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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.
Yeah the Math Palace method might seem challenging at first but this is the same method being used by Memory Champions to remember 1000+ digit numbers in record time.If you are rounding up and calculating you can use 4 or 5 memory palaces if you want. You can use two additional memory palaces one for the rounded up number and another for the amount you rounded up by. But usually you can just remember the rounded up number without any memory palace and you don’t have to remember the original number you rounded up to do the calculation.Let us take the example 503,401 – 398,972 = ???We can round up 398,972 to 400,000. Amount rounded up is 1028.You don’t have to use the number 398,972 again in your calculation so you don’t have to use a math palace to remember 398,972.The new calculation is 503,401 – 400,000 + 1028.You use a math palace just to remember 503,401 and 1028 as they are the main numbers in the calculation.Hope this answers your question.Welcome to the community John.
Feel free to post your questions in this community as you work your way through the book.
Hi C,
I prepared for case study interviews myself. Originally I was trying to get into Management Consulting (McKinsey, Bain), then somehow I got into analytics which also required the use of case studies.
I would suggest you post this question in Management Consulting Facebook groups. You will surely find someone there.
Hi Mathew,
Did your ISP list any reason for the block? I will try to resolve it from my end.
Sorry for the late reply. I was on vacation but looks like you figured it out.
The method in the book is just to round up to the nearest multiple of 10, 100 or 1000.
In your question 5492 = 8000 – ____, the nearest multiple of 5492 is actually 6000 not 8000.
So 5492 = 6000 – 508.
If you want to round up to the next multiple of 1000 which is 7000 then you add 1000 to 508 to get 1508.
If you want to round up to 8000 then you need to add 2 x 1000 = 2000.
You can subtract the first digit of both numbers and then subtract the difference by one.
In 5492 = 8000 – _____
8 – 5 – 1 = 2
9 – 4 = 5
9 – 9 = 0
10 – 2 = 8
So the rounded up number is 2508
5492 = 8000 – 2508
Hope this provides more clarity.
Welcome to the community.
Hope you and your family are safe during these difficult times.
Are you transitioning to online teaching? You will find that you can make a bigger impact for the same effort when you harness technology and teach online.
When are you getting yourself a golden retriever? ?
Just be careful about how you approach that one Yassine.
Waking up early not really a habit itself. It is actually the outcome of other good habits like going to bed at the same time everyday and getting enough sleep.
What you are looking for is the XIRR formula. It’s easiest to calculate this in excel.
You can also check in this online calculator below:
https://www.calculator.net/investment-calculator.html?ctype=endamount&ctargetamountv=1000000&cstartingprinciplev=200&cyearsv=25&cinterestratev=10&ccontributeamountv=200&ciadditionat1=monthly&printit=0&x=63&y=25Welcome to the community Yassine.
What habits are you looking to develop?
We are here to help you. ?
Welcome to the community Yassine.
What habits are you looking to develop?
We are here to help you if you need any help.
Welcome to the community.
I hope you enjoy reading it. Feel free to ask any questions you have in the community.
I would recommend you use the Bridge or the Vitruvian man method for 3 digit multipliers to reduce the cognitive load.
UT Method is recommended for two digit multipliers. However it is still possible to do the UT method with the a 3 digit multiplier.
Here is the illustration of the Method
If you want to multiply 6671 × 386 here are the steps.
Step 1: Add the same number of zeros as the number of digits in the multiplier.
So the multiplier 386 has 3 digits. So we add three zeroes in front of 6671 to get 000671
0 0 0 6 6 7 1 x 386
Step 2: Sum of two pair products is a single digit of the answer.
Use your middle and forefinger to keep track of whether to calculate U or the T. Place each finger in the middle of two pairs.
Step 2.1
Using 6 in 386, the pair product of 0 and 0 is 0 + 0 = 0 (U6T6 = 00 + 00).
Using 8 in 386, the pair product of 0 and 0 is 0 + 0 = 0 (U8T8 = 00 + 00).
Using 3 in 386, the pair product of 0 and 6 is 0 + 1 = 1 (U3T3 = 00 + 18).
