Number Properties

Commutative Property of Addition
a + b = b + a

Example: 3 + 2 = 2 + 3

Let, LHS, 3 + 2 = 5

RHS, 2 + 3 = 5

Therefore, LHS = RHS.

Commutative Property of Multiplication
a • b = b • a

Example: 2 x 3 = 3 x 2

Let, LHS, 3 x 2 = 6

RHS, 2 x 3 = 6

Therefore, LHS = RHS.

Associative Property of Addition 
a + ( b + c ) = ( a + b ) + c 

Example: 2 + (3 + 4) = (2 + 3) + 4

Let, LHS, 2 + (3 + 4) = 2 + (7) = 9

RHS, (2 + 3) + 4 = 5 + 4 = 9

Therefore, LHS = RHS.

Associative Property of Multiplication 
a • ( b • c ) = ( a • b ) • c

Example: 2 x (3 x 4) = (2 x 3) x 4

Let, LHS, 2 x (3 x 4) = 2 x (12) = 24

RHS, (2 x 3) x 4 = 6 x 4 = 24

Therefore, LHS = RHS.

Distributive Property
a • ( b + c ) = a • b + a • c

Example: 2 x (3 + 4) = (2 x 3) + (2 x 4)

LHS, 2 x (3 + 4) = 2 x (7) = 14

RHS, (2 x 3) + (2 x 4) = 6 + 8 = 14

Therefore, LHS = RHS.

Additive Identity Property
a + 0 = a

Example: 2 + 0 = 2

LHS = 2 + 0 = 2 = RHS

Multiplicative Identity Property 
a •  1 = a

Example: 2 x 1 = 2

LHS = 2 x 1 = 2 = RHS

Additive Inverse Property 
a + ( -a ) = 0

Example: 2 + (-2) = 0

LHS = 2 + (-2) = 2 – 2 = 0 = RHS

Multiplicative Inverse Property 
a x a-1 = 1

Note: a cannot = 0

Example: 2 x 2-1 = 1

LHS = 2 x 1/2 = 1 = RHS

Zero Property
a • 0 = 0

Example: 2 x 0 = 0

LHS = 2 x 0 = 0 = RHS

Advertisements

One thought on “Number Properties

  1. Pingback: Tips & Tricks – Breath Math

Comments are closed.