# Week 2 Video Lessons

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• #28122
Pasyanthi
Keymaster

Happy VM learning 🙂

• #28164

Hi Ken,

Digit sum concept is really interesting and I would like to explore more.

I have few queries.

1. Are digit sum and casting out 9 based on any Vedic sutra(s)?

2. Do we have any other applications of digit sum other than verifying answers and divisibility checks?

3. Do we have any applications of number patterns and Vedic designs?

Thanks.

• #28175
KennethWilliams
Keymaster

Hi Mallika,
Thanks for the questions.
1. Finding a digit sum is based on ‘By Addition’, Sutra 7, and casting out 9s is based on Sutra 5: ‘If the Total is the Same it is Zero’.
2. You will see more applications. It can be used in algebra too and for finding a missing digit or coefficient.
3. Patterns are always useful as they lead to more general concepts and ways of extending them and seeing connections with other patterns. It has been said that mathematics is all about the study of patterns. Fot the Vedic Square designs I am not aware of applications other than the fun in generating patterns: someone should look into this 🙂

• #28165
Anupama Cherukuri
Participant

Hi Ken,
I have the same question do we use digit sum in any other applications?
For. Ex.999 – the answer is 9 or 0.
So if we use digit sum in any other applications how can we know which digit we have to use 9 or 0.

• #28176
KennethWilliams
Keymaster

Hi Anupama,
See my reply to Mallika above.
For 999 the digit sum is 9 or 0.
There are many other times that we get 2 or more answers to a mathematics question. For example in solving quadratic equations we generally get 2 solutions.
There will never be any contradiction in using either 9 or 0. Using either will give the same answer. It’s like saying the time is 1pm, or the time is 13:00 hours – they are equivalent.

• #28166
Maurice Perry
Participant

• #28177
KennethWilliams
Keymaster

Hi Maurice,
The other word used in that video was ‘chisenbop’. That too you can google to find out more.

• #28188
Maurice Perry
Participant

Thank you Ken. I wasn’t sure how to spell it.

• #28184
Satya
Participant

Hi Ken,

Thank you for providing more details about digit sums through this thread – Definitely an interesting and fun topic to learn. In the 2nd video during The Digit sum check, it was mentioned that the sum verification may not be correct always as altering placement of digits in the same number might give same digit sum but can change the actual answer like wrong answer can still give the same digit sum etc.

So how confidently can we use this method and why is this method considered to be used with this uncertainty?

Thanks
Satya

• #28240
KennethWilliams
Keymaster

Hi Satya,
It is still worth using the digit sum check. Together with checking the first and last digits it means we can usually be highly confident of a result if not absolutely certain. Thanks to Mallika for her comments.
We will soon see another digit sum checking device, based on 11 rather than 9.

• #28185

Thanks Ken for the clarification.

Yes, Patterns are very useful in analyzing, predicting, forecasting and in giving projections.

Thanks Ken for all your work and contributions in VM. VM has changed my son’s attitude towards maths. I can’t thank you enough for that.

• #28186

Hi Satya,

Even though digit sum checking doesn’t spot the error all the time, it is very handy. I have taught this to my 10 year old son. It has spotted errors many times especially in 4 digit by 4 digit multiplications. As 4 digit by 4 digit multiplication is not easy to verify answers using inverse (division) operation.

Thanks.

• #28187
Satya
Participant

got it. Thank you Mallika

• #28189
Savita P Kulkarni
Participant

Hi friends,
This week i was late in starting.
I just finished video 5 ( first video for week 2) and I had fun practicing the digit sums, casting nines, digit sum puzzels, and divisibility tests for 3, 9. 6, and 15, and remainder on division by 9.
Thanks to Mallika, Satya, Maurice, Anupama for starting interesting conversations here and to Mr. Ken for answering the querries and putting more light on patterns, applications on digit sums, providing alternate examples like 1:00pm is same as 13:00hours.
Thanks,

• #28217
Savita P Kulkarni
Participant

Hi,
After watching 6th video, I am amazed by the uses of digit sums and the different methods to check errors. i wonder if there is any connection between Vedic math/ Vedic design/square and rangoli wherein patterns, points, and lines make such wonderful and artistic designs, may be….
Thank you,
Savita

• #28236
Anupama Cherukuri
Participant

Thank you so much for explaining. After Lesson 6 I understood more clear way 0 or 9 there will be no contradiction to the solution.
In the Practice HW book color the Vedic grid I am just curious to know if there are any other observations.
My observation is all the digits except 3,6 and 9 … the digit repeats 6 times. For 3 and 6 – digit repeats 12 times and 9 repeated 18 times.

• #28237
Savita P Kulkarni
Participant

Mental multiplication seems difficult at first, but with practice it gets easier and it is fun to solve.I am going to read more about ‘chisenbop’, thank you Maurice for initiating the discussion about it.

• #28238
Shikha Dhingra
Participant

Hi!
Thanks everyone for their valuable inputs. I am really excited to learn about nine point circle, casting out nine and checking errors using digit sum method . It really saves a lot of time spent during rechecking. I also taught this method to my 12 year old .He told me to give me more practice questions so that he can use this method. The practice homework assignments provides ample practice of particular method.
Thanks

• #28241
KennethWilliams
Keymaster

Please note that there is a question missing in the Week 2 Test. This is:
Use doubling and halving to find: 35 x 74.

