Properties of Real Numbers

Properties of Real Numbers

There are four main properties which include commutative property, associative property, distributive property, and identity property. Consider “m, n and r” are the real numbers. Then based on these properties, we can define the numbers as;

Commutative Property

If we 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 we 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 in the form of :

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. (zero is additive identity)
• For multiplication: a × 1 = 1 × a = a. (1 is multiplicative identity)