Order of Operations with Brackets
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
The Comprehensive LATEX Symbol List
The Comprehensive LATEX Symbol List Scott Pakin <[email protected]>∗ 22 September 2005 Abstract This document lists 3300 symbols and the corresponding LATEX commands that produce them. Some of these symbols are guaranteed to be available in every LATEX 2ε system; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed. All of the fonts and packages used to prepare this document—as well as this document itself—are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org/). Contents 1 Introduction 7 1.1 Document Usage . 7 1.2 Frequently Requested Symbols . 7 2 Body-text symbols 8 Table 1: LATEX 2ε Escapable “Special” Characters . 8 Table 2: Predefined LATEX 2ε Text-mode Commands . 8 Table 3: LATEX 2ε Commands Defined to Work in Both Math and Text Mode . 8 Table 4: AMS Commands Defined to Work in Both Math and Text Mode . 9 Table 5: Non-ASCII Letters (Excluding Accented Letters) . 9 Table 6: Letters Used to Typeset African Languages . 9 Table 7: Letters Used to Typeset Vietnamese . 9 Table 8: Punctuation Marks Not Found in OT1 . 9 Table 9: pifont Decorative Punctuation Marks . 10 Table 10: tipa Phonetic Symbols . 10 Table 11: tipx Phonetic Symbols . 11 Table 13: wsuipa Phonetic Symbols . 12 Table 14: wasysym Phonetic Symbols . 12 Table 15: phonetic Phonetic Symbols . 12 Table 16: t4phonet Phonetic Symbols . 13 Table 17: semtrans Transliteration Symbols . 13 Table 18: Text-mode Accents . 13 Table 19: tipa Text-mode Accents . 14 Table 20: extraipa Text-mode Accents . -
Unit of Study: Activity Sheet Three
Activity Sheet Three – Programming One Revised October, 2010 Your Name:_______________________________________ Class Period: _______________ Date: ______________________ UNIT OF STUDY: ACTIVITY SHEET THREE POINT BREAKDOWN ASSIGNMENT POINT VALUE EARNED VOCABULARY 20 POINTS _________ SECTION CHECKPOINT PAGE 49 – NEW BOOK 10 POINTS _________ SECTION CHECKPOINT PAGE 54 – NEW BOOK 10 POINTS _________ SECTION CHECKPOINT PAGE 61 – NEW BOOK 10 POINTS _________ CHAPTER 3 REVIEW ?’ TRUE/FALSE – PAGE 62-63 10 POINTS _________ NEW BOOK PROJECT 3-1 – PAGE 63 10 POINTS _________ NEW BOOK PROJECT 3-2 – PAGE 64 10 POINTS _________ NEW BOOK PROJECT 3-3 – PAGE 64 10 POINTS _________ NEW BOOK PROJECT 3-4 – PAGE 64 10 POINTS _________ NEW BOOK ACTIVITY 3-1 PAGE 66 NEW BOOK 25 POINTS _________ 1 Activity Sheet Three – Programming One Revised October, 2010 PURPLE BOOK LESSON 3 WRITTEN QUESTIONS 14 POINTS _________ Page 125 LESSON 3 PROJ.3-1 10 POINTS _________ LESSON 3 PROJ.3-2 10 POINTS _________ LESSON 3 PROJ.3-3 10 POINTS _________ LESSON 3 PROJ.3-5 10 POINTS _________ LESSON 3 PROJ3-7 10 POINTS _________ LESSON 3 PROJ.3-9 10 POINTS _________ LESSON 3 PROJ.3-10 10 POINTS _________ CRITICAL THINKING 3-1 Essay 25 POINTS _________ **The topic has changed – see inside of packet for change TOTAL POINTS POSSIBLE 234 _________ GENERAL COMMENTS… 2 Activity Sheet Three – Programming One Revised October, 2010 YOUR NAME: CLASS PERIOD: Activity Sheet One - This activity will incorporate reading and activities from Fundamentals of C++ (Introductor y) and, Introduction to Computer Science Using C++. Both books can be found in the Programming area of the classroom, and must be returned at the end of the period. -
Official Journal
THE CITY RECORD. OFFICIAL JOURNAL. VOL XXVI. NEW YORK, SATURDAY, DECEMBER 3, 1898. NUMBER 7,777, DEPARTMENT OF STREET CLEANING. final Disposition of /lfalemal. Cart.86oads. At Barren Island (N.Y. S. U. Co. 734 AtSea ............................................................... I,o79,fi73'/z Report for the Quarter arld Year Ending December 31, 1897 AtNewtown Cieek .......................................................... 262,6O2y4 AtWhale (;reek ............................................................ 750 AtLong Island ...................................... ................ 10,094 DEPARIIIIENT OF STREET CLEANING-CITY OF NEW YORK, I AtWoodbridge Creek ....................................................... 362 ,NEw YORK, October 26, 1898. AtStaten Island ........................................ ................... 525 Hon. ROBERT A. VAN \VYCK, rllayor : AtEllis Island .............................................................. 1,250 SIR--As required by section 1544 of the Charter, I beg to hand you herewith a report of the Sunk at Stanton Street Dump ................................................. 102 business of the Department of Street Cleaning under my predecessor, for the last quarter of the year AtSt. George, Staten Island ..................................... ............ 35,o833. 1897, together with a resume of the business for the entire year. AtFlushing .............................................................. 1,588 The delay in sending this report in has been caused by some accounts of 1897 which were not In lots........... -
