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Properties 6.19 Identify properties for addition and multiplication Multiplicative property of zero Inverse property for multiplication

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COMMUTATIVE PROPERTY

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C o mmutative Property a + b = b + a (a)(b) = (b)(a) O rder doesn’t matter

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C o mmutative Property O rder doesn’t matter 2 + 3 = 3 + 2 14 + 5 = 5 + 14 2(4) = 4(2) 2 x 27 = 27 x 2

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Does the Commutative Property work with Subtraction? 5 – 3 – 1 2 – 1 1 3 – 1 – 5 2 – 5 - 3 ≠

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Does the Commutative Property work with Division? 4 ÷ 2 ÷ 2 2 ÷ 2 1 2 ÷ 2 ÷ 4 1 ÷ 4 1/4 ≠

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Check for understanding…. Name the property: a.5 + 6 + 7 = 6 + 5 + 7 C o mmutative Property of Addition Name the property: b. 3(2)(5) = 5(3)(2) C o mmutative Property of Multiplication

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ASSOCIATIVE PROPERTY

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Try: (1 + 3) + 14 4 + 14 18 Now Try: 1 + (3 + 14) 1+1+ 17 18 =

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When you are multiplying, change the grouping. See what happens. You will get the same answer. Try: (2 x 3) x 4 6 x 4 24 Now Try: 2 x( 3 x 4) 2 x 12 24 =

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Does the Associative Property work with Subtraction? (14 – 3) – 2 11 - 2 9 14 – (3 – 2) 14 - 1 13 ≠

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Does the Associative Property work with Division? ≠

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Check for understanding….. 3 + (5 + 19) = (3+ 5) + 19 Associative Property of Addition (2 x 4) x 16 = 2 x (4 x 16) Associative Property of Multiplication 10 + 11 + 12 = 11 + 10 + 12 Commutative Property of Addition 20 x 14 x 8 = 14 x 8 x 20 Commutative Property of Multiplication

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ADDITIVE IDENTITY PROPERTY

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5 + 0 = 5 4 + 0 = 4 30 + 0 = 30 0.5 + 0 = ____ 0.5 If you add zero to any number, the number keeps its identity – It stays the same!

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MULTIPLICATIVE IDENTITY PROPERTY

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15 x 1 = 15 34 x 1 = 34 9 x 1 = 9 101 x 1 = 101 If you multiply a number by 1, the number keeps its identity --- It stays the SAME!

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Check for understanding…. What integer is the multiplicative identity? 1 What integer is the additive identity? 0

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MULTIPLICATIVE INVERSE PROPERTY

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Zero does NOT have a multiplicative inverse because you can NEVER have zero in the denominator of a fraction!

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Do all real numbers have a multiplicative inverse? NO, Zero does NOT have a multiplicative inverse because you can NEVER have zero in the denominator of a fraction!

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MULTIPLICATIVE PROPERTY OF ZERO

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The product of any number and zero is zero! a x 0 = 0 5 x 0 = 0

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