ࡱ> `b_ lFbjbjT~T~ 4N66 %\\8,LR8cc"```e7g7g7g7g7g7g7$9<p7`````7 8`e7`e76}460`R$<]5Q7"80R8y5`=`=866=6````````77`j```R8````=`````````\ e: Real Numbers Real numbers are divided into two types, rational numbers and irrational numbers Rational Numbers: Any number that can be expressed as the quotient of two integers. (fraction). Any number with a decimal that repeats or terminates. Subsets of Rational Numbers: Integers: rational numbers that contain no fractions or decimals. {,-2, -1, 0, 1, 2, } Whole Numbers: all positive integers and the number 0. {0, 1, 2, 3, } Natural Numbers (counting numbers): all positive integers (not 0). {1, 2, 3, & } Irrational Numbers: Any number that cannot be expressed as a quotient of two integers (fraction). Any number with a decimal that does non-repeating and non-terminal (doesn t repeat and doesn t end). Most common example is . Properties Commutative Properties of Addition and Multiplication: The order in which you add or multiply does not matter. a + b = b + a and a " b = b " a Examples: 2 + 4 = 6 and 4 + 2 = 6 5 " 6 = 30 and 6 " 5 = 30 Symmetric Property: If a + b = c, then c = a + b If , then Reflexive Property: a + b = a + b Nothing changes Associative Properties of Addition and Multiplication. The grouping of addition and multiplication does not matter. (Parenthesis) Examples: 2 + (4 + 7) = 13 and (2 + 4) + 7 = 13 4"(6 " 2) = 48 and (4 " 6) " 2 = 48 Transitive Property: If a = b and b = c, then a = c. If, and, then If 8 " 2 = 16 and 16 = 42, then 8 " 2 = 42 . Distributive Property: a (b + c) = ab + ac and a(b  c) = ab  ac Examples: 3(7 + 2) = 3(7) + 3(2) = 21 + 6 = 27 5(9 6) = 5(9) 5(6) = 45 30 = 15 Additive Identity: When zero is added to any number or variable, the sum is the number or variable. a + 0 = a Multiplicative Identity: When any number or variable is multiplied by 1, the product is the number or variable. a " 1 = a Multiplicative Property of Zero: When any number or variable is multiplied by zero, the product is 0. a " 0 = 0 Complete the Matching Column (put the corresponding letter next to the number) 1) 26 +0 = 26 a) Reflexive 2) 22 0 = 0 b) Additive Identity 3) 3(9 + 2) = 3(9) + 3(2) c) Multiplicative identity 4) If 32 = 64 2, then 64 2 = 32 d) Associative Property of Mult. 5) 32 1 = 32 e) Transitive 6) 9 + 8 = 8+ 9 f) Associative Property of Add. 7) If 32 + 4 = 36 and 36 = 62, then 32 + 4 = 62 g) Symmetric 8) 16 + (13 + 8) = (16 +13) + 8 h) CommutativeProperty of Mult. 9) 6 (2 12) = (6 2) 12 i) Multiplicative property of zero 10) 6 " 9 = 6 " 9 j)Distributive Complete the Matching Column (put the corresponding letter next to the number) 11) If 5 + 6 = 11, then 11 = 5 + 6 a) Reflexive 12) 22 0 = 0 b) Additive Identity 13) 3(9 2) = 3(9) 3(2) c) Multiplicative identity 14) 6 + (3 + 8) = (6 +3) + 8 d) Associative Property of Mult. 15) 54 + 0 = 54 e) Transitive 16) 16 5 = 16 5 f) Associative Property of Addition 17) If 12 + 4 = 16 and 16 = 42, then 12 + 4 = 42 g) Symmetric 18) 3 (22 2) = (3 22) 2 h) Commutative Property of Addition 19) 29 1 = 29 i) Multiplicative property of zero 20) 6 +11 = 11+ 6 j)Distributive C. 21) Which number is a whole number but not a natural number? a) 2 b) 3 c) d) 0 22) Which number is an integer but not a whole number? a) 5 b) c) 3 d) 2.5 23) Which number is irrational? a) b) 4 c) .1875 d) .33 24) Give an example of a number that is rational, but not an integer. 25) Give an example of a number that is an integer, but not a whole number. 