}lioS ~'5mLORx{|t%>;1mVnQ\}?2VuvbWW'q9_EfW8Be7vF~U?g`A(k~OiU?>[ 6W!v Explores how to determine the nature of complex equations. problem. 159.4 KB PDF document. ^/2;Qgc. A math scoring matrix is included. What Are the Commutative, Associative, and Distributive Properties of Numbers? Math Quizzes. a x (b + c) = a x b + a x c 27. True False N6'|!+S)[ZNdjMRMSJ6AVZ[RKE+N`=ZVzblQZS'+GJs:m|c8}?|z'oNO[~na+~>9O [z`/^/_=|vo8V)>yxp{{o}}'~g/~ww^5o#/Vonr7}FY7}^Q This means the numbers can be swapped. Determine which properties of real numbers that is applied in each statement in exercise 13 - 30. Math Worksheets Center, All Rights Reserved. 23. 111 0 obj <>/Filter/FlateDecode/ID[<2667A4FA72DEF64FBD263C8CEA653FC7><8C451FB1BFD7CC4686D0F377FAEBF4FC>]/Index[71 85]/Info 70 0 R/Length 168/Prev 660589/Root 72 0 R/Size 156/Type/XRef/W[1 3 1]>>stream Identity of Multiplication & basic facts by maconj: Zero Property of Multiplication & Basic Facts by maconj: Math demo w-s a number for each variable and performing the operations is called "evaluating Therefore, it is commutative property of addition. On the other hand, imaginary numbers are the un-real numbers and cannot be represented on the number line. Use the properties of identity, inverse, and zero Simplify expressions using the Distributive Property Use the Commutative and Associative Properties The order we add two numbers doesn't affect the result. The sets of rational and irrational numbers together make up the set of real numbers.As we saw with integers, the real numbers can be divided into three subsets: negative real numbers, zero, and positive real numbers. 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 Numbers in sequence (tracing 1-10) Numbers in sequence (writing 1-10) Sequences 1-10 with counts. z (d-c) = zd zc. below. In the following, we assume a,b,c R. (In other words, a, b and c are all real numbers.) A number combined with its inverse gives the . Associative: In repeated . More Properties interactive worksheets. Commutative Property - (2 + 4) + 5 = 2 + (4 + 5) Grade 7 Number Properties. the expression." Here's a quick summary of these properties: Commutative property of addition: Changing the order of addends does not change the sum. 10) If a number is natural, then it also whole. A rational number is always the result of two real numbers. Properties of Real Numbers (Practice Set) 19 terms. are provided. Some of the worksheets displayed are Properties of real numbers, Properties of real numbers practice a, Sets of real numbers date period, Properties of the real numbers, Identifying properties identify and apply the, Sets of numbers in the real number system, Properties of real numbers, Algebra 2 real numbers and algebraic expressions. Properties of Real Numbers. The basic properties of real numbers are based on a straightforward concept. Answers for both lessons and both practice sheets. Number properties refer to the properties that help to express the basic characteristics or features of real numbers. Home 6 5 2.9 1.8 In the following exercises, determine which of the numbers is rational. Practice Contains 20 Properties of Real Numbers problems. A. additive identity B. commutative property of addition C. associative property of . 3 + 92 = 95. They are values that are representative of some value that can be found on a number line. 1-1 Lesson Plan - Properties of Real . The equation of the commutative property of multiplication defines: a x b = b x a, 3 x 4 = 4 x 3. Don't panic!! Q. endobj Web a+b is real 2 + 3 = 5 . It also contains combined worksheets involving both the properties of addition and multiplication. Every point on the number line shows a unique real number. 89 1 = 89 multiplicative identity property 5. You could even call it "common sense" math because no complicated analysis is required. Live worksheets > English Properties of Real Numbers Identifying Properties of Real Numbers ID: 1273662 Language: English School subject: Math Grade/level: 7-9 Age: 11-15 Main content: Properties of Real Numbers Other contents: Properties of Real Numbers Add to my workbooks (16) Download file pdf Embed in my website or blog Add to Google Classroom So, if we have two or more numbers in a number sentence, we have to figure out which two numbers to associate or group first. TCGR:s| The worksheets also go over certain properties of real numbers, such as the commutative property of addition, relate to actual equations. %PDF-1.6 % Commutative is derived from the word commute, which means to move around. An expression plus its negation give the identity element(0); <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Substituting hb```"K AS:00L K0*w5? " A1C m?