So please note that questions 14 and 15 refer to this doubling and halving method.

• #28242

Hi All,

I want to share my observations.

We can get a remainder on division by 3 using digit sum.

For division by 3 :

As we all know if the digit sum of a given number is 3 or 6 or 9, then the number is divisible by 3 and the remainder will be 0.

If the digit sum of a given number is less than 3, then the digit sum will be the remainder.
Examples :
28 divided by 3 = 9 rem 1, digit sum of 28 is 1 and remainder is also 1.
812 divided by 3 = 270 rem 2, digit sum of 812 is 2 and remainder is also 2.

If the digit sum of a given number is greater than 3, we have to repeatedly subtract 3 from the digit sum until the answer is less than 3 and that answer will be the remainder.
Examples :
25 divided by 3 = 8 rem 1, digit sum of 25 is 7 and if we subtract 3 twice from 7 we get remainder as 1.
98 divided by 3 = 32 rem 2, digit sum of 98 is 8 and if we subtract 3 twice from 8 we get remainder as 2.

This holds good for any number to get a remainder on division by 3 using digit sum.

I am checking if there are any patterns to get a remainder for division by 6 using digit sum but no luck so far.

Thanks.

• #28296
KennethWilliams
Keymaster

Very interesting Mallika. Your observations are correct.
I’m glad to see you are researching like this.

• #28293
Savita P Kulkarni
Participant

Hi Mr. Kenneth,
There was allowed second attempt for quiz 1 only. But for quiz 2, I am able to go for the second attempt. Shall I take it ? Is it allowed?
Thanks, have a good weekend,
Savita

• #28295
KennethWilliams
Keymaster

Hi Savita,
The Pasyanthi Team said there is only 1 attempt after test 1. So I suspect you would not be able to complete a 2nd attempt. Try it if you like. But as you say it will be the same questions.

• #28294
Savita P Kulkarni
Participant

The second attempt has the same questions.

• #28612
Fabio Zanatta
Participant

Hello everyone,

I have a question on Russian multiplication.

I understand the method as follow:

I consider the multiplication 8×6=48. The 8 (4th finger on the left hand) have 3 fingers at his left. The 6 (2nd finger on the right hand) have only 1 finger at his right. I sum 3+1=4 and I have the first result digit.

Now, I multiply 4×2=8 because the 8 is the 4th number and 6 is the 2nd and I obtain the second result digit.

This is correct?

• #28614
KennethWilliams
Keymaster

Hi Fabio,

The first part is ok: 3+1=4.

The 8 comes from 2×4 where 2 is the touching finger on the left and the one below it, and the 4 is the touching finger on the right plus the 3 fingers below that.

• #28615
Fabio Zanatta
Participant

Thanks mr. Ken for the answer.

• #28830
Amara Deepthi
Participant

Hi Ken,

I was doing the homework manual. In that Lesson 3, Practice E, 11th problem – the question says there are 5 two figure numbers below 40 whose digit sum is 1. Bu there are only 4 numbers – 10,19,28 and 37. Even in the answer they didn’t mention the 5th number. Kindly clarify.

Regards,

Deepthi

• #28831

I also noticed it. It has only 4 combinations. This could be a printing mistake.

• #28832
KennethWilliams
Keymaster

Hello Deepthi,

Well spotted !

You are right there are only 4 answers, not 5.

• #28858
Amara Deepthi
Participant

Thank you for the clarification Ken

• #28834

In Week 2 , lesson one-digit sum puzzle, What is the and for  the last qs please? digit sum=4, one is 3 times the other?

• #29894
Participant

Are there circumstances, such as in multiple digit addition, where the traditional Western approach of calculating right to left is superior, or would you recommend attempting to retrain and teach left to right for all calculating?

• #29896
KennethWilliams
Keymaster

Hi Seth,

I hope you are not thinking that in VM we only calculate from left to right, because that is not so. Both are useful and the Vedic mathematician chooses the best method at any time: right to left or left to right.

Certainly right to left is better sometimes, and educationally it makes sense to learn right to left first of all because we start with learning about units before tens and so on.

We do focus more on the left to right direction on this course, but that is because people are very familiar with right to left methods already. And as you will see there are many advantages of working that way.

• #29897
Participant

Thank you, Ken!

• #30812

Great questions above and I found answers I was also looking for.

Thanks everyone

• #30895
VenkatKoppaka
Participant

a2 b2

c1 b1

• #31133
Preeti Pathak
Participant

Hello,

Enjoyed week 2 videos lessons, digit sum concept, calculating from left to right .

In Vedic Maths ,we can calculate from left to right or right to left whichever we find  useful , is very helpful .Its flexible. In the beginning, calculating from  left to right seems difficult but after practicing ,we can do it in a better way.

Thanks

• #31153
UshaT
Participant

<sup>a2</sup>

Test message

<sub>b3</sub>

• #31154
UshaT
Participant

test message