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Properties of Real Numbers (Section 2.6) 6 Properties: • Commutative Property • Associative Property • Distributive Property • Identity • Inverse • Zero Commutative Property We commute when we go back and forth from work to home. Algebra terms commute when they trade places xy y x This is a statement of 1) commutative property for addition: x y y x This is the statement for 2) Communtative of Multiplication: xy yx To associate with someone means that we like to be with them. The tiger and the panther are associating with each other. They are leaving the lion out. ( ) ( x y) z The panther has decided to befriend the lion. The tiger is left out. ( ) In algebra: x (y z ) This is a statement of the 3) Associative Property of Addition: ( x y) z x ( y z ) This is the statement for 4) Associative Property of multiplication: ( xy)z x( yz ) Sometimes executives ask for help in distributing papers. We add here: 4(2x+3) We multiply here: This is an example of 5) Distributive 4(2x+3) =8x+12 4 2x +3 8x 12 The Identity Property makes me think about my identity. 1) Identity property for addition asks, “What can I add to myself to get myself back again? 0x x_ 0x x_ The above is the identity property for addition. 0 is the identity element for addition. 7) Identity property for Multiplication asks, “What can I multiply to myself to get myself back again? 1 x x(_) 1 x x(_) The above is the identity property for multiplication. 1 is the identity element for multiplication. 8) Additive property of Inverse asks, “What do you add to a number to get zero?” X + (-X)= 0 9) Multiplicative property for Inverse is, a number which when multiplied by X yields 1. -The reciprocal X + 1/X = 1 10) Multiplicative Property of Zero The product of any number and zero is zero. a x 0= 0