# Advanced abacus theory and practice pdf

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- Japanese Abacus Use & Theory (English Edition) Takashi Kojima
- Advanced Abacus : Japanese Theory and Practice
- Rainey's Improved Abacus: An Explanatory Treatise on the Theory and Practice ...
- The Japanese Soroban: A Brief History and Comments on its Educational Role

## Japanese Abacus Use & Theory (English Edition) Takashi Kojima

To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies.

To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Philemon Sackey. Download PDF. A short summary of this paper. The Abacus is one of the worlds first real calculating tools -and early forms of an Abacus are nearly years old.

The word Abacus is derived from the Greek "Abax" meaning counting board and the original types of Abacus were stone slates with dust covering them and a stylus used for marking numbers.

Later this evolved into a slate with groves where rocks or other counters would be placed to mark numbers. Later it finally evolved into a framed device with beads sliding along bamboo rods. I have always been fascinated by the abacus -and have recently taken up the study of this tool. The modern Chinese abacus has been in use since about the 14th century. The Japanese Soroban has been in use since at least the 16th century.

I much prefer the Japanese Soroban as a more aesthetically pleasing and a more efficient calculating instrument. There are some key differences between the two types of instruments. Here is a picture of a traditional Chinese Abacus. As you can see this instrument has 2 beads above the reckoning bar and 5 beads below it.

I will try to instruct and teach only the best methods that I have found. Generally, these are the methods described by Takashi Kojima in his excellent book "The Japanese Abacus -It's Use and Theory" published first in the 's and later reprinted. I assume the reader wants to know the best prescribed procedures for learning how to use the abacus. I will try to take no shortcuts -and hope that this handbook serves as a fine introduction to the marvelous world of the Abacus.

One might ask why anyone should bother learning how to use the Abacus with the advent of such cheap calculators. The answers will be different for everyone -but for me it was a desire to learn and understand this ancient skill and to become skilled myself with this fascinating tool.

I also find the practice on the Soroban very relaxing -often helping me unwind after a day at work. I suppose it is as much a hobby as anything else. With practice and the help of this handbook, you can master the Abacus! If you don't have an instrument, you can find proven suggestions at the end of this handbook for tracking one down or making one yourself! The resulting frame looks like: This is the number We are almost done!

Just a final digit to add -the "9". So we "Add 9" to the unit rod H. Again, we don't have enough beads to do this with rod H so we must "Subtract 1" and "Add 10". To subtract 1, where we already have a value of 5, we must move away the heaven bead and move the four earth beads to the reckoning bar essentially "Subtract 5", "Add 4" on this rod.

Only after we deal with the unit rod H should we "Add 10" which is accomplished by going to Rod G and adding a single earth bead. When performing addition, always deal with the current rod first -and then if there is a carry move up a single bead on the rod to the left.

These are very essential concepts when adding! A problem like this may seem strange or even awkward at first -but with a bit of practice, you should be able to work a problem like this in just a few seconds. Even faster and more accurately than you might be able to do it on paper! Instead of having to deal with a possible carry in the 10's digit next rod to the left , you now deal with a possible borrow on that same rod.

In general, with subtraction you still work the problem and numbers from left to right -just deal with one rod at a time. If there are enough beads that "have value" on the current rod you can just subtract the desired number.

If you don't have enough beads with value -you must first subtract 10 by losing one beads worth of value on the rod to the left of the one you are working on and then add on your current rod to make up the difference. We will give some concrete examples to show how easy this is. Let us take the number 47 Place 47 :And let's subtract off First we start on Rod G and "Subtract 2" which is easily accomplished by moving 2 earth beads away from the reckoning bar.

We now have the value 27 not the final answer yet : Now we move on to the units rod H and "Subtract 1" by moving a single earth bead away from the reckoning bar. This yields us our final answer of Now let's subtract 4 from this. We can go right to the units rod and "Subtract 4" except that there are not enough single earth beads worth 1 each to subtract 4 so instead we must "Subtract 5, Add 1" to give us the same effect.

Here we move a single heaven bead worth 5 away from the reckoning bar and move a single earth bead worth 1 up to the reckoning bar to accomplish this. We now have our final answer of 22 which is the result of :Now we show how to borrow. Let's take the 22 on the frame and subtract off First we start with rod G and "Subtract 1" which is easy. Our result not yet the final answer is:Now we must "Subtract 4" from our unit rod H.

But we don't have 4 worth of beads to subtract on this rod -so instead we must "Subtract 10, Add 6" to produce the same result. To accomplish this, we subtract a single earth bead from rod G effectively "Subtract 10" since rod G has 10 times the value with respect to rod H which we are working with and then we "Add 6" to rod H here we need to move both a Heaven bead and an Earth bead towards the reckoning to accomplish the "Add 6".

This results in a frame with 8 which is our answer! However, it is not very convenient to do 23 separate adds on the number 47 just to give us the answer to 23x47! Therefore, there are specific techniques for performing multiplication on the abacus frame.

I've learned two different methods and know there are probably others as well -but I will teach only the method that was approved by the Japan Abacus Committee. I have found that this method is least prone to errors and is very simple once you learn the basic technique. Let's say you are given a problem like 23x The number 23 is called the multiplicand and the number 47 is called the multiplier.

In general you place the multiplicand here 23 near the center of the frame -and keep the last digit on a unit rod marked with a dot to help keep your place especially important in multiplication. Then enter the multiplier here 47 to the left of this number -skipping two clear rods going to the left do not worry if this number falls properly on a unit dot -it's not necessary. Now you have both numbers on the frame. In the method I will describe you will be producing the answer just to the immediate right of the multiplicand the number in the middle of your abacus frame.