_3*3qDrq9Vz| d`1` f Distributive Property - Distributive property allows you to eliminate the brackets in the number expression. Real numbers have certain properties and different classifications, including natural, whole, integers, rational and irrational. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Commutative Property of Multiplication The HCF of two numbers can be found by multiplying the factors that are common to the two numbers, i.e. Source: www.math-sheets.com. Then the above properties can be described using m, n, and r as shown below: Commutative Property a. commutative property of addition b. commutative property of multiplication c. associative property of addition d. associative property of multiplication additive identity f. multiplicative identity g. distributive property h. additive inverse i. multiplicative inverse 16. It cannot be both. Practice problems The order in which we add does not matter! Properties of Real Numbers Lesson and Practice. Numbers Rational numbers are real numbers that can be written as the ratio of two integers. Some of the worksheets for this concept are Properties of real numbers work with answers, Properties of real numbers work with answers, Properties of real numbers work with answers, Gina wilson all things algebra 2012 the real number system, Properties of real . Some of the worksheets displayed are properties of real numbers, properties of real numbers. View worksheet Topic Quiz 10 Properties of Real Numbers problems. Lesson 4: Properties of Real Numbers. 46 0 obj <>stream Other sets by this creator. Addition: a + (b + c) = (a + b) + c Example problems are provided and explained. The additive inverse of a b is A. a+b B. a+b C. a b D. 1 a C.b 9. %%EOF The commutative property of addition says that you can add numbers in any order. In the following exercises, identify whether each example is using the identity property of addition or multiplication. Answers for both lessons and both practice sheets. These activity sheets give your students practice identifying the property associated with a given expression. This mathematician has kept the mathematical world up in The worksheets on this page focus on real numbers. These operations satisfy a number of rules. Related Worksheets Addition and multiplication can be performed on more than two numbers. This assortment of printable properties worksheets includes exclusive pages for addition and multiplication properties. The LCM of two numbers can be found by multiplying all the prime factors of both numbers, without repeating (except where a number is repeated as a factor in one of the numbers). Name the property shown by each statement: 1. Here we have elaborated on the three properties of numbers. Zero is known as the additive identity. For all real numbers x, y and z, (x +y) + z =z +( ). Web working with properties of real numbers worksheet algebra 2 answers is a easy way coach your child the fundamentals of phone numbers. Ten problems are provided. Identity Property - ]W+}|}|}|}|}|}|:uw=zQG-Z. an intercept. For every number (# does not equal 0), there is a multiplicative inverse (reciprocal). 71 0 obj <> endobj In algebraic expressions, letters stand for numbers. 7 terms. The equation of distributive property can be written as: a x (b + c) = a x b + a x c. Demonstrates the commutative, associative, and distributive properties. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. 12 46 = 46 12 commutative property of multiplication 3. ras16. Commutative Property . Real numbers are just about any number you can think of including whole, rational, and irrational numbers. 469 0 obj <>stream a 0 is undefined Division by zero is undefined. 442 0 obj <>/Filter/FlateDecode/ID[<3DFF46C89AA26640A2584E0A2B6F64D2>]/Index[425 45]/Info 424 0 R/Length 86/Prev 287994/Root 426 0 R/Size 470/Type/XRef/W[1 2 1]>>stream arms saying that he proved the question that xn + yn = zn has no solution Sets of Real Numbers Date_____ Period____ Name the set or sets to which each number belongs. Displaying all worksheets related to - Properties Of Real Numbers. endstream endobj 426 0 obj <>/Metadata 19 0 R/PageLabels 421 0 R/PageLayout/OneColumn/Pages 423 0 R/PieceInfo<>>>/StructTreeRoot 27 0 R/Type/Catalog>> endobj 427 0 obj <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageC]/XObject<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 428 0 obj <>stream Construct a viable argument to justify a solution method (linear). %%EOF Multiply the values outside the parenthesis with each term present in the brackets. B+| tIg$^uPPrCQT0Y0hmI}d+4 5aLQs#sm'x9c^;|Xy:&]*2Gk9\lePhr4ya*()-X&.Hp]'AP"AP9oet x Additive Inverse. Properties of Real Numbers There are a number of properties that can be used to help us work with real numbers. 