Properties

Commutative Property Think ….Order The order of the numbers doesn’t change the result (answer to the problem) a + b = b + a 6 + 2 = 2 + 6 p X q = q X p 6 x 2 = 2 x 6

Associative Property Think “Grouping” The grouping doesn’t change the answer. (p+q) + r = p + ( q + r) (2 + 3) + 4 = 2 + (3 + 4) (p X q) X r = p X (q X r) (5 x 6) x 7 = 5 x (6 x 7)

Identity Property of Multiplication Any number multiplied by 1 will give you the original number. 23,487 X 1 = 23,487 a x 1 = a

Identity Property of Addition Any number added to 0 will give you the original number. 23,487 + 0 = 23,487 a + 0 = a

Zero Property of Multiplication When any number is multiplied with zero, the answer is zero. 98,756,432 X 0 = 0

Distributive Property Multiplying the sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the product. 9 X (20 - 3) = (9 X 20) – (9 X 3) 8 X (40 + 5) = (8 X 40) + (8 X 5) 8 X 45 = (8 X 40) + (8 X 5)

Distributive Property Examples 4 X 509 = (4 X 500) + (4 X m) 6 (5 + 8)= (6 X n) + (6 X 8) s (4 + 9)= (5 X 4) + (5 X 9)

Inverse Property of Addition The sum of any integer and its additive inverse is 0. a + (-a) = 0 3+ (-3) = 0

Multiplicative Inverse Property The product of a nonzero number and its reciprocal, or multiplicative inverse, is 1. NUMBERS ALGEBRA

Properties of Equality Reflexive Property a + b = a + b The same expression is written on both sides of the equal sign.

Properties of Equality Symmetric Property If a = b then b = a If 4 + 5 = 9 then 9 = 4 + 5

Properties of Equality Transitive Property If a = b and b = c then a = c If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5

Substitution Property If a = b, then a can be replaced by b. a(3 + 2) = a(5)

Name the property Distributive Substitution Reflexive Symmetric 5(4 + 6) = 20 + 30 5(4 + 6) = 5(10) 5(4 + 6) = 5(4 + 6) If 5(4 + 6) = 5(10) then 5(10) = 5(4 + 6) 5(4 + 6) = 5(6 + 4) If 5(10) = 5(4 + 6) and 5(4 + 6) = 20 + 30 then 5(10) = 20 + 30 Distributive Substitution Reflexive Symmetric Commutative Transitive