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# Properties of real_numbers

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### Properties of real_numbers

1. 1. Properties of Real NumbersProperties of Real Numbers CommutativeCommutative AssociativeAssociative DistributiveDistributive Identity +Identity + ×× Inverse +Inverse + ××
2. 2. Commutative PropertiesCommutative Properties Changing theChanging the orderorder of the numbers inof the numbers in addition or multiplication will notaddition or multiplication will not change the result.change the result. Commutative Property of AdditionCommutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a.states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property ofCommutative Property of MultiplicationMultiplication states: 4states: 4 • 5 = 5 • 4 or• 5 = 5 • 4 or abab == ba.ba.
3. 3. Associative PropertiesAssociative Properties Changing theChanging the groupinggrouping of theof the numbers in addition or multiplicationnumbers in addition or multiplication will not change the result.will not change the result. Associative Property of AdditionAssociative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 orstates: 3 + (4 + 5)= (3 + 4)+ 5 or aa + (+ (bb ++ cc)= ()= (aa ++ bb)+)+ cc Associative Property of MultiplicationAssociative Property of Multiplication states: (2states: (2 • 3) • 4 = 2 • (3 • 4) or• 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)(ab)c = a(bc)
4. 4. Additive Identity PropertyAdditive Identity Property There exists a unique number 0 suchThere exists a unique number 0 such that zero preserves identities underthat zero preserves identities under addition.addition. aa + 0 =+ 0 = aa and 0 +and 0 + a = aa = a In other words adding zero to aIn other words adding zero to a number does not change its value.number does not change its value.
5. 5. Distributive PropertyDistributive Property MultiplicationMultiplication distributesdistributes over additionover addition.. ( ) acabcba +=+ ( ) 5323523 ⋅+⋅=+
6. 6. Multiplicative Identity PropertyMultiplicative Identity Property There exists a unique number 1 suchThere exists a unique number 1 such that the number 1 preserves identitiesthat the number 1 preserves identities under multiplication.under multiplication. aa ∙ 1∙ 1 == aa and 1and 1 ∙∙ a = aa = a In other words multiplying a numberIn other words multiplying a number by 1 does not change the value of theby 1 does not change the value of the number.number.
7. 7. Additive Inverse PropertyAdditive Inverse Property For each real numberFor each real number aa therethere exists a unique real number –exists a unique real number –aa such that their sum is zero.such that their sum is zero. aa + (-+ (-aa) = 0) = 0 In other words opposites add toIn other words opposites add to zero.zero.
8. 8. Multiplicative Inverse PropertyMultiplicative Inverse Property For each real numberFor each real number aa there exists athere exists a unique real number such that theirunique real number such that their product is 1.product is 1. 1 a 1 1 =⋅ a a
9. 9. Let’s play “Name that property!”
10. 10. Let’s play “Name that property!”