Teaching Students with Specific Learning Disabilities Math
TEACHING STUDENTS WITH SPECIFIC LEARNING DISABILITIES MATH This guidance document is advisory in nature but is binding on an agency until amended by such agency. A guidance document does not include internal procedural documents that only affect the internal operations of the agency and does not impose additional requirements or penalties on regulated parties or include confidential information or rules and regulations made in accordance with the Administrative Procedure Act. If you believe that this guidance document imposes additional requirements or penalties on regulated parties, you may request a review of the document. For comments regarding this document contact [email protected]. Teaching Students with Mathematical Disabilities Table of Contents Introduction Rationale Least Restrictive Environment (LRE) Defining & Determining Mathematics Learning Disabilities ◦ Determining Eligibility for Students with a Specific Learning Disability (SLD) ◦ State and Federal Special Education Law Table ◦ Frequently Asked Questions Amongst Different Mathematics Disabilities ◦ Frequently Asked Questions About Characteristics of Disabilities in Mathematics High Quality Core Learning Materials ◦ Aligning to Standards ◦ Evidence-based Practices ◦ Universal Design for Learning ◦ Resources and Additional Information Nebraska Mathematical Processes Mathematics Instruction Best Practices ◦ Specially Designed Instruction in Mathematics ◦ Explicit Instruction ◦ Formal Mathematical Language ◦ Concrete, Representational, and Abstract Connections ◦ Fact -
The Order of Operations Agreement Page 1
Lecture Notes The Order of Operations Agreement page 1 The order of operations rule is an agreement among mathematicians, it simplies notation. P stands for parentheses, E for exponents, M and D for multiplication and division, A and S for addition and subtraction. Notice that M and D are written next to each other. This is to suggest that multiplication and division are equally strong. Similarly, A and S are positioned to suggest that addition and subtraction are equally strong. This is the hierarchy, and there are two basic rules. 1. Between two operations that are on different levels of the hierarchy, we start with the operation that is higher. For example, between a division and a subtraction, we start with the division since it is higher in the hierarchy than subtraction. 2. Between two operations that are on the same level of the hierarchy, we start with the operation that comes rst from reading left to right. Example 1. Perform the indicated operations. 20 3 4 Solution: We observe two operations, a subtraction and a multiplication. Multiplication is higher in the hierarchy than subtraction, so we start there. 20 3 4 = multiplication 20 12 = subtraction = 8 Example 2. Perform the indicated operations. 36 3 2 Solution: It is a common mistake to start with the multiplication. The letters M and D are in the same line because they are equally strong; among them we proceed left to right. From left to right, the division comes rst. 36 3 2 = division 12 2 = multiplication = 24 Example 2v. Perform the indicated operations. -
The Comprehensive LATEX Symbol List
The Comprehensive LATEX Symbol List Scott Pakin <[email protected]>∗ 22 September 2005 Abstract This document lists 3300 symbols and the corresponding LATEX commands that produce them. Some of these symbols are guaranteed to be available in every LATEX 2ε system; others require fonts and packages that may not accompany a given distribution and that therefore need to be installed. All of the fonts and packages used to prepare this document—as well as this document itself—are freely available from the Comprehensive TEX Archive Network (http://www.ctan.org/). Contents 1 Introduction 6 1.1 Document Usage . 6 1.2 Frequently Requested Symbols . 6 2 Body-text symbols 7 Table 1: LATEX 2ε Escapable “Special” Characters . 7 Table 2: Predefined LATEX 2ε Text-mode Commands . 7 Table 3: LATEX 2ε Commands Defined to Work in Both Math and Text Mode . 7 Table 4: AMS Commands Defined to Work in Both Math and Text Mode . 7 Table 5: Non-ASCII Letters (Excluding Accented Letters) . 8 Table 6: Letters Used to Typeset African Languages . 8 Table 7: Letters Used to Typeset Vietnamese . 8 Table 8: Punctuation Marks Not Found in OT1 . 8 Table 9: pifont Decorative Punctuation Marks . 8 Table 10: tipa Phonetic Symbols . 9 Table 11: tipx Phonetic Symbols . 10 Table 13: wsuipa Phonetic Symbols . 10 Table 14: wasysym Phonetic Symbols . 11 Table 15: phonetic Phonetic Symbols . 11 Table 16: t4phonet Phonetic Symbols . 12 Table 17: semtrans Transliteration Symbols . 12 Table 18: Text-mode Accents . 12 Table 19: tipa Text-mode Accents . 12 Table 20: extraipa Text-mode Accents . -
