 # What should I do to learn to calculate quickly?

Hi!

I recently saw a video from french primary kids calculating super fast super complicated math (https://www.youtube.com/watch?v=l1M_3B2qPts) and I since am super motivated to learn mental math. The school’s website (https://translate.google.com/translate?sl=fr&tl=en&u=http://www.ecole-saintebernadette.fr/calcul-mental-rapide-quelle-est-la-methode-utilisee-dans-notre-ecole/) mentions Trachtenberg’s method, vedic maths, Scott Flansburg’s method, and a respinned finger abacus. Where could I learn these methods? What exactly are they doing with their hands?

Thank you very much!

A Noob

3 Likes

Hi,

Let’s go with an example: 78 + 84

Instead of using Soroban, etc, do that: you see the units digits are 8 and 4, which gives us 12. And you see the tens digits are 7 and 8, which gives us 15. The answer will be 162.

But calculate like this it’s not fast and you jeopardize your result.

The way of calculate is transforming using the complements.

We have, as said before, in the units 8 and 4.

Which is bigger? the unit 8 of number 78. So, it’s this number we shall transform in the nearest number. That is, 80. We have added 2, because 78 + 2 = 80.

So, we have transformed 78 in 80. We have now the addition 80 + 84 which gives us 164, and because we have add 2 before, we substract that 2 now.

164 - 2 = 162

You can see through: (80 + 84) - 2 = 162.

I leave others members in Forum to leave theirs methods, that’s mine and I think it is very good.

We know both from Reddit 2 Likes

I was also a n00b 20 years ago.

And noone in my country (Greece) knew about mental calculation.

But I had a simple advantage. I grew up in the age of the internet. (I am an internet user since 1999).

So, I read almost everything that was on the internet, regarding on mental calculation. And by everything, I don’t mean just 50 or 100 pages, but literally, almost every information that was on search engines regarding calculation. Blogs, forums, videos, lectures, whatever.

Also, you have to save (‘control + s’ or export to pdf) most of these important pages, so you can build rich personal files for future reference.

Then, you try to improvise on this material and find which drills or exercises suit you the best.

For a very start, you could try to read all this subforum regarding mental calculation, and export it to your own pdf for instant reference.

Back in the early 00’s , I did the same with the Yahoo Mental calculation group.

Brute raw information is not knowledge.
But you definitely need information, in order to gain knowledge.

2 Likes

Like Nodas said, here.
I have been writing about fast methods her on this forum for the past 8 years.

It’s a kind of abacus where they put the numbers on their fingers.

Let’s take some of the tasks the students have to do from the video:

54 * 51
Use cross multiplication:
50*50 =2500.
Add (4+1) * 50 = 250.
2500 + 250 = 2750.
Last: 4 * 1 = 4.

54/7
I have talked about division here on this forum a lot.
In this case remember that 7*7=49.
Subtract from 54 to get a remainder of 5.
Now the part after the decimal point:
50 => 7 times. 1 left. So next digit is 1.

We get as an answer: 7,71…
Mental calculators know that there is a short sequence of digits that repeat.
See this:
1/7 = 0.14285714285714285714285714285714…
2/7 = 0.28571428571428571428571428571428…
3/7 = 0.42857142857142857142857142857142…
4/7 = 0.57142857142857142857142857142857…
5/7 = 0.71428571428571428571428571428571…
6/7 = 0.85714285714285714285714285714285…

If the answer s 7.71… we know it repeats as follows:
7.7 142857 142857 142857 142857 …

99 * 98
See this as (100-1) X (100-2)
Do the cross:
100X100 = 10,000
(-1-2)X100 = -300
-1X-2 = 2

999 * 996
Same as above with 1000-1 & 1000-4

1003 * 996
Same as above with 1000+3 & 1000-4

43132 * 11
This is a trick that goes as follows:
4 (4+3) (3+1) (1+3) (3+2) 2
You add the left and right digit.

244 * 125
I would do this as (244/8) * 1,000 = 30,5* 1000 = 30,500.