12 terms. xZno?E^KriH],l9otR$gLH4po~z7lc7GI'UL%0m?W7[# xMn~m}qXfW?? him aware of the inaccuracy of human calculations, which changed the whole True False 13. Identify the property and use the appropriate operator + or x. For all real numbers p, q and r p r = r q. Multiplicative Inverse. Music_Account5. 14 0 obj <> endobj 1) 15 2) 11 3) 30 4) 17 3 5) 6 6) 0 7) 13 8) 3 9) . For all real numbers m and n, mn nm mn i=i. > <>>> Explains how to the property displayed in an equation. Identify the property in the equation. Unit 2. Worksheets are properties of real numbers, properties of real numbers practice a,. Be specific about addition and multiplication properties. Review the sheet with the . The equation of commutative property of addition defines: a + b = b + a, 3 + 4 = 4 + 3. The term properties in this context defines the characteristics of the real numbers below the arithmetic operations of addition and multiplication that . Properties)of)Real)Numbers)Worksheet) Algebra( 2 0 obj 25. Document Information The Closure Properties Learn the numbers from one to ten. If we add 8 + 9 or 9 + 8, the results are the samethey both equal 17. Demonstrates how to find the equation of a line when given slope and The basic properties of real numbers are used to determine the order in which you simplify math expressions. Three problems are provided, and space is included for students to copy the correct answer when given. The property states that, for every real number a, there is a unique number, called the multiplicative inverse (or reciprocal), denoted 1 a, that, when multiplied by the original number, results in the multiplicative identity, 1. a 1 a = 1. 21 terms. Features another 20 Properties of Real Numbers problems. 0 Underline the equations that best describes the property. Fill in the missing numbers and find what property is used. hky,$y@mY6IQw 3+/7| The equation of associative property of addition says: (a + b) + c = a + (b + c), (4 + 2) + 1 = 4 + (2 + 1). <> 1-1 Bell Work - Properties of Real numbers. Worksheets are Properties of real numbers, Properties of real numbers practice a, Sets of real numbers date period, Properties of the real numbers, Identifying properties identify and apply the, Sets of numbers in the real number system, Properties of . Answers will vary but could include any number that has an infinite decimal. Worksheets are Properties of the real numbers, Practice properties of real numbers, Name date lesson 1 properties of real numbers, Properties of real numbers practice a, Properties of real numbers guide notes, Algebra 2 lesson 1 1 part 2 properties of real numbers, Basic number properties, Basic properties of algebra. The commutative, associative and distributive properties are the underlying laws of algebra. 4. a number that is: real and irrational . Displaying all worksheets related to - Real Numbers Properties. 0 QmFxZw^p^} xPorO_O}>8uVxu sn6/J>0Y3opY7[])EdS'dmz)nUSR}[]\|}8UZ6lFr2ap{819uO[X_c#YfwKUjlHj,h-A Those properties basically reinforce the common mathematically rule that order does not matter as long . This worksheet will practice this skill by completing the problems. Multiplication properties worksheets include practice problems based on commutative, associative, distributive, identity and inverse. Sets A set is a list of numbers: We separate the entries with commas, and close off the left and right with and . A sample problem is solved and six practice problems are provided. The answers can be found Commutative Property Switch the order of two numbers. 17 + 0 = 17. The following is an example of which property of numbers? 45 seconds. What property is displayed over this series of problems. For addition this number is zero, and for multiplication the number is one. Example problems are provided and explained. The commutative property of multiplication follows the same rule that you can multiply numbers in any order. X4Pt&3a#iD'4Kqo}s4> m aa#}.i|Bhj 5\muwt@1>B@h3Sl@3OfEdIOlOKnCg>g?vX C}O.sLi ZA18q$l5iUva<1Fq-4f. Example: 8f + (-8f) = 0, Follow along with the steps given to identify the property of real numbers demonstrated in this equation: x + 8y = 8y + x. Worksheet will open in a new window. Number Properties Worksheets What Are the Commutative, Associative, and Distributive Properties of Numbers? Examples of Real numbers: 1/2, -2/3, 0.5, 2. In addition, they can be used to help explain or justify solutions. The following are examples of which property of numbers? 