Adding the three number together we get 0 + 0 + 1 = 1.U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 1 _ _ _ _ _ _Step 2.2
Moving to the next set of digits
Using 6 in 386, the pair product of 0 and 0 is 0 + 0 = 0 (U6T6 = 00 + 00).
Using 8 in 386, the pair product of 0 and 6 is 0 + 4 = 4 (U8T8 = 00 + 48).
Using 3 in 386, the pair product of 6 and 6 is 8 + 1 = 9 (U3T3 = 18 + 18).
Adding the three number together we get 0 + 4 + 9 = 13.We attach 3 in 13 as the next digit. But 13 has two digits so we carry over the 1 in 13. So the last digit from the previous step which is 1 becomes 2 (got by carrying over 1+1).
= U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 2 3 _ _ _ _ _Step 2.3
Moving to the next set of digits
Using 6 in 386, the pair product of 0 and 6 is 0 + 3 = 3 (U6T6 = 00 + 36).
Using 8 in 386, the pair product of 6 and 6 is 8 + 4 = 12 (U8T8 = 48 + 48).
Using 3 in 386, the pair product of 6 and 7 is 8 + 2 = 10 (U3T3 = 18 + 21).
Adding the three number together we get 3 + 12 +10 = 25.We attach 5 in 25 as the next digit. But 25 has two digits, so we carry over the 2 in 25. So the last digit from the previous step which is 3 becomes 5 (got by carrying over 3 + 2).
= U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 2 5 5 _ _ _ _Step 2.4
Moving to the next set of digits
Using 6 in 386, the pair product of 6 and 6 is 6 + 3 = 9 (U6T6 = 36 + 36).
Using 8 in 386, the pair product of 6 and 7 is 8 + 5 = 13 (U8T8 = 48 + 56).
Using 3 in 386, the pair product of 7 and 1 is 1 + 0 = 1 (U3T3 = 21 + 03).
Adding the three number together we get 9 + 13 +1 = 23.We attach 3 in 23 as the next digit. But 23 has two digits, so we carry over the 2 in 23. So the last digit from the previous step which is 5 becomes 7 (got by carrying over 5 + 2).
= U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 2 5 7 3 _ _ _Step 2.5
Moving to the next set of digits
Using 6 in 386, the pair product of 6 and 7 is 6 + 4 = 10 (U6T6 = 36 + 42).
Using 8 in 386, the pair product of 7 and 1 is 6 + 0 = 6 (U8T8 = 56 + 08).
Using 3 in 386, the pair product of 1 and _ is 3 + _ = 3 (U3T3 = 03 + –-).
Adding the three number together we get 10 + 6 + 3 = 19.We attach 9 in 19 as the next digit. But 19 has two digits, so we carry over the 1 in 19. So the last digit from the previous step which is 3 becomes 4 (got by carrying over 3 + 1).
= U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 2 5 7 4 9 _ _Step 2.6
Moving to the next set of digits
Using 6 in 386, the pair product of 7 and 1 is 2 + 0 = 2 (U6T6 = 42 + 06).
Using 8 in 386, the pair product of 1 and _ is 8 + _ = 8 (U8T8 = 08 + –-).
Using 3 in 386, the pair product of _ and _ is _ + _ = _ (U3T3 = –– + –-).
Adding the three number together we get 2 + 8 + _ = 10.We attach 0 in 10 as the next digit. But 10 has two digits, so we carry over the 1 in 10. So the last digit from the previous step which is 49 becomes 50 (got by carrying over 49 + 1).
= U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 2 5 7 5 0 0 _Step 2.7
Moving to the next set of digits
Using 6 in 386, the pair product of 1 and _ is 6 + _ = 6 (U6T6 = 06 + –-).
Using 8 in 386, the pair product of _ and _ is _ + _ = _ (U8T8 = –– + –-).
Using 3 in 386, the pair product of _ and _ is _ + _ = _ (U3T3 = –– + –-).
Adding the three number together we get 6 + _ + _ = 6.6 becomes the last digit of the answer. .
= U6 T6
= U8 T8
= U3 T3
0 0 0 6 6 7 1 x 386 = 2 5 7 5 0 0 6This is your final answer.
Hope this clarifies.
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.
Ah I see. Most of this seem to be arithmetic operations which are covered in the material.
Let me know how it goes.