Mathematics Handbook/Multiplication

Properties

Commutative property

Addition

 a + b = b + a
 a + b + c = a + c + b 
           = b + a + c 
           = b + c + a 
           = c + a + b 
           = c + b + a 

To add two, three or more numbers the order of their arrangement in the sum does no matter.

Example:

              2 + 3 + 5 = 2 + 5 + 3   
                        = 3 + 2 + 5
                        = 3 + 5 + 2
                        = 5 + 2 + 3
                        = 5 + 3 + 2
                        = 10

Multiplication

 a x b = b x a 
 a x b x c = a x c x b 
           = b x a x c 
           = b x c x a 
           = c x a x b 
           = c x b x a 

To multiply two, three or more numbers the order of their arrangement in the product does no matter.

Example:

              2 x 3 x 5 = 2 x 5 x 3   
                        = 3 x 2 x 5
                        = 3 x 5 x 2
                        = 5 x 2 x 3
                        = 5 x 3 x 2
                        = 30 

Associative property:

1. (a x b) x c = a x (b x c)

To multiply a x b x c; it does not matter whether to first associate a and b, then associate the result with c or to first associate b and c, then associate the result with a associate

Distributive property

1. a(b + c) = ab + ac → a is distributed over b and c

 (a + b)(c + d) = a(c + d) + b(c + d) 
 (a + b)(c - d) = a(c - d) + b(c - d)
 (a - b)(c + d) = a(c + d) - b(c + d)

Rules

1. a x 0 = 0
2. a x 1 = a
3. a x a = a²
4. a x -a = -a²