When we are done -the multiplicand will be gone and the answer will remain along with the multiplier still to the left. Lets place the 23 and 47 on the frame as we described above except that I am only going to skip one blank column rod to conserve space in the diagrams! Some prefer skipping just one column and you might have to do it if you have a small abacus -but generally it is better to skip two full columns :Now we are ready to multiply.

It's similar to how you would work it on paper -except that the order of multiplication is a bit different and should be followed exactly as I outline here. First you work mostly with the multiplier.

You take the right-most digit of the multiplier in this case a '3' and you multiply it by the left-most digit of the multiplicand in this case a '4'. The result is 12 -and so you add on the frame in the two rods to the right of the multiplicand in this case FG. Since rods FG have no value, it's just a simple matter of "Add 1" to F and "Add 2" to G to produce the following frame: Now we multiply the same multiplier digit '3' against the next multiplicand digit '7' and put that result on GH since we last left off at G with the last multiplication result.

Simple enough and here is the resulting frame:Now we are done with the first digit of the multiplier and so we must clear it from the frame -we simple clear the '3' off rod F. We will use this rod if there are more numbers in the multiplier left and in this case there is another number left! Now we move on to the next digit of the multiplier -in this case the '2'.

We multiply this times the left-most digit of the multiplicand just as we did above for the first digit of the multiplier. Important note -the result of 2x4 is a single digit 8 -but enter this as 08 so that you always use up 2 rods so you are technically doing: "Add 0" on E followed by "Add 8" on F.

The resulting frame looks like:We are almost done -we just need to multiply the '2' times the remaining multiplicand digit of '7' and add the result of 14 to rods FG remember we pick up where we left off so long as we haven't moved on to a new multiplier digit.

In this case we "Add 1" to F which requires a carry to E which you should already know how to do from the addition examples. And then you "Add 4" to G. You clear off the multiplier digit '2' which has now been processed and see that there are no more multiplier digits left if there were, you just repeat the above processing. No matter how many digits you multiply, just apply the technique above and remember to work on the correct rod and it will go smoothly.

For me at least, division was a little intimidating. As it turns out Dave was right when he said, "Trust me. It's not that hard! It might be helpful to think of division as being nothing more than a series of subtractions The techniques I use below are pretty much as they are described in "The Japanese Abacus -It's Use and Theory" by Takashi Kojima.

Earlier in the handbook Dave wrote about the importance of the Unit rod. Unit rods are those rods marked with a dot. Unit rods seem particularly important in solving problems of division because the resulting quotient is often not a perfect whole number. In other words it forms a decimal.

Because of this you should plan ahead and set up the problem on your abacus so that the unit number in the quotient falls on a unit rod. Also, in order to help you keep track of your calculations it is a good idea to set the unit number of your dividend on to a unit rod. As for the divisor, if it's a whole number it doesn't seem to matter much whether it follows any such rule. Normally when setting up division problems on the abacus the dividend is set a little to the right of center and the divisor is set to the left.

## Advanced Abacus : Japanese Theory and Practice

Students will be able to represent quantities and solve mathematical computations using a. Russian abacus, Students will explore Russian American history through a variety of activities. Russians arrived they brought with them their religion language and culture to share with the. American Company kept extensive business records using the s chyoty or Russian abacus The. Innocent established a residence and seminary in Sitka He also created an elementary school in. House was restored to its appearance by the National Park Service and is cared for by Sitka. National Historical Park today This special building is one of only three or four Russian.

[PDF] Advanced Abacus: Theory and Practice EPUb by Takashi Kojima. BErsamaKAboiNETR - Read and download Takashi Kojima's book Advanced.

## Rainey's Improved Abacus: An Explanatory Treatise on the Theory and Practice ...

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Published by Charles E. Tuttle in Rutland, Vt. Written in English. Thanks to an attentive, professional teacher and director, our son goes for abacus classes and even school with great pleasure! In the center, he fell in love with mathematics, developed a good memory, and most valuable is that now he is not afraid of mathematics, and even become more confident in.

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### The Japanese Soroban: A Brief History and Comments on its Educational Role

Abacus mental arithmetic involves the skilled acquisition of a set of gestures representing mathematical algorithms to properly manipulate an imaginary abacus. The present study examined how the beneficial effect of abacus co-thought gestures varied at different skill and problem difficulty levels. We adopted a mixed-subject design, with level of difficulty and skill level as the within-subject independent variables and condition as the between-subject independent variable. Our results showed a clear contrast in calculation performance and gesture accuracy among learners at different skill levels. Learners first mastered how to calculate using a physical abacus and later benefitted from using abacus gestures to aid mental arithmetic. Hand movement and gesture accuracy indicated that the beneficial effect of gestures may be related to motor learning.

To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Philemon Sackey.

isoBenIng - Read and download Takashi Kojima's book Advanced Abacus: Theory and Practice in PDF, EPub online. Free Advanced Abacus: Theory.

#### Program Details

Mental Abacus Book 2 focuses on advanced abacus topics, and it is a complete learning package on multiplication and division. Every concept and technique involved is explained thoroughly with plenty of examples and various diagrams. Advanced concepts, theories and techniques are explained not only by plain words, but also with massive illustrations. Numerous examples with demonstration further strengthen the study effectiveness. Just enter any multiplication or division equation, Abaculator will show you every step with detailed description and explanation.

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. About About this book Chapters Table of contents 35 chapters About this book Introduction A Computer Science Reader covers the entire field of computing, from its technological status through its social, economic and political significance. The book's clearly written selections represent the best of what has been published in the first three-and-a-half years of ABACUS , Springer-Verlag's internatioanl quarterly journal for computing professionals. Among the articles included are: - U. Bigelow - Programmers: The Amateur vs.