# MyReckonings.com

## Dead Reckoning: Calculating Without Instruments

Chapter 2: Primitives

Background and Topics

This chapter describes techniques related to multiplication, division and repeating decimals, greatest common divisor (GCD), error-checking and divisibility tests, and factoring numbers.

Notes and Errata (If you have any more to contribute, please email me! This is a compendium of feedback)  A printer-friendly summary table for all chapters is found here.

Hey, why are the Errata and Notes for Chapter 2 so long?

First, the Notes are good things--they offer additional information. Chapter 2 is by far the most fact-filled chapter of them all, and it makes up over a third of the book.  There are many statements per page--it is the most concise chapter of a book that is fairly terse overall.  Typos have occurred that do not affect the validity of the methods but are pointed out here.  The errors are mostly mistakes in examples that may mislead the reader, not errors in the methods.  A few errors were carried over from primary references, and some of the errors and typos were corrected in galley proofs but did not appear in the final layout. I've tried to be as thorough as possible in providing this errata. Finally, this book was written prior to the web, and I did not have the much-appreciated resources of all of you to review the book!

 Color Code Type Meaning Note A clarification or elaboration of the text. Typo A simple mistake that does not affect the method presented. Error An error that may affect a method or the reader interpretation of it.

Additional Materials Related to Topics in This Chapter

Developing a "Number Sense" through Mental Multiplication: Mental multiplication is an excellent way to develop an appreciation for the properties and relationships of numbers, sometimes called a number sense.  This extensive paper describes simpler methods of multiplying numbers for newcomers to this field that can also be taught to children, as well as more complex methods that may be new even to those with a long interest in this area.  A section on squaring numbers, a popular subject, is also included.  The paper is available here.

Mental Calculation Class Handout: In 2005 I gave a talk to 4th and 5th graders on mental calculation methods for addition, subtraction and multiplication. I prepared a double-sided handout sheet for the kids to keep as a reference. I later added an additional sheet that would be appropriate for older students who understood algebraic notation. I've attached the three pages here. Although this is meant to one component of a talk, the reference sheets can provide a more readable overview than the book. It shows diagrams in a few cases and includes a number of examples. It is useful generally for adults as well. I hope that readers here will find it personally useful, and I'm happy if teachers want to discuss and distribute it in their classrooms. While the methods are not at all original, the presentation is, and I would appreciate it if it were not generally published, as I am available for talks and this represents some of my material (hence the copyright notice at the top).

A Method for 4x4 Digit Mental Multiplications: A few years ago I wrote a long post to the Yahoo Mental Calculation Group on a convenient method of mentally calculating a 4-digit by 4-digit multiplication. I have polished it into a paper that is available here.

Cited Reference Materials

In the near future, this section will contain relevant sections of some of the references cited at the end of this chapter.