Multiplication of numbers between 11 and 19:
14
17 X

13
15 X

12
13 X

15
17 X

11
15 X

15
19 X

This is done by realizing that each task can be written as:
(10+a)(10+b) = 100 + 10(a+b) + a*b

Squares of numbers ending in 5 and 1.
45^2 = (4 * 5) | 25
The | denotes a hundred separator.
4*5 = 20.
So 2025

55^2. 6 * 5 = 30 => 3025
85^2. 8 * 9 = 72 => 7225

41^2 = 4^2 * 10^2 + 4 * 2 * 10 + 1^2 = 1600 + 80 + 1

51^2 = = 5^2 * 10^2 + 5 * 2 * 10 + 1^2 = 2500 + 100 + 1

81^2 = = 8^2 * 10^2 + 8 * 2 * 10 + 1^2 = 6400 + 160 + 1

41 X 49
These have the form (45-a)(45+a).
The answer is 45^2 - a^2
We just did 45^2 and the answer is 2025.
a=4, so a^2 = 16.
2,025-16 = 2,009.

46 X 54
These have the form (50-a)(50+a).
The answer is 50^2 - a^2
50^2 = 2500
a = 4. a^2 = 16
2,500-16 = 2,484

35 X 47
Could be done as 41^2 - 6^2
Or just cross multiplication.

45 X 63
Could be done as 54^2 - 9^2
Or just cross multiplication.

5453 X 999
I probably done as 5453 * 1000 - 5453 =
5,447,000 + (6,000 - 5,453).
If you know your complements you immediately know that 6,000 - 5453 = 547.

If you see anything in the videos that you cannot understand, just ask.

3 Likes

Me too.

1 Like

Whooo! This looks fantastic! Thank you very much

1 Like

Can you detail divisions more please?

Sure. Give me an example of the division you want to be able to do mentally.

Anything actually. And if there’s a method for dividing by 2 digits divisor, could you explain or link towards somewhere?
Thanks

Let’s take a 2 digit divisor: 29, Let’s do 100 / 29…
What I do is, I overshoot. So I take 30 as the divisor and for every 30 I subtract I have to add 1 because we are actually dividing by 29.
Effectively - in order to make it easier - I change it into a 1 digit divisor.

Let’s go:

100 goes into 30 3 times.
3 * 30 90. Subtract from 100. Remains 10. 3 *1 = 3, so add 3 for a total remainder of 13.
Answer so far 3 R 13.

13 becomes 130 and 130 goes into 30 4 times, making 120.
Remainder 10. Add 4 => 14
Answer so far 3.4 R 14.

14 becomes 140 and 140 goes into 30 4 times, making 120.
Remainder 20. Add 4 => 24
Answer so far 3.44 R 24.

24 becomes 240 and 240 goes into 30 8 times, making 240.
Remainder 0. Add 8 => 8
Answer so far 3.448 R 8.

8 becomes 80 and 80 goes into 30 2 times, making 60.
Remainder 20. Add 2 => 22
Answer so far 3.4482 R 22.

22 becomes 220 and 220 goes into 30 7 times, making 210.
Remainder 10. Add 7 => 17
Answer so far 3.44827 R 17.

17 becomes 170 and 170 goes into 30 5 times, making 150.
Remainder 20. Add 5 => 25
Answer so far 3.448275 R 25.

etc.

29 is slightly under 300.
If the number is higher than 30, I undershoot.If the divisor is 31, then for every 30 I subtract I have to subtract another one.
For example 100 / 31:

100 goes into 30 3 times.
3 * 30 90. Subtract from 100. Remains 10. 3 *1 = 3, so subtract another 3 for a total remainder of 7.
Answer so far 3 R 7.

7 becomes 70. 70 goes into 30 2 times, making 60
Remains 10. Subtract another 2 for a total remainder of 8.
Answer so far 3.2 R 8.

8 => 80 and goes into 30 2 times, making 60
Remains 20. Subtract another 2 for a total remainder of 18.
Answer so far 3.22 R 18.

18 => 180 and goes into 30 5 times, making 150. (we cannot use 6, because that would lead to a negative remainder.)
Remains 30. Subtract another 5 for a total remainder of 25.
Answer so far 3.225 R 25.

25 => 250 and goes into 30 8 times, making 240.
Remains 10. Subtract another 8 for a total remainder of 2.
Answer so far 3.2258 R 2.

Since 2/31 is small (\approx 0.065), you can now decide to stop and call out 3.2258… (or even 3.2258065…)

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