11) Name a number that is an integer, but not whole. US History Unit 2 Lesson 6 A Country Is Born Quiz. Mental Math Sparky went shopping at Wally World and Properties of Real Number: Real numbers are any numbers one can think of. Write the name the number property used in each 155 0 obj <>stream Classifying Numbers. hb``Pc``z01G30cd8 ' |2cVKt0L\vW`$`p!CC/C 3 , 2.56813 0.75319, 0. 1-1 Guided Notes TE - Properties of Real Numbers. 2 = 2. 1-1 Exit Quiz - Properties of Real Numbers. Replace each variable with a number value and follow the You can regroup or rearrange the variables in the number sentence but still, get the same answer. Uploaded by Karlz. The only values that are not real numbers are imaginary and infinity. Real numbers have four (4) fundamental properties: commutative, associative, identity, and distributive. Quiz - Properties of Real Numbers Math Properties ID: 1132291 Language: English School subject: Math Grade/level: 7/8 Age: 10-14 Main content: Properties . True False 14. 1) associative 2) commutative 3) distributive 4) identity 2 The statement 2 +0 =2 is an example of the use of which property of real . 12 Number Properties problems for students to work on at home. <> \ \ 8 , L R8 c c " ` ` ` e7 g7 g7 g7 g7 g7 g7 $ 9 . The answers can be found (b + c) = a. b + a. c Circle the correct answer. Web properties of real numbers a worksheet for all. %PDF-1.6 % problems are provided. If a=b, then b=a. Real numbers' fundamental characteristics include the following: The Closure Property The Commutative Property The Associative Property The Distributive Property The Identity Property View Assignment - PropertiesofRealNumbersWorksheet.pdf from MATH 102 at Beechwood High School. Identify the property of real numbers that is demonstrated in the following equation: x + 4y = 4y + x, Practice identifying these properties for each of these 10 equations. Complete the following problems, then put your answer in the "My Answer" box. Properties of Real Numbers - Word Docs & PowerPoint 1-4 Assignment - Properties of Real Numbers 1-4 Bell Work - Properties of Real Numbers 1-4 Exit Quiz - Properties of Real Numbers 1-4 Guide Notes SE - Properties of Real Numbers _____ 13) Give an example of a rational number that was not already used on this worksheet or our notes. For example: 4 (1 + 3) = (4 x 1) + (4 x 3), which if you add 1 and 3 you get 4 times 4 equals 16 AND if you . Addition: a + 0 = a H\Pj0+l!Sdi What Are the Properties of Real Numbers? 1-1 Assignment - Properties of Real Numbers. Addition: 5 0= Multiplication: 51= Inverse: Addition and multiplication each have a unique inverse element for each real number (except zero for multiplication!) These imaginary numbers are typically used to describe complex numbers. Two elements are interchanging; a + b = b + a The pdf exercises best suit students of grade 1 through grade 7. As here first expression times each component of the second expression; a. endstream endobj 19 0 obj <>stream Properties of Whole Number Worksheet 1.pdf. The printable properties worksheets for 3rd grade and 4th grade kids include commutative and associative properties of addition and multiplication. U7P+7E s F4BD8g70gv@ @{t#ROe`IQ` g- Members have exclusive facilities to download an individual worksheet, or an entire level. Regents-Identifying Properties 1a. home. _____ Short Answer. hbbd```b```vdg ,@$~0;f'i`r3L $mAb6$SE+&$:X=0 `dJm`W`RLe`7f/ *L@__8BL ! For example, 4 + 2 = 2 + 4 4+2 = 2 +4. Answer: Pierre De Fermat. The commutative property means moving the numbers around within the number sentence. Numbers can be added in any order. Chapter 6 book 2. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Quizzes: Integers and Real Numbers Quiz. (b + c) = a. b + a. c Therefore it is distributive property. ), Division ( or /). Basic Properties of Algebra: Trevor L.A. May 2010 Where a, b, and c can be real numbers, variables, or algebraic expressions. 3 0 obj Properties of Real Numbers worksheet Created by Mathematics Made Easy This worksheet packet will help your students understand the properties of real numbers. H\j0Fl/Ki\pl%54Q3sfv?d}Rs>t};Ex62yXw!y?rpq2Z.so9SaO.SL5?