/r/mentalmath

Photograph via snooOG

Want to learn how to do math in your head, or even just wrap your head around a mathematical concept? This is the place!

Mental Math: It's the thought that counts!

Thanks to /u/claymazing for the inspirational subtitle!


Official /r/MentalMath wiki
(Self-contained downloadable ZIP file)

New additions (June 30, 2017):

  • Division by 10n+9
  • Rule of 72 (2× principal)
  • Rule of 96 (2.5× principal)
  • Rule of 114 (3× principal)
  • Rule of 132 (3.5× principal)
  • Rule of 144 (4× principal)
  • Rule of 156 (4.5× principal)
  • Rule of 168 (5× principal)
  • Combining rules (Up to 25× principal)

Mental Math Sites:


Free online mental math books:


Using math symbols in your post:

HTML Entites:

Example: Make a √ symbol by typing: √

Courtesy of jamt9000, you can also display subscripted and superscripted characters:

  • *_subscript_* makes subscript

  • *`superscript`* makes superscript

  • *_sub_`sup`* makes subsup

  • *`sup`_sub_* makes supsub

  • *`169`*⁄*_231_* makes 169231

NOTE: The ` character is called the grave accent. On desktops and laptops, you’ll find it on the tilde (~) key. On most mobile devices, it can usually be accessed by holding down either the apostrophe or tilde keys.

/r/mentalmath

4,607 Subscribers

3

The Doomsday Algorithm - Calculating days of the week. Could use a little guidance.

I understand the concept, I just don't understand the method.

Right now I'm working on just being able to figure out days of the week for 1900 to 2100.

My method right now is, for example, if I want to work out 2/14/1988....

I start with knowing that the doomsday for 1900 is a Wednesday (3).

Using the /12 method, xx84 is a 7.

3+7=10, but we can call that 3 because we ignore multiples of 7.

88 is a leap year because it's divisible by 4, so we know the 29th of Feb is a Wednesday (3).

29-x=14. So x=15.

We can ignore the multiples of 7 again (2x7=14) so we're left with 1.

1=Monday.

However, the day of the week for this example is 0 (Sunday).

What am I doing wrong?

4 Comments
2024/11/30
12:35 UTC

1

Thanksgiving Mental Math Competition

Hey everyone! For those who enjoy speed arithmetic, we're hosting a Thanksgiving Arithmetic Dash over the next nine days. This is a three-minute speed-based math contest consisting of simple arithmetic questions - and we will be awarding certificates to the top 10% of participants in each country, state (if US), and age group.

We hope it is fun, and a cool way to compete against others from your country, state, or age!

The contest is here: https://mathdash.com/contest/thanksgiving-arithmetic

We also recommend that you participate in the practice contest beforehand in order to get a feel for the format - the practice contest is here: https://mathdash.com/contest/thanksgiving-arithmetic-practice

Good luck!

3 Comments
2024/11/20
02:19 UTC

16

It’s basically forbidden

2 Comments
2024/10/11
20:33 UTC

4

Arithmetic Speed Drill

If you're looking to sharpen your arithmetic speed and accuracy, I’ve come across a solid app that might interest you. It’s been a great tool for boosting my mental math skills, both for interview prep and general speed training.

One of the features I like is that it lets you save your scores, making it easy to track your progress over time. There’s also a "Daily" mode that offers a global set of problems to solve each day, giving you the chance to challenge yourself and see how you stack up against others worldwide.

Check it out on Android and iOS: https://exatest.pages.dev/[Exatest](https://exatest.pages.dev/)

5 Comments
2024/10/03
21:30 UTC

1

Calculation League Season 2

Calculation League is getting ready to start Season 2! Information is on the website (https://mentalcalculation.org/). Qualification sessions run from October 14 through November 24. Any questions about qualifying or anything relevant to the competition should be directed to contact@mentalcalculation.org.

Website also contains a variety of practice simulators (GMCA Simulators (mentalcalculation.org)), 1 and 2 player app (League App with FAQs (mentalcalculation.org)) and match videos (Videos (mentalcalculation.org))

0 Comments
2024/10/02
21:33 UTC

9

I made a thing.

So I initially thought to myself that I want a tool to assess my mental math to see how well I perform. So I wrote a python program to quiz me on multiplication of large numbers, finding determinants, Integration, finding eigenvalues, division etc. It can both time you and you can go un-timed. I was thinking since this sub is about metal math abilities, it might be a good idea to make it online(currently it is completely offline and doesn’t use any non standard libraries that aren’t included when you install python to minimize dependency) So let me know about the following:

A) Would you guys like something like this? If you want I can give you all the github repo.

