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Hey guys, I am Sriram. I love working around numbers.
I started Mental Math book and I have a small question. I feel DS method is faster and easier than DD method. But how do you know when DS method isn’t correct and when to use DD method.
Hi Sriram,
Welcome to the community.
The DS Method is used when you need to check your answer quickly. You will be able to check the answer with 90% accuracy if you use the DS method.
The only way to know if the DS method is not correct is to double check your answer with the DD method.
Hope this helps.
The DD method will catch decimal point placement and number transposition errors. For example, as the videos say, if you write 16.1 / 7 = 23, then the DD method will produce 1 instead of 10, while the DS method won’t catch it. Then, if you write 242 instead of 224, the DS method will provide the same answer for each, while the DD method won’t.
But I do have a question myself. Where would the DS method catch something that the DD method wouldn’t? The lecture videos didn’t say in that section.
Hi Areadien,
As far as I know, there is no scenario where the DD method will fail where the DS method succeeds.
The DD method is more accurate than DS Method. You can be sure 90% of the time with the DS method. However, with the DD method, you will have more than 95% certain.
We still cover the DS method because it is a lot faster to do than the DD method.
Actually, I came up with one. I multiplied 35 * 67 and got 2455 instead of 2345, and I knew it was wrong only because of the DS method.
So the DS method will fail where the DD method succeeds when the correct answer is added to a non-zero multiple of 11 that is not a also a multiple of 9. So coming up with 3335 would have made the DS and DD methods both succeed, but the answer would have been wrong.
Hi Areadien,
Yes, you are right. Both methods are not 100%. They are meant to check your answer with a reasonable level of accuracy but there will always be cases where they don’t catch the error.
I’ve just read 2 chapters of this book, where I have looked at the DS & DD Method of Checking which is intriguing.
However, they don’t seem to be very accurate.
I have found another example that contradicts what was mentioned in chapter 2.
If you do 16 x 15 = 2.40 (which is incorrect because the right answer should be 240).
Both the DD and DS method say the answer is correct. In Chapter 2, it says that the DD method should catch out scenarios where the decimal place is in the wrong place. Am I missing something here?
I would like to know where does the DD/DS method originate from? Do they have mathematical proofs to show the error rate in their usage?
Just to add onto my last comment, I’m finding several examples of where the DS method is just wrong.
Taking the same equation 15 x 16 = 240.
When applying the DS method on the left-hand side you get a 6 x 7 = 42 = 6 (when taking the digit sum)
Here are a number of different examples of where there is an incorrect answer but the DS method says it is correct (i.e. digit sum of right-hand side = 6)
- 15 x 16 = 339
- 15 x 16 = 42342
- 15 x 16 = 4542
- 15 x 16 = 402
- 15 x 16 = 204
- 15 x 16 = 222
- 15 x 16 = 15
- 15 x 16 = 132
- 15 x 16 = 123
- 15 x 16 = 321
- 15 x 16 = 33
- 15 x 16 = 42
- 15 x 16 = 96
This doesn’t look like 90% accuracy to me. Please let me know your thoughts.
Both DS and DD methods are simple checks to quickly verify your answer without having to do the calculation again.
The only way to be 100% sure that you have the right answer is to do the calculation again.
The only time that the DS method will fail is if the Digit Sum of the incorrect answer matches the Digit Sum of the Right answer.
7 x 6 = 42 (DS is 6).
So 15 x 16 should have DS 6 on both sides.
However if you calculate incorrectly and the incorrect answer also has then digit sum 6 then the DS method will fail.
The probability of that happening is approximately 10% of the time. It is exactly around 11.11% of the time. The remaining 88.88% of the time (approximately 90%) it should correctly identify the mistake.
How do we calculate this probability?
The incorrect answers digit sum can be between 1 to 9. The digit sum will identify the error 8 out of 9 times. But 1 out of 9 times it will match with the correct answer digit sum.
So 8/9 = 88.88% (approximately 90%) the DS method will identify the error. But 1/9 times it will fail.
In the example 15 x 16, the DS method will fail if the incorrect answer has DS 6. But it won’t fail if the answer has DS between 1 to 5 and 7 to 9.
DD method has a similar error rate. However since the methods use different computations usually what fails in one method should be caught in the other method. However there are going to be exceptions where both methods fail.
Both these methods are meant to be simple quick checks and nothing is going to replace doing the calculation again which is the only way I know of to get 100% accuracy.
Hope this clarifies.
I am through seven chapters. I tried this number 8396*11= 92356.
When I tried DD method to check, it seems to not work. 9-8 (O-E) * 0(1-1)= (2) 9-7.
I understand that there might be some exceptions but just wanted to be sure whether this comes under exception or a silly mistake of mine.
Thanks in advance
To check 8396 x 11 = 92356 using the DD Method
Here are the steps:
DD of 8396 is:
= Odd Digits – Even Digits
= (6+3) – (9 + 8)
= 9 – 17 = -8
If DD is negative we must add +11 so
= -8 + 11 = 3
DD of 11 is 0 (1 -1)
DD of 92356 is:
= (6+3+9) – (5 + 2)
= 18 – 7
= 11
11 is a two digit number. So we calculate the digit difference of that again and we get 0.
So the calculation is correct
3 x 0 = 0
Hope this clarifies.
Yes, it does! thanks a lot.
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