How can I start mental calculating

Hi there everyone …
This my first post in this section , and I’m wondering how can I start mental calculation for someone know nothing about it !
Like what is the best book to start? (a list maybe)
Links that could help me (like a previous important topic in this section) …
That would be very helpful
And thanks🙂


I read part of Secrets of Mental Math and it was good. He also has a course.

Here are some discussions that might have useful information:

Kinma mentioned some books here:

Nodas mentioned some books here:

More discussions:


Thanks very much Josh, that was definitely very helpful to me:)

My regards…

Hi Badr Ibrahim,

Next to all the advice given to you, it is important to actually do mental calculation.
ABC, Always Be Calculating.
At the very least try to do every calculation in your head.
Even if it is to find your limit.

When you find your limit, post it here.
In most cases people will give you short cuts, algorithms, etc.

Tell us what you want to do mentally.
Is it addition, multiplication, division, logarithms?
Then tell us where your weak point is.
You want to do 2x2 multiplication mentally?
Tips, tricks?

General addition?
Carry-less subtraction?

Maybe you are overwhelmed by the info.

Here is a test. Try to do these and maybe give some feed back:

135 + 265
135 + 267
137 + 267
25 X 25
25 X 35
23 X 69
105 X 95
209 - 91
22 / 7 with rest
22 /7 with decimals
235 / 123


Hi Kinma!

I will tell my story briefly!
Two years earlier I watched arthur benjamin tedx show , I was really impressed , I just remembered the first time I saw Ben memorizing a shuffled deck in less than half minute , I said to my-self this is what I want to do , and here I’m “national record holder” in my country Sudan , so If you are asking me what I want ? I just want to do what the hell arthur benjamin did in that show ! Multiplying all these numbers so fast , that whole “human calculator” thing , and particulary I want to be able to compete in championships like memoriad or any other mental calculating comptetions…
So just show me … show me the way to do it! And I will do whatever it takes.

My regards

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For the test you provided…
I did the first 9 problems in about 5 minutes
I stoped with the last two , it took me a while to solve them but its just not time helping : (
(all mentally)

For Benjamin’s method, see here:

Will write more later today or tomorrow.

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135 + 265
135 + 267
137 + 267

The 3 build on eachother.
I hope you immediately see that 35 + 65 =100.
If you do not, work on complements:

If you do, also make sure you work on complements.
We will revisit them later.

When you immediately see that 135+265=400 then the next 2 are easy too.

25 X 25

There is a basic trick/shortcut for this:
(2x3) | 25 = 625

25 X 35 = (30-5)(30+5) = 30^2 - 5^ 2 = 900 - 25 = 875

23 X 69 = 23 X 70 - 23 = 20 X 70 + 3 X 70 -23 =1400 + 210 - 23 = 1600 - 13 = 1587

105 X 95 = 100^2 - 5^5 =10,000 - 25

209 - 91

Revisit complements.
The complement of 91 is 9, so 209-91 immediately turns into 109+9.

22 / 7 with rest

I hope you immediately see 3 rest 1

22 /7 with decimals

If you immediately see this as 3 rest 1, then the only thing left to be done is expanding 1/7. 1/7 = 142857 repeating, do the answer is

235 / 123

This is more difficult to do quickly.
123 X 2 = 246 =235 +11

So 235 / 123 = 2 rest -11
I have written a lot about division with negative remainders. Let me know if your went to know more about this.


The first 3 problems
135 + 265
135 + 267
137 + 267
I did it as the way you described it : ) I’m not that bad as I thought …

For mutiplying 25×25 I did the usual (20×25=500 +25×5=500+125=625
So for the next problem I knew it would be just 700 (35×20) + 175 (30×5+5×5)

For 23×69 I did the same as you : )

For 105×95 I did as usual = 9500 (95×100) + 475 (90×5+25) =9975

For 209-91 I was like counting and summing, as for 91 to be 100 it would take (9) steps and another 9 to complete 109 and then jumping 100 more steps to hit 209 so it would be 100+9×2= 118 I don’t know but sounds it won’t work for big numbers, yet it a method designed by practice somehow.

22/7 easy

22/7 with decimal I figured how it will work but skipped it because I can’t handle more than 4 numbers in my sence’s memory …

For The last problem I did the same as you.

I will work more in complements and get used to all these basic tips , for a while but … is that what mental calculating athletes do in comptetions like memoriad ?! For example they multiply 8 numbers by 8 I guess , and divide 8 n by 5 , I mean all these things are just incredible .
But I totally get it, that I need to improve my basic calculating skills , I even reviewed the regular multiplying tables, so what are my next step ?
Learn all basic tips? Okay which material I can use for that? A book ? Maybe List of books? A website ?
And secondly , is how to practice? For a beginner?

Oh’ Badr OMG that’s incredible.

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Mustafa :heart:
It’s nice to see you around here …

Throughout the years I have written a lot on this form about mental calculation. All from my own experience.
Feel free to use that.

Excellent method.
I use that too.

The 8x8 is usually dune using the criss cross method
I know some people, like Willem Bouman for example who know all tables until at least 100.
They can do this as essentially a 4x4 using 2 digit numbers.


Let’s say you want to focus for now on multiplication. Start by 2x2s.
Then 3x3 using Criss cross.
Then 4x4, etc

For practice I make my own spreadsheets in Google docs. That way I can also practice from my phone.

A good book to start with is:

The Mental Calculator’s Handbook
by Jan van Koningsveld and Robert Fountain


Hi, I’ve not tried it myself, but I would suggest taking a look at the trachtenberg system.


Okay that is impressive !

Okay, totally got it : )


Thanks Kinma for your time, I really appreciate it, I will let you know if I had another question, I will tell my progress with time in this post so to see if I’m heading toward the right directions.

Thanks again…
My regards…

I googled that “trachtenberg system”, it’s the first time to know about it, I’ll definitely go a little deeper with that!

Thanks Matt! …

Important tip.
Calculate from left to right.
Most people learn to calculate from right to left in school.
Mental calculation imho is easier when doing it starting from the most significant digit.
As far as I know most mental calculators do it this way.

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I will make sure I will do it in that way, it will take a while geting used to that, but its absolutely worthy.