Section 1.5 Properties of Real Numbers

Properties of Real NumbersList of Properties of Real NumbersCommutativeAssociativeDistributiveIdentity InverseCommutative PropertiesDefinition: Changing the order of the numbers in addition or multiplication will not change the result.

Commutative PropertiesPropertyNumbersAlgebraAddition2 + 3 = 3 + 2 a + b = b + aMultiplication4 5 = 5 4 ab = baAssociative PropertiesDefinition: Changing the grouping of the numbers in addition or multiplication will not change the result.

Associative PropertiesPropertyNumbersAlgebraAddition3 + (4 + 5)= (3 + 4)+ 5a + (b + c)= (a + b)+ c Multiplication(2 3) 4 = 2 (3 4)(ab)c = a(bc)

Distributive Property Multiplication distributes over addition.

Additive Identity PropertyDefinition: Zero preserves identities under addition. In other words, adding zero to a number does not change its value.

Example: a + 0 = a and 0 + a = aMultiplicative Identity PropertyDefinition: The number 1 preserves identities under multiplication. In other words, multiplying a number by 1 does not change the value of the number.Example: a 1 = a and 1 a = aAdditive Inverse PropertyDefinition: For each real number a there exists a unique real number a such that their sum is zero. In other words, opposites add to zero.Example:a + (-a) = 0

Multiplicative Inverse Property

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 Property22.38Which Property?-3(5 4) = (-3 5)4Associative Property of Multiplication23.39Which 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 Addition26.43Which 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 Addition29.46Which Property?[(-2/3)(5)]9 = -2/3[(5)(9)]Associative Property of Multiplication30.47

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 +