Name: __________________________________________________________________ Period: _____ Unit 5: Properties of the Real Number System PROPERTY What is it? COMMUTATIVE Change Order: changing the order of multiplication or addition problem does not change the answer. ASSOCIATIVE Multiplication and addition problems can be regrouped with parentheses. Grouping does not change the answer. IDENTITY (Answer is always the same as what you started with) INVERSE (Answer is always the Identity) DISTRIBUTIVE Additive Identity: The number that adds on to give you the same number you started with as an answer. Answer is the same as what you started with. Multiplicative Identity: The number that you multiply by to give you the same number you started with as an answer. Answer will always be the same as what you started with. Additive Inverse: What you will add on so the answer is the Identity, always has opposite sign. Multiplicative Inverse: What you will multiply by so the answer is the Identity, always the reciprocal. To remove parentheses by multiplying the outside number through the parentheses, or to put parentheses in by dividing out a GCF. 1 Examples/Information Additive Identity is ALWAYS: Multiplicative Identity is ALWAYS: _____ 1) The equation x + 4 = 4 + x is an illustration of the (1) associative property (2) distributive property (3) commutative property (4) additive inverse _____ 2) Which statement illustrates the associative property? 1 (1) 2 = 1 2 (2) 2(3 + 4) = 2(3) + 2(4) (3) 2(1) = 2 (4) 2(3 • 4) = (2 • 3)4 _____ 3) The equation 6(x + y) = 6x + 6y is an example of the (1) associative property (2) additive inverse (3) commutative property (4) distributive property _____ 4) The additive inverse of -3 is (1) 1 3 1 3 (4) 0 (3) (2) 3 _____ 5) If n represents an even integer, the next larger even integer is (1) n + 1 (2) n + 2 (3) 2n (4) 2n + 2 Matching: Write the letter of the property that justifies each statement below. 1 ___6) 2 = 1 2 A) Additive Identity ___7) 2(1 + 3) = 2(1) + 2(3) B) Multiplicative Inverse ___8) 2 + 1 = 1 + 2 C) Distributive Property ___9) (1 + 2) + 3 = 1 + (2 + 3) D) Associative Property ___10) 2 + 0 = 2 E) Commutative Property 2 Properties & Closure Homework For each example below, write the name of the property that is being illustrated. Choose your answers from this list: Commutative Property Associative Property Distributive Property Additive Identity Additive Inverse Multiplicative Identity Multiplicative Inverse 1) (2 + 3) + 7 = 2 + (3 +7) _____________________ 2) (15)(25) = (25)(15) _____________________ 3) 8(x + 4) = 8x + 32 _____________________ 4) 14 + 27 = 27 + 14 _____________________ 5) 6(3 5) = (6 3)5 _____________________ 6) a(b + c) = ab + ac _____________________ 7) 5 + ( 5) = 0 _____________________ 1 =1 5 8) 5 _____________________ 183(1) = 183 _____________________ 10) 1926 + 0 = 1926 _____________________ 3 9) 4 5 _____ 1) Which is an example of the commutative property of addition? (1) (2 + 3) + 4 = 2 + (3 + 4) (3) 2(3 + 4) = 2 · 3 + 2 · 4 (2) 2 + 3 = 3 + 2 (4) 4 + 0 = 4 _____ 2) Which is an illustration of the associative property? (1) ab + 0 = ab (3) a + b = b + a (2) a(b + c) = ab + ac (4) a + (b + c) = (a + b) + c 3) Name the additive identity element. __________ 4) Explain the meaning of “additive identity.” ________________________________ __________________________________________________________________________ 5) Name the multiplicative identity element. __________ 6) Explain the meaning of “multiplicative identity.” ___________________________ __________________________________________________________________________ _____ 7) Give a word that has the same meaning as “multiplicative inverse.” (1) identity (2) reciprocal (3) opposite _____ 8) Give a word that has the same meaning as “additive inverse.” (1) identity (2) reciprocal (3) opposite Matching: Write the letter of the property that justifies each statement below. _____9) 5 + (3 + 2) = (5 + 3) + 2 A) Additive Identity _____ 10) - 5 + 0 = - 5 B) Additive Inverse _____ 11) 10(8) = 8(10) C) Associative Property _____ 12) - 4 + 4 = 0 D) Commutative Property _____ 13) 3(x + 2) = 3x + 6 E) Distributive Property _____14) - 8(1) = - 8 F) Multiplicative Identity æ1 ö _____ 15) 3 çç ÷ ÷= 1 çè3 ø÷ G) Multiplicative Inverse 6 Commutative Associative “Change Order” “Parenthesis Occupants Change” a+b=b+a a•b=b•a (a + b) + c = a + (b + c) (a • b) • c = a • (b • c) Distributive “multiply through by the outside number” 4(x + 8) = 4x + 32 Additive Identity Multiplicative Identity “zero plus any number = that number” “any number times one = that number” a+0=a a•1=a Additive Inverse Multiplicative Inverse “adding the opposite = zero” “any number multiplied by the reciprocal = 1” 1 a 1 a a + -a = 0 7