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Properties. Properties. A property is something that is true for all situations. Six Properties of Addition and Multiplication. Distributive Commutative Associative Identity Inverse Multiplicative Property of Zero. Distributive Property. A(B + C) = AB + AC 4(3 + 5) = 4 • 3 + 4 • 5.
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Properties • A property is something that is true for all situations.
Six PropertiesofAddition and Multiplication • Distributive • Commutative • Associative • Identity • Inverse • Multiplicative Property of Zero
Distributive Property • A(B + C) = AB + AC 4(3 + 5) = 4 • 3 + 4 • 5
Commutative Propertyof addition and multiplication Order doesn’t matter A • B = B • A A + B = B + A CO = Change Order
Associative Property of multiplication and Addition • Addition (a + b) + c = a + (b + c) Example: (6 + 4) + 3 = 6 + (4 + 3) • Multiplication (a · b) · c = a · (b · c) Example: (6 · 4) · 3 = 6 · (4 · 3) SO = Same Order
Identity Properties • If you add 0 to any number, the number stays the same. A + 0 = A or 5 + 0 = 5 If you multiply any number times 1, the number stays the same. A • 1 = A or 5 • 1 = 5
Inverse Properties • Addition: a + -a = 0 or 5 + -5=0 • Multiplication: a • 1 = 1 or 5 • 1 = 1 a 5
Multiplicative Property of Zero • Any number times zero will give you the product of 0 (zero) a • 0 = 0 4 • 0 = 0 or 0 • 4=0
Which Property? (2 + 1) + 4 = 2 +(1 + 4) Associative Property of Addition
Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition
Which Property? 8 + 0 = 8 Identity Property of Addition
Which Property? 6 • 4 = 4 • 6 Commutative Property of Multiplication
Which Property? 17 + (-17) = 0 Inverse Property of Addition
Which Property? 2(5) = 5(2) Commutative Property of Multiplication
Which Property? 3(2 + 5) = 3•2 + 3•5 Distributive Property
Which Property? 6(7•8) = (6•7)8 Associative Property of Multiplication
Which Property? 5 • 1 = 5 Identity Property of Multiplication
Which Property? (6 – 3)4 = 6•4 – 3•4 Distributive Property
Which Property? 1(-9) = -9 Identity Property of Multiplication
Which Property? 3 + (-3) = 0 Inverse Property of Addition
Which Property? 1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition
Which Property? -3(6) = 6(-3) Commutative Property of Multiplication
Which Property? -8 + 0 = -8 Identity Property of Addition
Which Property? 3•7 – 3•4 = 3(7 – 4) Distributive Property
Which Property? 6 + [(3 + (-2)] = (6 + 3) +(- 2) Associative Property of Addition
Which Property? 7 + (-5) = -5 + 7 Commutative Property of Addition
Which Property? (5 + 4)9 = 45 + 36 Distributive Property
Which Property? -3(5 • 4) = (-3 • 5)4 Associative Property of Multiplication
Which Property? -8(4) = 4(-8) Commutative Property of Multiplication
Which Property? ab = ba Commutative Property of Multiplication
Which Property? a + 0 = a Identity Property of Addition
Which Property? a(bc) = (ab)c Associative Property of Multiplication
Which Property? a•1 = a Identity Property of Multiplication
Which Property? a +b = b + a Commutative Property of Addition
Which Property? a(b + c) = ab + ac Distributive Property
Which Property? a +(b + c) = (a +b)+ c Associative Property of Addition
Which Property? a + (-a) = 0 Inverse Property of Addition