MANUALS

• League for Soroban Education of Japan
• Manual (60 pages, 8.76 mb PDF File)
• Dave Bernazzani's Soroban/Abacus Handbook (18 pages, 281 kb PDF File)
• Jesús Cabrera: Jesús Cabrera, retired (astro)physicist, spent the better part of a year writing two Wikibooks and a 360 page PDF document called 'THE EASTERN ABACUS - A Guide to Bead Arithmetic.' Many thanks to Jesús for these wonderful contributions.
• THE EASTERN ABACUS - A Guide to Bead Arithmetic - 360 page pdf file
• Using an abacus - a Wikibook
• Traditional Abacus and Bead Arithmetic - a Wikibook

BASIC ARITHMETIC

• Edvaldo Siqueira: Professor Kato's method for Pre-determining the Decimal Place in problems of Division & Multiplication
• Division
• Multiplication
• Totton Heffelfinger:
• Multiplication and Decimals
• Division Revision
• Placing Quotient numbers
• Learning Basic Multiplication
• Digit Sum Quick Check - checking answers
• Further thoughts on Mechanization
• Japanese soroban finger techniques
• Predetermine a Unit Rod (an alternative)
• Shifting the Unit Rod

CHINESE DIVISION AND MULTIPLICATION

• Masaaki Murakami:
• Specially Crafted Division Tables
• His Soroban Trainer web app includes some traditional or Chinese division (kijoho) exercises . See below in Learning Resources.
• Totton Heffelfinger:
• The following techniques were taught to me by members of the Soroban/Abacus newsgroup. In particular, I'd like to thank Torsten Reincke whose contributions bring us all to a greater understanding and more thoughtful use of abacus.
• Multiplication Techniques
• Traditional Multiplication
• Modern Multiplication
• Division Techniques
• Traditional Short Division
• Traditional Long Division
• Shifting the Unit Rod
• Suan Pan and the Unit Rod - Multiplication
• Suan Pan and the Unit Rod - Division
• Chinese Division Rules on a Soroban
• Jesús Cabrera's Manual and Wikibook also deal with traditional multiplication and division.
• Masaaki Murakami's Soroban Trainer app includes some traditional or Chinese division (kijoho) exercises . See below in Learning Resources.

ADVANCED DIVISION AND MULTIPLICATION METHODS

• Totton Heffelfinger: Takashi Kojima Techniques
• The Elimination of the Initial Digit of a Multiplier Beginning with One
• Multiplication by Complementary Numbers
• Fernando Tejón: Techniques for multiplication problems having two or more multipliers Multifactorial Multiplication
• Steve Treadwell: Easy Division
• Hannu Hinkka: Russian Multiplication - an old technique that requires no multiplication tables.
• Fabrice Bouillerot: Fabrice shares his very interesting technique for using complementary numbers while solving problems of long division. Merci beaucoup, Fabrice. Division by Complementary Numbers (DCN)
• Masaaki Murakami:
• Division with Excessive Quotient
• Regressing Multiplier to the power of 10
• Multiplication with Excessive multiplicand
• masaaki shows us 6 techniques for multiplication - from the 1939 book 'Educating Soroban in Practice' by Gen'ichi Nikai
• Two techniques where the divisor begins with One
• Division by Complementary Numbers
• Milton Zuluaga: Milton shares a marvelous multiplication technique taught to him by the Cultural Attaché of the Chinese Embassy in Colombia (South América) back in 1996. Multiply 316 X 29 - this link will take you off site to Goggle Drive

THE OTHER SIDE; NEGATIVE NUMBERS

• Masaaki Murakami: The Other Side of Soroban- A guide to adding, subtracting, multiplying and dividing Negative Numbers
• Fernando Tejón: Techniques for using complementary numbers: one technique simplifies problems of subtraction; the other solves problems of subtraction where the resulting answer is a negative number. Complementary Numbers
• Totton Heffelfinger:
• Negative number tutorial  (0 - 95 = -95)
• Multiplying Negative numbers

ROOTS

• Edvaldo Siqueira: Professor Kato's method for extracting Square Roots
• Totton Heffelfinger:
• Takashi Kojima's method for extracting Square Roots
• The Square Root of 2 to seven decimal places
• Square Roots - Welton J. Crook
• Cube Roots - Welton J. Crook
• Shane Baggs: This is an excellent presentation of a very powerful technique for finding the cube root of a number. Many thanks to Shane for all of his hard work and research and for updating this method for all of us to use. Japanese Cube Root Algorithm
• Steve Treadwell:
• Modification to the Crook square root algorithm pdf
• Modification to the Crook cube root algorithm pdf
• Improvements to the Kato Square Root Method
• Masaaki Murakami: Square Root by Half Square with Kijoho. This JavaScript application will guide you, step by step, in solving square roots on the abacus by Prof. Kato's method and using Chinese division (kijoho). You can download it to your computer from its GitHub repository, or launch it directly into your browser from here.