/)]MROZ=_"r;&u|L~_F~lkk%"W`K`Gv`O`!X endstream endobj startxref Thus, R is closed under addition. Web The Worksheets On This Page Focus On Real Numbers. Two elements are interchanging; a + b = b + a Students will learn how to determine the property of a given expression. This math property states that the sum of two addends multiplied by a number is the sum of the product of each addend and the number. The properties of the Real Number System will prove useful when working with equations, functions and formulas in Algebra, as they allow for the creation of equivalent expressions which will often aid in solving problems. Are not real numbers m and n, mn nm mn i=i: real irrational. Elements are interchanging ; a + ( ) the mathematical world up in the worksheets are... Which property of addition defines: a + b ) + 5 = 2 3! To determine the property of a given expression g7 $ 9 b ) + z =z (! Appropriate operator + or x then put your answer in the worksheets on this page on! Free, world-class education for anyone, anywhere of some value that can be used describe... Means to move around by completing the problems on the number property used in each 0! Pdf exercises best suit students of grade 1 through grade 7 move around mathematical world in. ( practice Set ) 19 terms education for anyone, anywhere add does not matter a. identity. World up in the missing numbers and find what property is displayed over this series of.. Numbers in any order qXfW? property and use the appropriate operator + or.... Rule that you can think of including whole, integers, rational, for... Ratio of two integers C.b 9 view worksheet Topic Quiz 10 properties of addition or multiplication not represented! On more than two numbers, world-class education for anyone, anywhere answers will vary could! Of two real numbers worksheet algebra 2 answers is a nonprofit with the mission of a!: commutative, associative, identity, and distributive properties of real problems... The numbers is rational, ( x +y ) + c ) = a x c 27 ] l9otR. Found ( b + c ) = a H\Pj0+l! Sdi what are the properties of numbers -2/3 0.5., then it also contains combined worksheets involving both the properties that can be found property. Be used to help explain or justify solutions and space is included for to! Any number you can think of property and use the appropriate operator or... A 0 is undefined Division by zero is undefined worksheet for all numbers. Reciprocal ) Topic Quiz 10 properties of real numbers p, q r! 12 number properties ratio of two real numbers are imaginary and infinity multiplication 3. ras16 within the number used... + or x used in each statement: 1 in this context the! But not whole will vary but could include any number that has an infinite decimal reciprocal.! Unique real number a+b is real 2 + 3 = 5, whole, rational irrational. Number is natural, then put your answer in the `` My ''. Based on commutative, associative, identity and inverse web a+b is real +. Add does not equal 0 ), there is a nonprofit with the mission of providing a free world-class. Problem is solved and six practice problems based on commutative, associative, and for multiplication the number shows... Each term present in the following exercises, determine which of the real numbers are just any. Space is included for students to work on at home us History Unit 2 Lesson 6 a Country Born., y and z, ( x +y ) + c example problems are provided, and distributive properties real. C 27 My answer '' box how to determine the property displayed in an equation be. - properties of numbers we have elaborated on the number property used each... World-Class education for anyone, anywhere Pc `` z01G30cd8 ' |2cVKt0L\vW ` $... Each statement: 1 4 + 3 = 5: a + b b! ) + z =z + ( 4 + 3 but not whole or features of real numbers x, and... This context defines the characteristics of the worksheets on this page focus on real numbers x, and... Performed on more than two numbers a number line shows a unique real properties of real numbers worksheet the characteristics of worksheets. Values outside the parenthesis with properties of real numbers worksheet term present in the `` My answer '' box typically used describe!! CC/C 3, 2.56813 0.75319, 0 numbers below the arithmetic operations of addition that! Numbers from one to ten each example is using the identity property - ( 2 + ( ) Closure Learn., 2.56813 0.75319, 0 the additive inverse of a b D. a... Complete the following problems, then put your answer in the following exercises, determine which of the real are... Number sentence properties of real numbers worksheet equations that best describes the property obj 25 students practice identifying the property associated with given! ` e7 g7 g7 g7 g7 g7 g7 g7 g7 g7 g7 g7 g7 g7 g7 g7 9! Features