Properties of Operations and Identities

• Commutative Property of Addition
• a + b = b + a
• Example:
• a + b = b + a
• a = 7
• b = 5
• (7) + (5) = (5) + (7)
• 12 = 12
• Commutative Property of Multiplication
• ab = ba
• Example:
• ab = ba
• a = 9
• b = 6
• 9 · 6 = 6 · 9
• 54 = 54
• Associative Property of Addition
• (a + b) + c = a + (b + c)
• Example:
• (a + b) + c = a + (b + c)
• a = 4
• b = 1
• c = 2
• (4 + 1) + 2 = 4 + (1 + 2)
• (5) + 2 = 4 + (3)
• 7 = 7
• Associative Property of Multiplication
• (ab)c = a(bc)
• Example:
• a = 9
• b = 8
• c = 5
• (9 · 8) · 5 = 9 · (8 · 5)
• (72) · 5 = 9 · (40)
• 360 = 360
• Distributive Property of Multiplication Over Addition
• a (b + c) = ab + ac
• Example:
• a (b + c) = ab + ac
• a = 12
• b = 7
• c = 5
• 12 · (7 + 5) = (12 · 7) + (12 · 5)
• 12 · (12) = (84) · (60)
• 144 = 144
• Additive Identity Property
• a + 0 = 0 + a = a
• Example:
• a + 0 = 0 + a = a
• a = 5
• (5) + 0 = 0 + (5) = 5
• 5 = 5 = 5
• Multiplicative Identity Property
• 1(a) = a(1) = a
• Example:
• 1(a) = a(1) = a
• a = 3
• 1(3) = 3(1) = 3
• 3 = 3 = 3
• Quotient Property
• a (1/b) = a/b
• Example:
• a (1/b) = a/b
• a = 1
• b = 2
• 1 (1/2) = 1/2
• ½ = ½
• Multiplicative Inverse Property
• a (1/a) = 1
• Example:
• a (1/a) = 1
• a = 3
• 3 (1/3) = 1
• 1 = 1
• Multiplication Property of Zero
• 0(a) = a(0) = 0
• Example:
• 0(a) = a(0) = 0
• a = 1
• 0(1) = 1(0) = 0
• 0 = 0 = 0