LOGARITHMS

• Deji Adegbite: Thanks to Deji who's done an exceptional job in illustrating his techniques for calculating logarithms on a soroban.
• Calculating Logarithms on a Soroban
• Explanation of the technique

OTHER ARITHMETIC PROBLEMS

• Fernando Tejón: Methods for solving problems involving linear equations. Linear Equations
• Gary Flom:
• Euclidean norm of a vector
• Abacus Algebra - techniques for doing algebra on a soroban.
• Hannu Hinkka: Binary Method for Calculating GCD - an alternative to an earlier tutorial
• Joe VanCleave: Abacus Tax Calculation Procedure
• Dino Marcantonio: Thanks to Dino who has written two excellent tutorials showing us how to turn an abacus into a very powerful inch-foot calculator.
• Dino's Foot-Inch Calculator
• Multiply & Divide Fractions of an Inch
• Totton Heffelfinger:
• Cooking with Soroban
• Find the GCD and LCM of two numbers
• Magic Number Trick
• Working with Percentages

NON-DECIMAL ARITHMETIC

• Steve Treadwell:
• Balanced ternary arithmetic on the abacus.pdf
• Decimal/Binary Conversion on the Soroban.pdf
• Multiplication and Division in binary
• Octal Arithmetic on the Soroban
• Hexadecimal Arithmetic Octal Code
• Octal Hexadecimal Conversion
• Decimal Hexadecimal Conversion
• Hannu Hinkka:
• Using Hexadecimal Tables - Long Division and Conversion to Decimal
• Convert Octal to Hexadecimal - using an Octal Division Table
• Marcos Labriola: Marcos kindly shares these powerful techniques that illustrate how easy it is to alternate between Decimal, Binary and Octal number systems. Thank you Marcos.
• Conversion from Decimal to Binary
• Decimal & Octal Conversion Techniques
• Totton Heffelfinger:
• Converting Hexadecimal and base 10
• Add & Subtract Hexadecimal numbers
• Multiplying Hexadecimal Numbers, using an Octal Table
• Convert Hex to Decimal by Dividing by Hex A
• Adding Hexadecimal numbers using the Binary number system

TECHNIQUES FOR TRADITIONAL ABACUSES (OTHER THAN MODERN 4+1 TYPE)

• Hannu Hinkka: The Five Bead Advantage - demonstrating how a 5th earth bead has its advantages.
• Joe VanCleave: The Nine Bead Abacus, it's Theory and Derivation
• Jesús Cabrera: A Short Guide to the 5th (lower) bead In this excellent tutorial Jesús shows us how to efficiently make use of the 5th lower bead on a 1:5 bead soroban.
• Totton Heffelfinger:
• The following techniques were taught to me by members of the Soroban/Abacus newsgroup. In particular, I'd like to thank Torsten Reincke whose contributions bring us all to a greater understanding and more thoughtful use of abacus.
• Multiplication Techniques
• Traditional Multiplication
• Modern Multiplication
• Division Techniques
• Traditional Short Division
• Traditional Long Division
• Shifting the Unit Rod
• Suan Pan and the Unit Rod - Multiplication
• Suan Pan and the Unit Rod - Division
• The Leap of Faith
• Calculating Feet and Inches - base 12 & an inverted suan pan
• Jesús Cabrera's Manual and Wikibook also deal with the use of traditional abacuses.

ABACUS FILES

• Anzan (Mental Arithmetic):Two experts share their thoughts on the Abacus Method of Mental Calculation.
• Anzan by Yukio Tani.pdf - from the book The Magic Calculator - the way of the abacus
• Anzan by Takashi Kojima.pdf - from the book The Japanese Abacus - Its Use and Theory
• Multiplication - one method that some experts like to use.
• 25 anzan addition subtract  exercises with answers ( 340 kb .zip file)
• Print Abacus.pdf - Some experts recommend using this aide to help visualize an abacus. Place the printed abacus on the desk and visualize solving problems. It's important to actually move the fingers as if doing calculations on a real abacus.
•  
• Explanation of the two kanji characters that make up the word soroban.
  
• Master Craftsman: While the process of making soroban has become largely mechanical, here are 7 extraordinary YouTube videos showing a master craftsman hand crafting soroban. The narrator explains the process in Japanese but the videos need little or no explanation.  ▪ Link to the 7 YouTube videos
• Magazines and Periodicals
• The Abacus, in its Historic and Scientific Aspects (1.97 mb PDF File) - by Cargill G. Knott, D. Sc. [Edin.], F. R. S. E. [December 16th, 1885]
• Retyped version of Knott's article. Thanks to Nanami Kamimura and Fernando Ota for working to bring us this much easier to read alternative.
• Li (1959) Origins of Chinese Abacus  (735 kb PDF File) - appeared in the Journal of the ACM Volume 6, Issue 1, January 1959
• Stchoty Le Magasin Pittoresque 1839 p87&88 - two page French language, 19th century article about the Schoty. Sourced by Fernando Ota. Reference Gallica (Bibliothèque national de France)
• Early Calculation (5.61 mb PDF File) - off site link to very interesting 56 page article featuring many early calculating methods and devices. Thanks to both Ed Thelen and Michael R. Williams.