Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative...
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Transcript of Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative...
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Properties of Real NumbersObjective: To apply the properties of operations.Commutative PropertiesAssociative PropertiesIdentity Properties Inverse Properties Distributive Property
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On Tab 2: Commutative PropertiesChanging the order of the numbers in addition or multiplication will not change the result.
Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a
Commutative Property of Multiplication states: 4 5 = 5 4 or a b = b a.
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On Tab 3: Associative PropertiesChanging the grouping of the numbers in addition or multiplication will not change the result.
Associative Property of Addition states: 3 + (4 + 5) = (3 + 4)+ 5 or a + (b + c) = (a + b)+ c
Associative Property of Multiplication states: (2 3) 4 = 2 (3 4) or (a b) c = a (b c)
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On Tab 4: Identity PropertiesAdding zero to a number does not change its value.2 + 0 = 2 & 0 + 2 = 2a + 0 = a & 0 + a = aMultiplying a number by 1 does not change the value of the number.5 1 = 5 & 1 5 = 5 a 1 = a & 1 a = aAdditionMultiplication
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On Tab 5: Inverse PropertiesOpposites add to zero. 3 + -3 = 0 a + (-a) = 0A number multiplied by its reciprocal is always 1. AdditionMultiplication
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On Tab 6: Distributive Property Multiplication distributes over addition & subtraction.
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Lets play Name that property!
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State the property or properties that justify the following.3 + 2 = 2 + 3Commutative Property
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State the property or properties that justify the following.10(1/10) = 1Inverse Property of Multiplication
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State the property or properties that justify the following.3(x 10) = 3x 30 Distributive Property
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State the property or properties that justify the following.3 + (4 + 5) = (3 + 4) + 5 Associative Property
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State the property or properties that justify the following.(5 + 2) + 9 = (2 + 5) + 9 Commutative Property
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(2 + 1) + 4 = 2 + (1 + 4)Associative Property of Addition1.
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3 + 7 = 7 + 3Commutative Property of Addition2.
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8 + 0 = 8Identity Property of Addition3.
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6 4 = 4 6Commutative Property of Multiplication5.
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17 + (-17) = 0Inverse Property of Addition6.
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2(5) = 5(2)Commutative Property of Multiplication7.
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even + even = evenClosure Property8.
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3(2 + 5) = 32 + 35Distributive Property9.
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6(78) = (67)8Associative Property of Multiplication10.
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5 1 = 5Identity Property of Multiplication11.
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6(3 2n) = 18 12nDistributive Property12.
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2x + 3 = 3 + 2xCommutative Property of Addition13.
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ab = baCommutative Property of Multiplication14.
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a + 0 = aIdentity Property of Addition15.
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a(bc) = (ab)cAssociative Property of Multiplication16.
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a1 = aIdentity Property of Multiplication17.
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a +b = b + aCommutative Property of Addition18.
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a(b + c) = ab + acDistributive Property19.
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a + (b + c) = (a +b) + cAssociative Property of Addition20.
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a + (-a) = 0Inverse Property of Addition21.
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Properties of Real NumbersObjective: To apply the properties of operations.Commutative PropertiesAssociative PropertiesIdentity Properties Inverse Properties Distributive Property