Forum Replies Created
-
Posts
-
Please try to open the PDF in chrome or microsoft edge browser and let me know if you still have an issue.
Apologies for the late reply. Somehow missed this question.
Please try to open the PDF in Adobe Acrobat Reader. It can be downloaded & installed for free here: https://get.adobe.com/reader/
Let me know if you still have trouble.
Rounding up 84,791 to 100,000 we get 15209. This can be written as the following:
84,791 = 100,000 – 15,209
Here are the steps to find the amount you rounded up which is 15,209
The last digit adds up to 10 and all the other digits except the last digit add up to 9.
Keeping this principle in mind we do the following:
First digit 8 in 84,791 adds up with 1 to get 9. So 1 is the first digit of the amount rounded up 15,209.
8 + 1 = 9
Second digit 4 in 84,791 adds up with 5 to get 9. So 5 is the next digit of the amount rounded up 15,209.
4 + 5 = 9
Third digit 7 in 84,791 adds up with 2 to get 9. So 2 is the next digit of the amount rounded up 15,209.
7 + 2 = 9
Fourth digit 9 in 84,791 adds up with 0 to get 9. So 0 is the next digit of the amount rounded up 15,209.
9 + 0 = 9
The last digit add up to 10 so
Last digit 1 in 84,791 adds up with 9 to get 10. So 9 is the next digit of the amount rounded up 15,209.
1 + 9 = 10
Putting the numbers together we get 15209
I have written the steps for clarity. You should be able to immediately find the amount you rounded up by looking at the number.
Let me know if this clarifies.
Abhishek
Hi Ish,
Please see my reply to your earlier question. https://www.udemy.com/speed-mental-math-tricks/learn/v4/questions/5108794
Let me know if it clarifies.
Thank you
Hi Hamza,
You are not carrying over 1 across.
5459 x 11 =
First digit 5 becomes the first digit of the answer so
5459 x 11 = 5 _ _ _ _
Adding the first two digits we get 5 + 4 = 9
5459 x 11 = 5 9 _ _ _
Adding the next two digits we get 4 + 5 = 9
5459 x 11 = 5 9 9 _ _
Adding the next two digits we get 5 + 9 = 14
Since 14 has two digits we need to carry over the 1 so 599 becomes 600
5459 x 11 = 6 0 0 4 _
This is where you are making the mistake. You are not carrying the number across. You are adding it only to 9. Another way to think about it is when you add 1 to 9 you get 10 which is also a two digit number, so you have to carry over the number again to the next 9. This will also result in two digit number so you carry over the 1 to the next 5 to make it 6.
Finally 9 becomes the last digit of the answer.
5459 x 11 = 6 0 0 4 9
Let me know if this clarifies.
Hi Rupesh,
The steps I mentioned in my first reply are correct. The second step in your last reply is incorrect:
2. In ten digit 90 - 92 = 0_. The correct second step is 9 – 9 = 0. In the third step I am borrowing 1 from the answer 10 to get 9.Here are the steps from my original reply again with additional comments.
In 590 – 492:
1. Subtracting the first two digits (5 – 4) we get 1.
590 – 492 = 1 _ _
2. Subtracting the second two digits (9 – 9) we get 0. [This is the step you are doing incorrectly. You should subtract one digit at a time. The intermediate answer after step 2 is now 10 not 1. I think you are subtracting 90 – 92 instead of subtracting 9 – 9.]
590 – 492 = 1 0 _
3. We can’t subtract the last digits 0 and 2. So we borrow 1 from our answer 10. [Note: Our answer is not 1. It is 10. I think you are borrowing one from 1 instead of borrowing one from 10.] If you borrow one from 10, the calculated digits become 9.
590 – 492 = 9 _ (Got by borrowing 1 from 10 which is 10 – 1 = 9)
4. Since we borrowed 1 in the last step, we attach the borrowed 1 to 0 to get 10. Then we can subtract 10 – 2 to get 8.
590 – 492 = 9 8 (Got by attaching the borrowed 1 to 0 and subtracting 10 – 2)
You are trying to do the problem by subtracting 90 – 92 in the second step instead of subtracting one digit at a time which is 9 – 9. If you do 90 – 92 in the second step then there will only be 3 steps in the calculation instead of 4 and the third step of the calculation will be more complicated. Here are the steps if you do 90 – 92 in the second step:
1. Subtracting the first two digits (5 – 4) we get 1.
590 – 492 = 1 _ _
2. To subtract the next two digits (90 – 92) we need to borrow 1 from the answer 1 so it becomes 0.
590 – 492 = 0 _ _
3. Because we borrowed 1 in our previous step, we attach one to 90 to get 190. Subtracting 190 – 92 we get the answer 98.
590 – 492 = 0 9 8 (Got by attaching the borrowed 1 to 90 and subtracting 190 – 92)
You are subtracting 90 – 92 instead of 9 – 9. If you subtract 90 – 92, after borrowing 1 you must now subtract 190 – 92 to get the correct answer 98. Subtracting one digit at a time (i.e. 9 – 9) instead of subtracting two digits at a time (i.e. 90 – 92) simplifies the problem.
Let me know if this clarifies.
Warm Regards,
Abhishek
There are two ways to approach this problem. The normal LR method which is a bit tedious when you have to borrow numbers and the rounding up LR method which is more efficient to use when you have to borrow numbers.
In this problem you have to borrow numbers.
Normal LR Method
Here are the steps for the LR method without rounding up.
