Multiplication Properties of Real Number

Multiplication Properties of Real Number



1) Closure Property of Multiplication

a × b is a real number

If you multiply two real numbers, the product is also a real number.

Example: 6 × 5 = 30  where 30 (the product of 6 and 7) is a real number.

2) Commutative Property of Multiplication

              a × b = b × a 
if you multiply two real numbers in order,the product will always be the same or equal.

 Example: 3 × 4 = 4 × 3 = 12


3)Associative Property of Multiplication
                     
                        (a × b) × c = a × (b × c)

 If you are multiplying three real numbers, the product is always the same regardless of their grouping.

 Example: (5 × 2) × 4 = 5 × (2 × 4) = 40
4) Multiplicative Identity Property of Multiplication
                           a × 1 = a
If you multiply a real number to one (1), you will get the original number itself
Example: 52 × 1 = 52  or  1 × 52 = 52
5) Multiplicative Inverse Property
              a × (1/a) = 1  but  a ≠ 0
If you multiply a nonzero real number by its inverse or reciprocal, the product will always be one (1)
Example:  4 × (1/4) = 1

The Property of Multiplication together with Addition

6) Distributive Property of Multiplication over Addition
Suppose a, b, and c represent real numbers.

 a(b + c) = ab + ac or (a+b)c = ac + bc 

 The operation of multiplication distributes over addition operation

 Example: 4 (5 + 8) = 4 × 5 + 4 × 8 or (5 + 8) 4 = 5 × 4 + 8 × 4







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