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Properties of Real Numbers 1. Objective: To apply the properties of operations. 2. Commutative Properties 3. Associative Properties 4. Identity Properties 5. Inverse Properties 6. Distributive Property On Tab 2: Commutative Properties Changing 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. On Tab 3: Associative Properties Changing 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) On Tab 4: Identity Properties Adding zero to a number does not change its value. 2+0=2 a+0=a & & 0+2=2 0+a=a Multiplying a number by 1 does not change the value of the number. 5∙1=5 a∙1=a & 1∙ 5=5 & 1∙a=a On Tab 5: Inverse Properties Opposites add to zero. 3 + -3 = 0 a + (-a) = 0 A number multiplied by its reciprocal is always 1. 1 6 1 6 6 1 6 2 6 6 1 a 1 1a a 1 a 1 a 1a On Tab 6: Distributive Property Multiplication distributes over addition & subtraction. 32 5 3 2 3 5 ab c a b a c Let’s play “Name that property!” State the property or properties that justify the following. 3+2=2+3 Commutative Property State the property or properties that justify the following. 10(1/10) = 1 Inverse Property of Multiplication State the property or properties that justify the following. 3(x – 10) = 3x – 30 Distributive Property State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property 2. 3+7=7+3 Commutative Property of Addition 3. 8+0=8 Identity Property of Addition 5. 6•4=4•6 Commutative Property of Multiplication 11. 5•1=5 Identity Property of Multiplication 21. a + (-a) = 0 Inverse Property of Addition Properties of Real Numbers 1. Objective: To apply the properties of operations. 2. Commutative Properties 3. Associative Properties 4. Identity Properties 5. Inverse Properties 6. Distributive Property