B) If yes to C, should I make it online so everyone could complete and then use the data to propose a sort of Mental ability Index?(MAI)

4 Comments
2024/09/18
19:48 UTC

3

Some interesting links

https://www.sorobanexam.org/ Soroban/Mental math exam generator with multiple options

https://deadreckonings.com/2010/11/22/a-2011-lightning-calculation-calendar/ Has many mental calculation methods

0 Comments
2024/09/12
04:26 UTC

5

Anyone playing this soraban game?

I finished the 'Addition, Medium' challenge in 1:29 #simplesoroban https://play.google.com/store/apps/details?id=br.net.btco.soroban

4 Comments
2024/08/22
18:11 UTC

11

Mental math resources. Please advice

Which resources would you recommend for being comfortable with dividing/multiplying/calculating percentages quickly without paper? For example how many percent higher is 5.2 than 3, or 1200 percent higher than 1000? Just to be able to do it quickly and accurately. If there are any materials/videos or similar as well, I’m open. Need to be fast for an upcoming case interview!

4 Comments
2024/08/18
12:48 UTC

6

Mental Math: How to perform math calculations in your mind

In this book, you will learn techniques that will help you perform addition, subtraction and
multiplication and calculate squares, cubes and square roots. You will also learn how to
calculate all the decimal digits of all the divisions with divisors up to 50 or even higher.

Mental Math: How to perform math calculations in your mind , Papadatos, Aristofanis - Amazon.com

Mental Math: How to perform math calculations in your mind , Papadatos, Aristofanis - Amazon.com

0 Comments
2024/08/02
20:26 UTC

7

Should I learn to "hear" or "see" numbers when doing mental math?

I'm new to mental math. How should I be practicing for proper form? I don't mean the tricks, I mean what practicing should look like and how the numbers should look in my head.

4 Comments
2024/08/01
06:46 UTC

8

Most efficient/quickest way to do subtraction mental math

I've always been told to do mental math from left to right for addition, but what's the fastest/most efficient way to do subtraction mentally??

I've always tried visualizing writing it down in my head, but I feel like there is a more effective way. Should I try rounding up instead?

6 Comments
2024/07/31
03:16 UTC

11

I made a site to learn (and infinitely practice) mental math

About a year ago, I shared my mental math website, Mental Math Pro, on this subreddit. A small number of people really loved it, so I kept it alive even though it wasn't getting much traffic.

Fast forward to this year, and the site is now attracting 1,500 visitors a month! I'm not entirely sure what changed, but I'm happy it did (and I'm SO happy I kept it alive!! 🙂)

Now I've taken all the new user's feedback, completely redesigned the site, and am relaunching it as a 2.0 version.

You can find it here: https://mentalmathpro.com/

I hope you love it. Plus, I'm always looking for ways to improve so all feedback is welcome!

2 Comments
2024/07/24
15:40 UTC

3

beginner resources

Hello everyone, I hope you're all doing well. I'm new to this subreddit and to the whole mental math thing. I've become really interested in mental math and wanted to ask if you could provide me with resources on how to get into this world, whether it's websites, YouTube channels, books, or anything else—everything is welcome. I would really appreciate it. Have a great day!

6 Comments
2024/07/24
08:23 UTC

4

Calculation League

Calculation League (https://mentalcalculation.org/) concluded in late-June! The competition will return in September/October and we are always looking for new competitors! The website contains a video section (https://mentalcalculation.org/videos) with videos of 27 of the matches as does the small Youtube page (https://www.youtube.com/channel/UCoy3CCWjlXgfta2bXEkFZKg). Standings, statistics, playoff bracket etc available on the website. Anyone interested in competing or getting more information about the competition can register on the website or e-mail contact@mentalcalculation.org.

0 Comments
2024/07/07
20:17 UTC

22

I started doing soroban (abacus) and can ‘see’ answers without even thinking

I've seen kids go through Kumon and realise rote learning is just repetition until you do it without thinking. But abacus seems even easier and faster because as your fingers naturally memorise all the basic additions with one digit you pretty much just repeat it with longer sums.

Abacus simplifies calculations by moving left to right and uses complimentary numbers a lot. So if eg. you 37+46, you do 37+50 (which is moving just 1 bead), then minus 4 (which is actually minusing the 5 bead and adding 1.