1. Subtracting the first two digits (5 – 4) we get 1.
590 – 492 = 1 _ _
2. Subtracting the second two digits (9 – 9) we get 0.
590 – 492 = 1 0 _
3. We can’t subtract the last digits 0 and 2. So we borrow 1 from our answer 10, so the calculated digits change to 9.
590 – 492 = 9 _
4. Next we subtract 10 – 2 to get 8.
590 – 492 = 9 8
LR Method With Rounding Up
As mentioned in the video lessons, you will be able to simplify this problem by rounding up the second number. Rounding up is recommended when you have to borrow numbers during subtraction.
1. So 492 can be rounded up by 8 to get 500. So if we write 492 as (500 – 8) the problem becomes:
590 – (500 – 8) = _ _
2. Subtracting 590 – 500 we get 90.
590 – 500 = 90
3. Adding the amount we rounded up 8 to 90 we get 98.
90 + 8 = 98.
There are only 3 steps to do this subtraction if you round up.
Hope this clarified. Let me know if you have any further questions.
The process is the same covered in the lecture.
12 – 54 = -42
Digit Sum 3 – 9 = -6
Hi Rupesh,
You can solve this with the flag pole method by making 3 in 13 the flag and 1 in 13 the pole. Please check the video on flag pole method.
Let me know if you have trouble applying it.
I am working on a couple of new mental math techniques and one of those new techniques is for division. It will take me a few weeks to make the videos and you will receive an email when I update the course with the same. When that is ready you will have an alternative to the flag pole method for division.
Thank You
Warm Regards,
Abhishek
Hi Irene,
You will be able to find the practice sheets in the resources section after each lesson. If you are having trouble finding these PDFs, you can directly download the rich text pdf workbooks from this link – ofpad.com/mathexercises. If you open these PDFs using the free software Adobe PDF reader you can directly enter the answers in the PDF without having to print them out. You can download Adobe PDF reader from this link – https://get.adobe.com/reader/
Let me know if you need any further assistance downloading the workbooks.
Warm Regards,
AbhishekCan you install the latest Adobe software and let me know? You can install the latest one here – https://get.adobe.com/reader
Hi Faisal,
Doing multiple additions is the same. Except instead of adding 2 digits in one step, you add the digit of all numbers. It is just as easy to do.
So in the first step you add the first digit of all numbers i.e. 1 + 6 + 2 + 4 + 2 + 2 = 17
1457
6532
2354
4563
2342
+2313
17Next step you add the second digit of the all the numbers i.e. 4 + 5 + 3 + 5 + 3 + 3 = 23
1457
6532
2354
4563
2342
+2313
17
+23Combining the result from the previous two steps (17 & 23) we get 193.
1457
6532
2354
4563
2342
+2313
193Next step 5 + 3 + 5 + 6 + 4 + 1 = 24
1457
6532
2354
4563
2342
+2313
193
+24Combining the result from the previous two steps (193 & 24) we get 1954.
1457
6532
2354
4563
2342
+2313
1954Next Step 7 + 2 + 4 + 3 + 2 + 3 = 21
1457
6532
2354
4563
2342
+2313
1954
+21Combining the result from the previous two steps (1954 & 21) we get 193561.
1457
6532
2354
4563
2342
+2313
19561You have the final answer 19,561
Hi
The DS Method for division with reminder works a little bit differently. You need to convert the decimal to a reminder.
47 / 12
Quotient 3
Reminder 11
This can be written like the following.
Dividend = Divisor x Quotient + Reminder
47 = 12 x 3 + 11
DS is the following:
2 = 3 x 3 + 2
2 = 2
There is a method to check answers with the decimals. I will be adding an additional lecture for that in a couple of weeks. Until then please use this method instead.
Always happy to help Patrik. If you enjoyed the course so far, please dont forget to leave a review for other future students. It really helps a lot.
3Hey Patrik,
This is a great question. The short answer is you will benefit from rounding up when you have to carry over (for addition) and borrow (for subtraction) a lot of numbers.
Lets take addition for example. Say you want to add 9898 + 4343. If you did the straight forward LR addition, you will have to carry over a number in almost every step. You could do this, but if you round up the first number, it will make things so much more easier. 9898 (rounded up is 10,000). 10,000 + 4343 = 14343. Then subtract the amount you rounded up which is 102 to get 14241. Try to do that in your head, with and without rounding up and you will realize you are flexing fewer neurons when you round up.
Now do you round up for every calculation? You don’t. Lets say you want to add 4343 + 1234. You don’t have to carry over any number to do this calculation so the straight forward LR addition makes sense. But for the fun of it, try to do the same problem by rounding up. You might find that rounding up only increases the mental effort required to do the math.
Okay we talked about addition, so what about subtraction? Rounding up is more valuable for subtraction than it is for addition. This is because borrowing numbers in your head is a lot harder to do compared to carrying over numbers. In subtraction you round up the number when you have to borrow a lot of numbers. Example 53,441 – 49,898. In this subtraction, except for the first numbers (5 – 4) you have to borrow a number during every step. So it makes sense to round up the second number before doing the subtraction. Rounding up we get 50,000 and we rounded up by 102. Subtracting 53,441 – 50,000 we get 3441. Adding 102 we get 3,543. Now try doing the same problem without rounding up. It might seem more strenuous to do it without round up.
Do you round up before doing every subtraction? Not really. Subtract 9889 – 4343. You can do the straight forward LR subtraction here to get the answer. You can do rounding up and solve the math but it will only result in an unnecessary step.
Let me know if this clarifies.