Properties
1. Associative Property - The parentheses move and the members stay where they are.
a + (b + c) = (a + b) + c (2 + 5) + 8 = 2 + (5 + 8)
2. Commutative Property - The members move on one side of the equation.
2 + 6 + 8 = 6 + 8 + 2 (9 + 3) + 5 = (3 + 9) +5
3. Distributive Property - I call this the "Halloween Property." When trick or treating one person stands at the door and distributes goodies to the children.
a(b + c) = ab + ac 3(2 + 5) = 3x2 + 3x5 = 6 + 15 = 21
4. Identity Property - What do you add to any number to keep it itself? What do you multiply to any number to keep it itself?
7 + 0 = 7 7x1 = 7
5. Inverse Property - To every number there is an "opposite" that will create a total of 0 or a product of 1.
6 + (-6) = 0 -x + x = 0 2/3 x 3/2 = 1 -5 x -1/5 = 1
6. Reflex Property - Everything equals itself.
a = a -10 = -10
7. Transverse Property - If a = b and b = c, then a = c.
8. Multiplicative Property of 0 = Anything times 0 is 0.
9 x 0 = 0 y x 0 = 0
9. Multiplicative Property of -1 = Anything times -1 is its inverse.
8 x (-1) = -8 (-y) x (-1) = y
10. Symmetric Property - Anything in a mirror image equals itself.
ab = ba 2(3) = (3)2
