n, and r, which are real in nature, the distributive property is represented as:
m (n + r) = mn + mr and (m + n) r = mr + nr.
Example of distributive property is: 5(2 + 3) = 5 × 2 + 5 × 3. Here, both sides will yield 25.
Identity Property
There are additive and multiplicative identities.
For addition: m + 0 = m. (0 is the additive identity)
For multiplication: m × 1 = 1 × m = m. (1 is the multiplicative identity)