The result is coming up with answers without thinking at all, you just look at the answer and there it is.

I practice it mentally by adding car license plate numbers I see in front of me when I'm driving.

5 Comments
2024/07/03
03:32 UTC

13

Where can I find a list of Techniques

New here. I’m looking to improve my mental math skills for interviews. Is there anywhere I can find a list of techniques? I came across Vedic math and saw it some “sutras”, is this what I would be looking for?

3 Comments
2024/06/11
03:58 UTC

19

What are some benefits to improving your mental math abilities?

I have been practicing my mental math abilities through various online websites and programs. I have also been solving puzzles constantly whenever I have free time or while I'm commuting. Are there any other benefits to doing these types of games and exercises besides "looking cool" in front of people?

3 Comments
2024/06/02
06:43 UTC

4

Is there a mental calculator who specialize polynomial equations, trigonometry, and definite integrals?

1 Comment
2024/05/24
16:32 UTC

8

Help with dividing large numbers mentally

I’m currently studying for the GMAT and I noticed that one of my weaknesses is doing mental division with large numbers quickly. I’ve found some helpful tricks online to divide faster but I struggle when I can’t break a number down into the multiplication tables I have memorized.

For example….if I was dividing 729/3 A trick I learned is to divide my 30 first and get as close as you can to that number 729/30= 30*24=720 729-720=9 Then divide by 3 9/3=3 Then the answer is the multiplier of 30 with the divisor of 3 tacked on to it 243

My issue here is that I struggle to quickly figure out that 72/3=24 or 24*3=72 since it’s outside of the multiplication tables I have memorized.

Does anyone have any helpful tips or tricks to get better and faster at this?

6 Comments
2024/05/16
14:39 UTC

1

How can I learn to instantly calculate the number of letters in a sentence.

ex: I want food: 9, There is no war in Ba-sin-se: 21 (probably)

I know there are people who do this and I want to know how it works.

0 Comments
2024/04/10
16:46 UTC

3

Skills development

I'm back at practicing again after a few year lapse.

I try to practice every day.

My progression usually looks like.

  1. single digit mult and addition - sub 1 second

  2. subtraction complements - sub 1 second

  3. two digit addition/subtraction - sub 2 second

  4. two digit multiplication

11-19 - sub 3 ( usually gets down to sub 2 rote)

21-29 - sub 3 (usually get down to sub 2 rote)

squares 11-99 - sub 1 second ( peg for difference of squares) - rote

generic two digit crosswise multiplication - sub 3

3 and 4 digit squares - a^2 + 2ab + b^2 sub 5

3 and 4 digit multiplication - crosswise - no specific target.

and then I usual roll into maintenance and focus on precalculus - algebra and trig

then calc, linear alg, number theory, analysis, stats etc till life distracts me and I lapse again.

Any suggestions for additional mental calculation practice in the progression?

I know some of you practice mental calculation for competition so you might have useful suggestions I have never tried.

thanks,

snoo.

0 Comments
2024/04/08
17:47 UTC

1

Personal project website to practice mental arithmetic

Hi,

I have made some UI/UX changes to https://quickmaffs.com/

The next problem is now generated automatically, hopefully this makes for a better experience!

1 Comment
2024/04/08
16:21 UTC

3

Mental multiplications.

Two rules are elementary for multiplication, memory and cross calculations. The first thing is to memorize the multiplication tables from 1-1000. This involves memorizing the result of multiplying numbers up to ten by all numbers up to a thousand, the second rule is to perform cross multiplication. This involves multiplying the numbers starting with the largest. 2223 22=4. 22=4. We have 44, 32=6, 44+6=50. 32=6 We have 506. 2223=506.

1 Comment
2024/04/07
01:11 UTC

12

My basics as a human calculator.

I'm the kind of person who can multiply three-digit numbers in seconds and calculate the roots of six-digit numbers, essentially a human calculator. My general recommendation for anyone who wants to master mental calculation is to learn a series of tables, for multiplications for example, it is advisable to memorize the tables from 1 to 1000. If you want to master division, I recommend memorizing the result of dividing a thousand by the first 9 natural numbers. To master the square root, you must memorize the squares of the first 31 natural numbers. To master the calculation of cube roots Memorize the cubes of the first ten numbers. I will be uploading better explained tips when I have more time.

31 Comments
2024/04/05
19:14 UTC

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