26) Give an example of a number that is a whole number, but not a natural number. 27) Give an example of a number that is a natural number, but not an integer. Properties Worksheet: Complete the Matching Column (put the corresponding letter next to the number) 1) If 18 = 13 + 5, then 13 + 5 = 18 a) Reflexive 2)6 ( (2 ( 5) = (6 ( 2) ( 5 b) Additive Identity 3) 5(7 + 2) = 5(7) + 5(2) c) Multiplicative identity 4) 15 + (10 + 3) = (15 +10) + 3 d) Associative Property of Multiplication 5) 50 ( 1 = 50 e) Transitive 6)    U V l m z  8 >   2 ( bH6^`ºҐҌ҈҈҈ hVH*hVh"H3h\Ih h#|fh_CJ0aJ0hPCJ0aJ0hPCJ aJ hPh.CJ0aJ0h#|fCJ aJ h#|fh#|fCJ aJ h_>*h#|f h#|fh#|fh_h_>*h_h_6CJ$aJ$h_h_h_CJ0aJ02 _`r U l m   8  & Fgd.@ ^@ gd.gd_^gd_@ ^@ gd#|f & Fgd_ & Fgd_ & Fgd_$a$gd_  t ( < ^gd#|f & Fgd#|f p^p`gd"H3 & Fgd"H3 & Fgd#|f$a$gd0jJgdP Fb46`F & FgdV8^8gdV & FgdV^gd  & Fgd  & Fgd gd  & Fgd"H3gd"H3 & Fgd"H3 & Fgd#|f  DISUvwEF"./;<bp$&(89Z[伲hdB*H*phhdhdB*H*phhdB*ph%hdhdB*CJOJQJaJphhdhdB*phhh0jJ hVH*hVFF%&9X & Fgd. & Fgd0jJ & F p^gd0jJ & FgdV^gd0jJ & Fgd0jJ & Fgd0jJgd0jJ h^`hgd0jJ & F 88^8`gd0jJ wF<([+I+ & F fddd[$\$^fgddddd[$\$gdd & F fddd[$\$^fgdd  )*+z{-;<HI *+\|  E F J!Q!T!U!V!!!hd>*B*phhdhd>*B*phhdB*CJOJQJaJphhdB*H*phhdhdB*H*ph%hdhdB*CJOJQJaJphhdB*phhdhdB*ph9 F V!!!P"Q"R"S"T"U"V"W"X"Y"Z"["\"]"^"_"gddddd[$\$gdd!!!!!!K"N"O"P"Q"h"~""""## # #######$:r;t;;;<<L<=>L?N?V?X?p?r?t?x?@ɶɶzuuuu h'H*h'B*ph h'CJH*U jh'CJ h'CJh'h'CJh'h'CJ(aJ(h'hd%hdhdB*CJOJQJaJphhdhd>*B*phhd>*B*phhdhdB*ph(hdhd>*B*CJOJQJaJph-_"`"a"b"c"d"e"f"g"h"~""#8#p###p::8;;@<B<D<<@=gd'  !gd' & Fgd'h^hgd'gdd7 " 4 = 4 " 7 f) Associative Property of Addition 7) 13 +0 = 13 g) Symmetric 8) 11 + 8 = 11 + 8 h) Commutative Property of Multiplication 9) If 30 + 34 = 64 and 64 = 82, then 30 + 34 = 82 I) Multiplicative property of zero 10) 11 ( 0 = 0 j) Distributive 11) Which property is represented by: 5+ (4 + 7x) = (5 + 4) + 7x? a) Associative Property of Add. c) Distributive Property b) Commutative Property of Add. d) Symmetric Property 12) Which property is illustrated by 5(a + 6) = 5(a) + 5(6) a) associative prop. of add. b) distributive c) transitive d) symmetric 13) What is the formula for area of a rhombus? a) A = lh b) A = h(b1 + b2) c) A = d1d2 d) A = lwh 14) What property is represented by: If 4 + 14 = 18 and 18 = 6 " 3, then 14 + 4 = 6 " 3 ? a) Symmetric Property c) Commutative Property of Add. b) Transitive Property d) Awesome Property 15) Which property is represented by: 3 + 9 = 9 + 3 ? a) Transitive Property c) Reflexive Property b) Symmetric Property d) Commutative Property of Add. 16) Which property is represented by: If 3 + 11 = 14, then 14 = 3 + 11 ? a) Transitive Property c) Reflexive Property b) Commutative Property of Add. d) Symmetric Property 17) Write a statement that illustrates the Additive Identity property: 18) Write a statement that illustrates the Multiplicative Identity property: 19) Write a statement that illustrates the Symmetric property: 20) Write a statement that illustrates the Associative Prop.of Add.:     PAGE  PAGE 1 @===*>>>???H@@AAAAXBZBBLCCCXDZDDEEE Fgdd`gd'gd'@@NDVDDE~EEFF F"F&F(F,F.F2F4F8F:FFFHFJFLFNFPF\F^F`FbFdFfFhFjFlFӾh0JmHnHuhj h'0Jjh'0JUhGjhGU h'h' h'>*h' h%\h'" F$F&F*F,F0F2F6F8FJFLFNFdFfFhFjFlFgddh]hgd' &`#$gdj21h:pd/ =!"#$% ^ 2 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~_HmH nH sH tH @`@ NormalCJ_HaJmH sH tH DA`D Default Paragraph FontRiR  Table Normal4 l4a (k (No List 4@4 Header  !B^B d Normal (Web)dd[$\$4 @4 'Footer  !.)@!. 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