I've been preparing for my upcoming UCMAS competition and wanted to share some of the resources that have helped improve my mental math speed and accuracy:

1. UCMAS Practice Sheets iOS app – Great for daily speed drills, and to track your progress.
2. Flash Anzan Training – An online tool that rapidly displays numbers, helping with visualization and speed calculation.
3. Free Abacus Worksheet Generator – Generates unlimited worksheets for abacus and mental arithmetic practice.
4. Anzan Mega Arithmetic Program – A structured training program combining memory techniques and IQ exercises.
5. UCMAS Practice Worksheets – Official worksheets to sharpen UCMAS techniques.
6. Mental Calculation/Anzan Software – A software tool to practice Anzan by visualizing a soroban (abacus) in your head.
7. Mental Anzan Training - Video Lesson – A useful demo video showing real-world Anzan training techniques.

Would love to hear if anyone else has good recommendations! What tools or techniques do you use for training?

I’ve used these mental temperature conversion tricks for years. Maybe you’ll find one or both useful.

FIRST

These tricks are based on 1 degree of C being equal to 1.8 degrees F

It’s usually much easier to use 2 than 1.8 in calculations

And easier to use .5 than .55555555…

SECOND

All conversions between C° and F° start or end with adding or subtracting 32

If I forget which, I think about the freezing point of water 0 C° needs adding 32 for 32° F or I think about boiling water at sea level 212° F needs 32 subtracted first so 180/1.8 = 100 ° C

THIRD

One goal in these methods is to reuse the product or quotient to simplify the process

C° to F°

(easier than F° to C°)

• double the C°

• subtract itself/10

• add 32

F° = C°(2) - C°(.2) + 32

You get to reuse the C°(2) by moving the decimal point over one, i.e., divide it by 10.

EXAMPLES

15° C

30 - 3

= 27

+ 32

= 59° F

——

32° C

64 - 6.4

= 57.6

+32

= 89.6° F

—-

41° C

82 - 8.2

= 73.8

+ 32

= 105.8° F

F° to C°

(harder than C° to F°)

• subtract 32

• halve that

• add the answer to itself/10 + itself/100 then note the repeating digit

• round

C° = (F° - 32) (.5) + (F° - 32) (.05) + (F° - 32) (.005) …

You get to reuse the (F° - 32)(.5) by moving the decimal point over one, i.e., divide it by 10, 100....

EXAMPLES

F° = 100

100 - 32

= 68

68 / 2

= 34

C° ‎ =  34 + 3.4 + .34 …

(continues as 37.7777...)

= 37.78° C

After summing the first two terms (37.4), you know what digit repeats in the series and don’t need to keep calculating. The …4 at the end of this example always turns into a 7 with the next addition.

Round the series (…7). Don’t round …4 because you known the series is 37.77777... forever.

———

54° F

54 - 32

= 22

22 / 2

= 11

C° ‎ =  11 + 1.1 …

(continues as 12.22222…)

= 12.22° C

——

120° F

120 - 32

= 88

88 / 2

= 44

C° ‎ = 44 + 4.4 ...

(continues as 48.88888….)

= 48.89° C

——

23° F

23 - 32

= - 9

-9 / 2

= -4.5

C° = - 4.5 + (-.45) ...

(continues as -4.9999… which rounds to 5.0 at every point)

= - 5° C

Has anyone written about a method for mental math which is general, and aims to tackle the fundamental challenge which is the limited capacity and accuracy of short term working memory?

In other words, NOT tricks specific to the structure of arithmetic. Those are just hacks for arithmetic given the constraints of working memory, not techniques to extend effective working memory.

And also, NOT just advice or tools for practicing. AFAICT, practice produces only the relatively incremental benefits of improving skill by memorizing more basic operations and making basic operations more automatic and reliable, but it doesn’t on its own allow managing a significantly larger number of automatic operations when working a single problem.

Instead, something more like “here’s a mnemonic system which is optimized not just for remembering numbers, but for encoding the current state of a mental calculation, so that you can handle calculations of arbitrary complexity without getting lost, like with paper”?

(So, the major system for translating numbers to words is not enough, since it is just for remembering numbers and not the state of an in-progress calculation.)

To put it differently, I am not primarily interested in doing mental math rapidly. I am wondering about techniques that allow mentally performing arbitrarily large calculations.

Is there any formula or short Trick for getting value of x! So it can be done in head? Like we know 5! = 120 But if I ask what is 26! =? Then is there a short trick or something to quickly find it instead of doing 26×25×24×...×2×1?

How to Divide by Long Numbers in Mental Math

I am doing the long division in the example, and I want to achieve a precision of three digits.

https://preview.redd.it/hb5nd0mivu6e1.png?width=331&format=png&auto=webp&s=5a88f14698da24191ed4415c29ee1786eb34b369

In this method, is it inherent that you cannot have a precise remainder, or am I doing something wrong?

https://preview.redd.it/4spl773ltu6e1.png?width=942&format=png&auto=webp&s=ff4ffd1b2704aed40587083abaed046aef05ea00

https://preview.redd.it/fhhmkl6stu6e1.png?width=572&format=png&auto=webp&s=a1e8bcb71742efc2130726ada7e517c2ed6f3949

Hi

My Son is 8 years and I want to start learning and teaching mental maths to him. Where should we start? Books, YouTube? Please guide.

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?

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!

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/)

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))

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)

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

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

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!

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

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.

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?

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!

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!

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.

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.

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?