Algebraic Properties: The Rules of Algebra Be Cool - Follow The Rules!

Commutative Property of Addition a + b = b + a Number Examples: = 4 + 3, 7=7 (-2) + 7 = 7 + (-2), 5=5 THIS PROPERTY DOES NOT APPLY TO SUBTRACTION!

Commutative Property of Multiplication a*b = b*a or ab = ba Number Examples: (3)(5) = (5)(3) 15=15 (-9)(7) = (7)(-9) (-63) = (-63) THIS PROPERTY DOES NOT APPLY FOR DIVISION!

Associative Property of Addition (a + b) + c = a + (b + c) Number Examples: (6 + 7) + 8 = 6 + (7 + 8) = = 21

Associative Property of Multiplication a(bc) = (ab)c Number Examples: 4 [(5)(6)] = [(4)(5)] 6 4 (30) = 20 (6) 120 = 120

Distributive Property a(b + c) = ab + ac OR a(b - c) = ab - ac Number Examples: 3(4 + 5) = 3(4) + 3(5) = = 27, or 3(9) = 27 7(8 - 3) = 7(8) - 7(3) = = 35, or 7(5) = 35

Distributive Property (factoring) ab+ac=a(b+c) OR ab-ac=a(b-c) Number Examples: 6x + 12 = 6(x+2); 15x +20= 5(3x +4)

Additive Identity Property (Adding Zero does not change a number's identity!) a + 0 = a Number Examples: = 4 (-9) + 0 = (-9)

Multiplicative Identity Property (Multiplying by 1 does not change a number's identity!) a * 1 = a Number Examples: 4 * 1 = 4 (-12) * 1 = (-12)

Additive Inverse Property a + (-a) = 0 Number Examples: 8 + (-8) = 0 (-11) + 11 = 0

Multiplicative Inverse Property a * (1/a) = 1 Number Examples: 7 * (1/7) = 1 (1/3) * 3 = 1 (-8) * (1/-8) = 1

Transitive Property If a=b and b=c, then a=c Number Examples: If 8= 10-2 and 7+1=8 then 10-2=7+1

Other Properties 1. Addition Property of Zero A+0=a 2. Multiplication Property of Zero: Ax0=0 3. Property of Equality (what you do to one side must be done to the other) 4. Symmetric Property: a=b, b=a