Section 1.5 Properties of Real Numbers

Properties of Real NumbersCommutativeAssociativeIdentity + Inverse + Zero PropertyReflexive Distributive

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 ab = ba.Verbal Hints for Commutative PropertyCommuteSwitch PlacesMove to a new locationAssociative 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 (ab)c = a(bc)

Verbal Hints for Associative PropertyRegroupThey simply group with a new friend( ) change places but numbers stay the sameAdditive Identity PropertyThere exists a unique number 0 such that zero preserves identities under addition.a + 0 = a and 0 + a = aIn other words adding zero to a number does not change its value.Multiplicative Identity PropertyThere exists a unique number 1 such that the number 1 preserves identities under multiplication.a 1 = a and 1 a = aIn other words multiplying a number by 1 does not change the value of the number.Verbal Hints for Identity PropertyThe value that returns the input unchangedRemember I in the word identity Additive Inverse PropertyFor each real number a there exists a unique real number a such that their sum is zero. a + (-a) = 0In other words opposites add to zero.Verbal Hints for Additive InverseOpposite numbersSame number but different signZero Pairs

Multiplicative Inverse PropertyFor each real number a there exists a unique real number such that their product is 1.

Verbal Hints for Multiplicative InverseFlip the numberReciprocal Zero Property of MultiplicationAny number multiplied by 0 is equal to 0

A 0 = 0

-23 0 = 0

0 = 0

0.25 0 = 0

zero times any value is 0Reflexive PropertyA number is always equal to itself

A = A-2 = -25 = 5A real number is always equal to itselfDistributive Property Multiplication distributes over addition.

Verbal Hints for Distributive PropertyMultiplication distributes across addition or subtraction.Multiply across the parentheses!!!!!

Lets play Name that property!

State the property or properties that justify the following.3 + 2 = 2 + 3Commutative Property

State the property or properties that justify the following.10(1/10) = 1Multiplicative Inverse Property

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

Which Property?3 + 7 = 7 + 3Commutative Property of Addition2.Which Property?8 + 0 = 8Identity Property of Addition3.Which Property?6 4 = 4 6Commutative Property of Multiplication5.Which Property?17 + (-17) = 0Inverse Property of Addition6.Which Property?2(5) = 5(2)Commutative Property of Multiplication7.Which Property?(2 + 1) + 4 = 2 + (1 + 4)Associative Property of Addition1.Which Property?even + even = evenClosure Property8.Which Property?3(2 + 5) = 32 + 35Distributive Property9.Which Property?6(78) = (67)8Associative Property of Multiplication10.Which Property?5 1 = 5Identity Property of Multiplication11.

Properties Using NegativesWhich Property?(6 3)4 = 64 34Distributive Property13.Which Property?1(-9) = -9Identity Property of Multiplication14.Which Property?3 + (-3) = 0Inverse Property of Addition15.Which Property? 1 + [-9 + 3] = [1 + (-9)] + 3Associative Property of Addition16.Which Property?-3(6) = 6(-3)Commutative Property of Multiplication17.Which Property?-8 + 0 = -8Identity Property of Addition18.Which Property?37 34 = 3(7 4) Distributive Property19.Which Property? 6 + [(3 + (-2)] = (6 + 3) + (- 2)Associative Property of Addition20.Which Property?7 + (-5) = -5 + 7Commutative Property of Addition21.Which Property?(5 + 4)9 = 45 + 36Distributive Property22.43Which Property?-3(5 4) = (-3 5)4Associative Property of Multiplication23.44Which Property?-8(4) = 4(-8)Commutative Property of Multiplication24.

Properties Using FractionsWhich Property?51/7 + 0 = 51/7Identity Property of Addition25.Which Property?3/4 6/7 = 6/7 + 3/4 Commutative Property of Addition26.48Which Property?12/5 1 = 12/5Identity Property of Multiplication27.Which Property? (fraction)(fraction) = fractionClosure Property28.Which Property?-8 2/5 + 0 = -8 2/5Identity Property of Addition29.51Which Property?[(-2/3)(5)]9 = -2/3[(5)(9)]Associative Property of Multiplication30.52

Properties Using VariablesWhich Property?6(3 2n) = 18 12nDistributive Property31.Which Property?2x + 3 = 3 + 2xCommutative Property of Addition32.Which Property?ab = baCommutative Property of Multiplication33.Which Property?a + 0 = aIdentity Property of Addition34.Which Property?a(bc) = (ab)cAssociative Property of Multiplication35.Which Property?a1 = aIdentity Property of Multiplication36.Which Property?a +b = b + aCommutative Property of Addition37.Which Property?a(b + c) = ab + acDistributive Property38.Which Property?a + (b + c) = (a +b) + cAssociative Property of Addition39.Which Property?a + (-a) = 0Inverse Property of Addition40.Properties of Real NumbersCommutativeAssociativeDistributiveIdentity + Inverse +