Issue 138 - The Case For Bar Numbers

Vedic Mathematics Newsletter No. 138

A warm welcome to our new subscribers.

This issue’s article is titled THE CASE FOR BAR NUMBERS and describes the advantages of using bar numbers. “This equivalence between numbers and polynomials means that whatever manipulations and combinations we apply to numbers can be applied similarly to polynomials, and vice versa.”





This describes the eventful year that the IAVM has had, and those planned for the coming year.

Find it here.



This will take place on June 8th and 9th and will be organised by the IAVM.



A new development is taking place in Ireland which might be of interest to the VM community. We are about to begin making plans to develop the ability to practice the techniques of mental arithmetic through our own mother tongue.

We have a long tradition of mental mathematics but like everywhere else this knowledge is being lost, due to the ubiquitous availability of smart phones and other calculating devices. So far the educational authorities in Ireland have not responded to the opportunity to promote Vedic mathematics within the formal education system. However there is one possibility for its promotion and that is to adapt the knowledge into Irish.

The idea here is to establish a number of workshops to actively redevelop the language of mental computation as a means of unifying concepts from Vedic mathematics, modern computation and concepts based on the traditional knowledge of Ireland. This project is still at an early stage and it will be necessary to obtain some form of sponsorship and support from some of the language organisations in Ireland.

Wish us well!

Brian has started a Facebook Group to give some ideas:



Dr S.K. Kapoor is describing the internal formats of this important text in a series of articles. These will be gradually uploaded here under the heading ‘Phase 5’:



I have a dyslexic student called Keya who came to me in class 5 with absolutely  no arithmetic at all. I worked with her for 10 months , supported by her stepfather who did the practice work with her.  we kept in touch even though I was not teaching her . when she was ready for high  I asked her Mother if I could teach her again as I was afraid that by just doing the school maths she would lose her patterning work which is what sustained her. 

So I taught her once a week all last year. She came second in her year in the school exam but more importantly we have made great strides with our work. I gave her your videos which she loved and we accomplished Stairway Step I . I also gave her Sawyer's introduction to algebra which Mum is doing with the two girls. This year we began Stairway book 2 .She can now see the cube root of a six digit perfect cube and can cube all numbers up to 100 mentally . We are proceeding rapidly towards the duplex work and I shall take Crowning Gem for her next week. she is 13 years old .She has a formal diagnosis of extreme dyslexia and has Irlin's syndrome. Her love and enthusiasm  for Vedic mathematics is intense to say the least. 

So I am telling you this story because I have always maintained that Dyslexics can accomplish in V.M, But and I say but, they need the foundation of Pebble Maths .

I am also teaching a class 4 at our local Steiner School. Approximately one third of the class are special needs children and they had no maths at all when I started with them 2 weeks ago. I collected pebbles for them so each child had a bag of 19 and we began. They loved it and quite a few children asked the teacher if I could come back. Last week I did zig zag and number partners for 10 which was challenging . However after the lesson two boys came up to me full of joy and told me that they understood everything and it is so easy .  Now I think they both have Asperger's and in my experience these children do very well with the pebble work even though they can’t understand the school way. Again they are verry suited for Vedic Maths. My fervent hope is that the whole class will be able to accomplish the basics at least of add subtract multiply and divide by the end of the year after which, if I am still able to work with them I shall introduce Vedic work. 

The video series are selling well and are mainly bought by parents of children who cannot understand anything at school.

I am so grateful for all the support that you have given me over the years and I am seeing the benefits in these young ones who would not have a chance without the beauty of everyone’s efforts. 

Vera’s website is here:



This new publication by Kenneth Williams follows on from Book 1.

See details including Contents and Illustrative Examples here.




Please note the bar digits in the article below are written with the bar under the number (the bar is normally written on top).

Kenneth Williams

The idea behind bar numbers is one we use in everyday life since we tend to seek the most efficient solution for every task. In mathematics we make use of the nearest base. When subtracting 19 from some number. For example, we would most likely subtract 20 and add 1 back on.

Or, if we have to add 2 hours and 55 minutes to the current time, we will most likely add 3 hours and subtract 5 minutes.

In the Vedic system we allow the possibility of negative digits. We might write 21, in which the 2 is two 10s, as usual, but the 1 with a bar under it means -1.

So, 21 is the same as 19, but without the large digit, 9.

This is the most efficient way to indicate a digit is negative. And any digit or group of digits in a number could be negative. It also means that a number can have many representations, not just one, so the adept student can alter a number to an equivalent form for their own convenience.

Similarly, ‘eleven minutes to three’ can be written as 311:  instead of 2:49. Both are perfectly valid.

The term ‘bar numbers’ refers to any number in which at least one digit is negative.


This does mean that time must be devoted to teaching this topic, but the advantages far outweigh this.

Some other consequences of a system that uses bar digits are:

  • digits 6, 7, 8, 9 can always be removed from a number, if we wish,
  • 0 and 1, which are especially easy to work with, appear twice as frequently,
  • in calculations, numbers tend to cancel each other out,
  • and this also gives us great flexibility and therefore more control over calculations.


Now consider polynomials, like say 2x2 + 3x + 4.

The coefficients (2, 3, 4 here) of a polynomial are not restricted to being positive, or to being single digit numbers.

We could have, for example, 2x2 – 13x – 1, in which some terms are negative.

But, as we know, when it comes to numbers we do not allow negative digits, or values over 9. This is an unnecessary restriction.

So, 2x2 + 3x + 4 is instantly translatable to 234 when x = 10.

But 2x2 – 3x + 4 would require some work to evaluate: when it can easily be written as 2 4.

This equivalence between numbers and polynomials means that whatever manipulations and combinations we apply to numbers can be applied similarly to polynomials, and vice versa.

Nor is this restricted to the cases where x = 10.

Just as 2345 means the number 234 in base 5,
234x is exactly equivalent to 2x2 + 3x + 4.

End of article.


Your comments about this Newsletter are invited.

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Editor: Kenneth Williams

The Vedic Mathematics web site is at:


18th February 2024


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