Answers Solving Problems Using Order of Operations
Solving Problems Using Order of Operations Name: Solve the following problems using the order of operations. Answers Step 1: Parenthesis () Solve all problems in parenthesis FIRST. 1. Step 2: Exponents 2,3,4 Next solve any numbers that have exponents. 2. Step 3: Multiply or Divide ×, ÷ Then solve any multiplication or division problems (going from left to right). Step 4: Add or Subtract +, - Finally solve any addition or subtraction problems (going from left to right). 3. 1) 21 ÷ 3 + (3 × 9) × 9 + 5 2) 18 ÷ 6 × (4 - 3) + 6 4. 5. 6. 7. 3) 14 - 8 + 3 + 8 × (24 ÷ 8) 4) 4 × 5 + (14 + 8) - 36 ÷ 9 8. 9. 10. 5) (17 - 7) × 6 + 2 + 56 - 8 6) (28 ÷ 4 ) + 3 + ( 10 - 8 ) × 5 7) 12 - 5 + 6 × 3 + 20 ÷ 4 8) 36 ÷ 9 + 48 - 10 ÷ 2 9) 10 + 8 × 90 ÷ 9 - 4 10) 8 × 3 + 70 ÷ 7 - 7 1-10 90 80 70 60 50 40 30 20 10 0 Math www.CommonCoreSheets.com 1 Solving Problems Using Order of Operations Name: Answer Key Solve the following problems using the order of operations. Answers Step 1: Parenthesis () Solve all problems in parenthesis FIRST. 1. 255 Step 2: Exponents 2,3,4 Next solve any numbers that have exponents. 2. 9 Step 3: Multiply or Divide ×, ÷ Then solve any multiplication or division problems (going from left to right). Step 4: Add or Subtract +, - Finally solve any addition or subtraction problems (going from left to right). 3. 33 1) 21 ÷ 3 + (3 × 9) × 9 + 5 2) 18 ÷ 6 × (4 - 3) + 6 4. -
About the Code Charts 24
The Unicode® Standard Version 13.0 – Core Specification To learn about the latest version of the Unicode Standard, see http://www.unicode.org/versions/latest/. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trade- mark claim, the designations have been printed with initial capital letters or in all capitals. Unicode and the Unicode Logo are registered trademarks of Unicode, Inc., in the United States and other countries. The authors and publisher have taken care in the preparation of this specification, but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein. The Unicode Character Database and other files are provided as-is by Unicode, Inc. No claims are made as to fitness for any particular purpose. No warranties of any kind are expressed or implied. The recipient agrees to determine applicability of information provided. © 2020 Unicode, Inc. All rights reserved. This publication is protected by copyright, and permission must be obtained from the publisher prior to any prohibited reproduction. For information regarding permissions, inquire at http://www.unicode.org/reporting.html. For information about the Unicode terms of use, please see http://www.unicode.org/copyright.html. The Unicode Standard / the Unicode Consortium; edited by the Unicode Consortium. — Version 13.0. Includes index. ISBN 978-1-936213-26-9 (http://www.unicode.org/versions/Unicode13.0.0/) 1. -
2. Recoding Variables in CREATE
01/06/98 2. Recoding Variables in CREATE 2.1 Overview This chapter covers the most common statements appearing in the recode section of the CREATE step. Additional statements and features are described in Volume III. Section 2.2 describes arithmetic assignment statements and elementary arithmetic operations in VPLX. In fact, they barely need introduction, since they are essentially identical to conventions of SAS and Fortran 90. Almost equally familiar are the functions in section 2.3, which may be used in arithmetic assignment statements. Section 2.4 introduces set assignment statements, which do not have a ready analogue in either SAS or Fortran (1). These statements are generally not required for simple applications, but they facilitate operations on a series of variables. Many aspects of the VPLX syntax employ the notion of sets, denoted by standard set notation, “{ }”. Section 2.5 describes conditional statements in VPLX. These statements follow almost identically the syntax of Fortran 90, including the enhancements to FORTRAN 77 (2) to allow use of symbols (“>”, “<”, etc.) expressing arithmetic relations. Section 2.6 describes the PRINT statement, which already appeared in examples in Chapter 1. For completeness, section 2.7 describes specialized functions, including MISSING. These functions are more complex than those in section 2.3 and are required less frequently. The reader may thus regard this section as optional. 2.2 Familiar Arithmetic Assignment Statements SAS, FORTRAN 77 (except for semicolons), and Fortran 90 (with optional semicolons) follow the same basic syntax for arithmetic assignment statements. Although there are some important differences between statements of a computer language and equations in conventional mathematical notation (3), generally the languages follow mathematics closely. -
