48 - Multiplication by Nine


ISSUE No. 48

A warm welcome to our new subscribers.
Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods. The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics. If you are working with Vedic Mathematics - teaching it or doing research - please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue or tell us about a course or talk you will be giving or have given.
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This issue's article is from Amy Kee in San Francisco who has come up with a neat way to extend the method of multiplying a single-digit number by nine, to multiplying a 2-digit number by nine. There is a diagram in this email, if you don't see it you can view it at our web site, www.vedicmaths.org, under newsletters.



For single digit multiplication we always mark the Number by folding the finger down as a
marker (as I refer to it as the "Bent Finger" or the "Bend"). In this example 3 x 9, the third
finger was bent. So the answer to the first digit is the # of fingers before the bend which is 2 and the second digit is the # of fingers after the bend which is 7, therefore the answer for 3 x 9 is 27.

For double digit multiplication we always mark the First Number by creating a space or "Vshape" (as I refer to it as the "Split"). In this example 38 x 9, a split is created between the third and fourth finger. The Second Number is mark by the Bend at the eighth finger. So the answer to the first digit is the # of fingers before the split which is 3 and the second digit is the # of fingers after the split and before the bend which is 4, and the third digit is the # of fingers after the bend which is 2, therefore the answer for 38 x 9 is 342.

Here is my new discovery on finger computation and the rule for the answer:

In this example 32 x 9, for the First Number "3" we marked it with a split created between the third and fourth finger. The Second Number "2" is marked by the Bend at the second finger. So the answer to the first digit is the # of fingers before the split which is 2 and the second digit is the # of fingers after the split and before the bend, so we have to also include the # of fingers on the left hand which is 1 (finger on left hand before the bend) + 7 (2 on left hand after the split and 5 on right hand) = 8, and the third digit is the # of fingers after the bend which is 8, therefore the answer for 32 x 9 is 288.

The rule is that when multiplying double digits by nine, using fingers only, you will always get a three digit answer. Please remember, you are counting from your left hand to your right hand with this rule. The first digit is the number of fingers standing before the split. The second digit is the number of fingers standing after the split and before the bent finger. In the case of a smaller second digit you will include the number of fingers standing before the bend on the hand or hands that were before the split. The third digit is the number of fingers standing after the bent finger.

Two more examples.

44 x 9 = 396
The split and the bend is at the fourth finger on left hand,
First digit is the 3 fingers standing before the split
Second digit is the 3 fingers before the bend plus 1 finger after the split on the left hand and the 5 fingers on the right hand.
Third digit is the 6 fingers after the bend ( left thumb and 5 fingers on right hand).

87 x 9 = 783
The split is at the eighth (middle) and ninth (ring) finger and bend is at the seventh (index) finger on the right hand.
First digit is the 5 fingers on the left hand and 2 fingers standing before the split on the right hand.
Second digit is the 5 fingers on the left hand and the 1 finger standing before the bend and 2 fingers after the split on the right hand .
Third digit is the 3 fingers after the bend on the right hand.





This is an introductory course taken entirely over the internet. The course "An Introduction to Vedic Math" is available at the Vedic Math School:
It consists of 31 exercises, over 8 chapters, which can be taken on-line and the exercises are also marked for you on-line. There are many relevant puzzles too. A certificate is awarded for successful completion. For more details go to the Vedic Math School website, where you will need to first register with the School and then enroll for the course. The course fee, $10, has been kept low to make it accessible to as many people as possible.


This will follow the current course which is still in progress. It is on "Chase of transcendental fields and enlightenment state". More information later.


Dr Narinder Puri (well known VM expert in India) from Roorkee was invited by the Chairman, Rajasthan Board of Secondary Education, Civil Lines, Ajmer, Rajasthan to conduct programs for teachers' training. This was a result of the recent announcement made by the Education Minister of Rajasthan, Mr Ghanshyam Tiwari in one of the local T.V channels that Vedic Maths will be introduced at school level in standard 9th & 10th.


We have been developing an interactive internet course for teaching Vedic Mathematics based on some of the books by Kenneth Williams.

Currently this has reached a stage where we can demonstrate a working prototype of part of the course.

Development of this project is currently very slow. This is due to only being able to cope with so much extra work in our spare time. Therefore we are looking for a Business Angel or partner to help fund our wages and the costs of hosting the site properly, so that development of this material can proceed at a faster rate.

The partner will entitled to a share in the earnings from running the course. We are not interested in transferring ownership of the course material in any way, shape or form.

Currently we are developing material based on the books by Kenneth Williams, but will consider adjusting the development if the partner has some specific requirements e.g. the partner is an educational body and has a particular educational curriculum they need to conform to.

Please be aware that the costs for this will be based on supporting both Clive Middleton and Kenneth Williams, who are both based in the United Kingdom.

If you are seriously interested in supporting this project, then please contact for further information and a demonstration of some of the course material produced so far.


Here is a method of multiplying two 2-figure numbers that both end in 5. It is from Jim Myers of San Antonio, Texas, USA.

45 * 25
The digit value of the answer of course is always 5.
If sum of numbers to left of the 5s (in this case 4 and 2) is even, the 10's value is 2; if odd, the value is 7. Hence, 25 or 75 respectively.
The only numbers of importance are the number to the left of the 5s.
In this case, multiply the 4 by the 2 and add half their sum (ignore remainder, if any) to the product, e.g., (4 * 2) + ((4 + 2) / 2) = 11. Answer is 1125.

45 * 35
(4 * 3) + ((4 + 3) / 2) = 15 - the sum is odd, hence 7 in the 10s position. Answer is 1575.

115 * 35
(11 * 3) + ((11 + 3) / 2) = 40. Answer is 4025.


This course consists of three textbooks, a Teacher's Guide and an Answer Book and is aimed at 11-14 year old pupils. It has now been re-published with larger text and colour. The prices of the books for this course are very low and this is an ideal opportunity for a teacher to introduce Vedic Mathematics into their school. You can see all the details at the publisher's web site at www.mlbd.com. If you would like us to place an order for you we will be pleased to do so or assist. Or we can get the books for you and only charge you the cost price: email us at .


Each of these Newsletters starts with a main article and an index of these is now available at www.vedicmaths.org



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Editor: Kenneth Williams

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20th October 2005


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