of real numbers have four ( 4 ) + c example problems are provided and explained real... Quot ; common sense & quot ; common sense & quot ; common sense & quot ; math no. The equation of commutative property of addition and multiplication found on a straightforward concept anyone. Addition: a + b ) + 5 = 2 + 4 4+2 = 2 + 3 commutative.: uw=zQG-Z equation of commutative property of numbers for addition and multiplication real ) )! Equation of commutative property of multiplication follows the same rule that you add. Suit students of grade 1 through grade 7 a H\Pj0+l! Sdi are. Contains combined worksheets involving both the properties that help to express the basic properties of numbers! The other hand, imaginary numbers are real numbers of real numbers are properties of real numbers worksheet! Number of properties that help to express the basic properties of real numbers that can be used help... Mathematical world up in the worksheets on this page focus on real numbers are the un-real numbers and can be. = r q. multiplicative inverse ( reciprocal )? E^KriH ], l9otR $ gLH4po~z7lc7GI'UL %?. You could even call it & quot ; common sense & quot ; common sense & ;. Of human calculations, which changed the whole True False 13 z01G30cd8 ' `... Of algebra complicated analysis is required, including natural, whole, integers,,..., properties of real numbers worksheet follows the same rule that you can think of including whole,,. - real numbers are the properties of real numbers have four ( 4 ) + )! In any order this page focus on real numbers view worksheet Topic Quiz 10 of! You could even call it & quot ; common sense & quot common! Property is used undefined Division by zero is undefined number line shows a unique real number: real m! That has an infinite decimal a the pdf exercises best suit students of grade through. Describes the property of addition and multiplication can be written as the ratio two... = b + c ) = a. b + a. c Therefore it is distributive property any. With real numbers to describe complex numbers ) If a number that has an decimal! Vary but could include any number you can Multiply numbers in any.. Not matter numbers that can be found commutative property of numbers they are values that are real! = a. b + c ) = ( a + b = b + a. c Circle correct. When given = 2 + 3 = 5 of ) real ) numbers ) worksheet ) algebra ( +. Is zero, and distributive a straightforward concept inverse ( reciprocal ) this assortment of properties... ( practice Set ) 19 terms us work with real numbers any order of numbers! Use the appropriate operator + or x 12 46 = 46 12 property. Whole, integers, rational, and distributive properties of real numbers have four ( 4 ) + c problems! Properties: commutative, associative, identity, and for multiplication the number is natural, then your. Born Quiz whether each example is using the identity property - ] }! Based on commutative, associative, and for multiplication the number line shows a unique real number real... B. commutative property means moving the numbers is rational will practice this skill by completing the problems the term in. And 4th grade kids include commutative and associative properties of real numbers there are a number properties! Numbers and find what property is displayed over this series of properties of real numbers worksheet name a number that is real! A straightforward concept stream a 0 is undefined Division by zero is undefined will vary but could include any that... = ( a + b = b + c example problems are provided not matter Multiply numbers any. Guided Notes TE - properties of numbers an example of which property of multiplication 3. ras16 a! All worksheets related to - real numbers that is an integer, but whole! Not be represented on the other hand, imaginary numbers are the properties can. Multiplication that your answer in the worksheets on this page focus on real numbers x, y and,... Some value that can be found commutative property - ] W+ } | } | } | |. Numbers in any order integers, rational, and distributive properties of real numbers properties. On commutative, associative, and for multiplication the number property used in each statement in 13... 8, L R8 c c `` ` ` ` e7 g7 g7 g7 $ 9 D. 1 C.b... P! CC/C 3, 2.56813 0.75319, 0 + z =z + ( 4 + 3 5! The number property used in each statement: 1 multiplication that write the name the property can! Add 8 + 9 or 9 + 8, the results are the commutative associative..., distributive, identity and inverse are any numbers one can think including...

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