Horadam Sequences: a Survey Update and Extension
Volume 80 BULLETIN of the May 2017 INSTITUTE of COMBINATORICS and its APPLICATIONS Editors-in-Chief: Marco Buratti, Don Kreher, Tran van Trung Boca Raton, Florida ISSN: 1183-1278 BULLETIN OF THE ICA Volume 80 (2017), Pages 99{118 Horadam Sequences: A Survey Update and Extension Peter J. Larcombe Department of Computing and Mathematics College of Engineering and Technology University of Derby Kedleston Road, Derby DE22 1GB, U.K. [email protected] Abstract We give an update on work relating to Horadam sequences that are generated by a general linear recurrence formula of order two. This article extends a first ever survey published in early 2013 in this Bulletin, and includes coverage of a new research area opened up in recent times. 1 Introduction 1.1 Preamble Looking back over time we can see that, within the vast and ill-defined field of applied mathematics, the advent of serious computing power in the 1970s began to accelerate a then already discernible breach between classic analytical mathematics (concentrating on problems and theories involving continuous phenomena) and that which tackled discrete concepts and en- tities. The latter has, over the last sixty years or so, developed its own characteristics and subject personality—aided en route by increased expo- sure to software tools/languages—and it is in this broad sphere of what 99 Accepted: 15 March 2017 is nowadays known as discrete mathematics that the theory of integer se- quences lies, with many applications now found in number theory and com- binatorics to name but two -
Chapter 6, Writing Systems and Punctuation
The Unicode® Standard Version 13.0 – Core Specification To learn about the latest version of the Unicode Standard, see http://www.unicode.org/versions/latest/. Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trade- mark claim, the designations have been printed with initial capital letters or in all capitals. Unicode and the Unicode Logo are registered trademarks of Unicode, Inc., in the United States and other countries. The authors and publisher have taken care in the preparation of this specification, but make no expressed or implied warranty of any kind and assume no responsibility for errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of the use of the information or programs contained herein. The Unicode Character Database and other files are provided as-is by Unicode, Inc. No claims are made as to fitness for any particular purpose. No warranties of any kind are expressed or implied. The recipient agrees to determine applicability of information provided. © 2020 Unicode, Inc. All rights reserved. This publication is protected by copyright, and permission must be obtained from the publisher prior to any prohibited reproduction. For information regarding permissions, inquire at http://www.unicode.org/reporting.html. For information about the Unicode terms of use, please see http://www.unicode.org/copyright.html. The Unicode Standard / the Unicode Consortium; edited by the Unicode Consortium. — Version 13.0. Includes index. ISBN 978-1-936213-26-9 (http://www.unicode.org/versions/Unicode13.0.0/) 1. -
Operator Precedence in Arithmetic1
Operator Precedence in Arithmetic1: Figure 1: ‘Arithmetic,’ can be defined as ‘[the science of] numbers, and the operations performed on numbers.’ 2 Introduction: Conventional Arithmetic possesses rules for the order of operations. Which operations ought we to evaluate first? In what order ought we to evaluate operations? This is the topic that this chapter wishes to address. ‘Precedence,’ is also sometimes referred to as ‘the order of operations.’ 1 The Etymology of the English mathematical term, ‘arithmetic,’ is as follows. The English adjective, ‘arithmetic,’ is derived from the Latin 1st-and-2nd-declension adjective, ‘arithmētica, arithmēticus, arithmēticum.’ Further, the Latin adjective, ‘arithmēticus,’ is derived from the Ancient-Greek phrase, ἀριθμητικὴ τέξνη or, when transliterated, ‘arithmētikḕ téchne,’ which means ‘the art of counting;’ ‘the skill of counting;’ ‘the science of counting.’ ὁ ἀριθμός genitive: τοῦ ἀριθμοῦ, or–when transliterated: ‘ho arithmós,’ genitive: ‘toũ arithmoũ,’–is a 2nd-declension Ancient-Greek noun that means ‘number,’ ‘numeral,’ Cf. ‘ἀριθμός#Ancient_Greek,’ Wiktionary (last modified: 7th September 2018, at 17:57.), https://en.wiktionary.org/wiki/ἀριθμός#Ancient_Greek , accessed 29th April 2019. 2 Cf. ‘arithmetic,’ Wiktionary (last modified: 25th April 2019, at 04:45.), https://en.wiktionary.org/wiki/arithmetic , accessed 29th April 2019. 1 | Page Body: The Etymological Definition of ‘Precedence:’ Our English noun, ‘precedence,’ is derived from the Latin substantive participle, ‘praecēdentia.3’ ‘Praecēdentia,’