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You make the number smaller by dividing by prime numbers first 2, 3, 5, 7 and 11.
Mostly it will reduce the number unless its a prime number or a multiple of a prime number greater than 11
506 divided by 2 gives 253.
253 cannot be divided by 3,5 or 7. How do I know its not divisible so quickly? I use the divisibility test.
A number is divisible by 2 if the last number is even.
A number is divisible by 3 if the sum of the digits is divisible by 3
A number is divisible by 5 if the last digits are 0 or 5.
For 7 you need to actually divide to check.
So we try 11.
253 divided by 11 gives 23
23 is also a prime number so we can’t reduce it further.
This is the only way to reduce it.
You can combine the prime factors together if you want to reduce steps.
For example, the prime numbers of 506 is 2, 11 and 23.
We can combine 2 and 11 to get 22.
So we are left with 22 x 23.
Hope this helps
Welcome to the community Jim. How far into the book are you right now?
Any goal you hope to achieve by inculcating this new habit? Like a specific grade or something?
Welcome to the community. Looking forward to seeing your progress updates. Please make sure you complete all the workbooks and post it here.
What do you spend time learning? Is it school or university work or some new skill?
AbhishekFebruary 28, 2020 at 2:14 pm in reply to: Multiplying single-digit numbers into double-digit numbers: The DS method #10777
Ah very useful indeed. If you notice your steps, you are converting the single digit multiplication problem into another multiplication problem 4 x 6 = 24. I would therefore recommend learning the single digit multiplication table by heart.
The method is the same for negative and positive numbers. There is absolutely no difference.February 19, 2020 at 3:23 am in reply to: Do you have a facebook group to accompany your book? #10531
Currently there is no Facebook group. We only have the community forum here on the website.
The $45 price includes a 30% discount.
The current price on Udemy is $65 – https://www.udemy.com/course/speed-mental-math-tricks/
You can purchase the course at $45 from Ofpad.com – https://ofpad.com/mental-math-sp/
Unfortunately we cannot discount the course any further to be fair to people who paid full price.February 13, 2020 at 1:58 am in reply to: multiplying 4 digits by 11 with carry over numbers #10393
The steps are the same as 3 digit multiplication by 11.
Here is an example of 4 digit multiplication.
5763 x 11
The first digit becomes the first digit of the answer
5763 x 11 = 5 _ _ _ _
Adding the next two digits 5 + 7 gives 12. The second digit 2 in 12 becomes the second digit of the answer.
5763 x 11 = 5 2 _ _ _
Since 12 has two digits, we carry over the first digit 1 so 5 becomes 6.
5763 x 11 = 6 2 _ _ _
Adding the next two digits 7 + 6 we get 13. The second 3 in 13 becomes the third digit of the answer
5763 x 11 = 6 2 3 _ _
Since 13 has two digits, we carry over the first digit 1 so 2 becomes 3.
5763 x 11 = 6 3 3 _ _
Adding the next two digits 6 + 3 we get 9 which becomes the next digit of the answer.
5763 x 11 = 6 3 3 9 _
The last digit 3 becomes the last digit of the answer.
5763 x 11 = 6 3 3 9 3
Let me know if this example clarifies.
The first digit left of the decimal is odd and you alternate between odd and even.
For example, let us take 7324.
So the first digit left of the decimal is 4. So it becomes Odd (O)
7 3 2 4
Now you alternate between Odd (O) and Even (E)
E O E O
7 3 2 4
Hope this clarifies.
The round up method simply states that the last digits add up to 10 and the other digits add up to 9. There is no concept of left to right or right to left here. So was not sure what you meant?
Can you give me an example of what kind of scenarios you will need to do mental math for trigonometry or geometry? Those are generally not areas where we need to do mental math in the real world or in exams.
Multiplying large numbers come with practice and using the mind palace. You have to use a combination of rounding up and the methods we have covered to do the mental calculation. It will not be as easy and fast as multiplying lower digit numbers.
You don’t always have to make all numbers add up to 9.
The number of digits the rounded-up value will have will depend on how much you round up to.
If you round up 3898 to 10,000 you would have rounded up by 6102 which has 4 digits.
If you round up 3898 to 4,000 you would have rounded up by 102 which has 3 digits.
If you round up 3898 to 3,900 you would have rounded up by 02 which has 2 digits.
So in this scenario, you shouldn’t do the addition of 3 + 4 + 2 = 9.
Let me know if this clarifies.
When you round up 3898 to 4000 you will have to add a 3 digit number to 3898 to get 4000. So you don’t have to add the 3 + 4 + 2 to get 9.
The amount you round up will have one digit lesser than the original numbers.
Both 3898 and 4000 are 4 digit numbers so the amount you have to round up has to be a 3 digit number which is 102.
How many numbers
Thank you for taking the time to write suggestions.
1. I didn’t quite understand the first suggestion. Are you saying we teach to calculate from right to left in Chapter 8?
2. For the second point on including percentages, fractions etc, I will add it to my backlog and will work to incorporate it into the book and course. I have purposely kept some of the more complicated stuff out of the book so that it remains relevant to most people reading the book or watching the course. I will try to create a course companion so that it becomes useful.
3 & 4. For the next two points which are sort of interlinked which is to remember numbers in your head and carrying over numbers, I would encourage you to read this community post – https://ofpad.com/topic/is-only-the-calculation-performed-in-the-mind/
It probably has the exact answer that you are looking for. Let me know if it doesn’t answer the question.
5. Remembering to calculate from left to right comes with practice. If you do it enough number of times, it will become the only natural way to do mental math.
6. The only way to be 100% sure is to of course do the math problem again. Both methods rely on estimation and has an accuracy of >90%. Using both methods together will increase the accuracy even further because the chances of both methods not catching it combined is pretty slim. If I find a method that has even more accuracy, I will make sure I include it.
Let me know if this answers all your questions. If you do enjoy the book, please don’t forget to leave a review. It is really helpful to reach more students.
Glad you were able to figure it out.
No question is a bad question.
I will just highlight the steps here in case it will help other students get clarity.
We are dividing 47 / 12
12 x 3 = 36
So 3 is the quotient.
47 – 36 = 11
11 is the reminder.
If you wanted to calculate decimal places you would add 0 to 11 and continue dividing by adding a decimal point. But since we are interested in getting the reminder we won’t do that.
Hope this clarifies. Feel free to ask anything that you need help with.