Mental math

I can’t memorize numbers when In mental calculation. I am doing a sum, for example “5595 + 3742”, so my first dificulty is doesnt forget all that operation while I calculate in initial steps, so my second challenge is doesnt forget the partial results while I calculate other numbers and… Any advice to help me?

You need to be a bit more specific. Can you memorize only a few digits or no digits at al? Because if you can’t even memorize 1 digit then you are going to have a hard time doing large mental calculations.

But if you can memorize a few digits, like most people then you can just look up shortcuts and there are many techniques that help with mental math. I think Arthur Benjamin has a few good books. You can also search around on this forum.

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Thanks friend I have edited the text, I have not a good english, but I hope I can be understood

Do you have a memory system for numbers yet? There are some examples of systems on the how to memorize numbers page. There is also an introduction to number memorization in the free ebook.

Always do the steps in exactly the same order. Don’t look for shortcuts initially. You want the algorithm on autopilot so you are free to think.

Start out by writing out the calculation in the steps you would do mentally including the initial problem. Always lay it out the same way. As you develop some speed, leave one of the partial products unwritten - just leave the space where it should be and visualize the number. I found that I liked to keep the original problem up. Took a while to get weaned off that last step.

The goal is to look at an empty sheet of paper and just write down the answer


Do I have to use them in mental calculation? Maybe it answer all.

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I don’t do a lot of mental calculation, so I’m not sure, but if someone gave me some numbers to work with, I would create images and place them at points around me, or in a body journey of some kind. I think Arthur Benjamin was using the Major System in one of his demonstrations, but I might be mistaken.

There is a mention of the Major System in this thread: Secrets of Mental Math


Thinking is a mix of knowledge and reasoning. When you do arithmetic, you rely on a memorized multiplication table perhaps up to 10. Having these ‘facts’ at the tip of your tongue makes calculating much easier.

What facts would improve your performance? Well certainly you could extend your multiplication table out to 20x20 that’s about 150 entries.

The other thing that’s very useful to learn are the squares out to 100. Multiplication can be done with a squaring technique.

46*58 = (52+6)(52-6) = 52^2 - 36 = 2704 -36 = 2668

There’s a lot of calculating techniques based on knowledge of the squares. No messy criss cross sums.

Squares between 40-60 & 90-110 can be be calculated lightening fast by special methods.

If you want more info on multiplication methods do search on Kinma


Doing your calculation from left to right appears to be fairly critical to reducing mental load when accumulating a result in any of the functions that could be described as cumulative. I tend to be only holding a single subtotal as I go but I generally play with small numbers because I am not terribly bright. If I wanted to hold 50+ digit numbers I would definitely be chatting with the card memorizers and playing with the major system. I had pi to a few hundred digits with the major system and a journey a couple of years ago. All gone now and it took me a while to build my journey. The card guys are able to read back 52 digits in under a minute of examination.

Alternately the Anzan kids can visualize a sum when flashed 4 and 5 digit numbers with less than a second between numbers and some have demonstrated doing it with multiple sums simultaneously. Again I darn well can’t.

As key facts become more readily accessible the mental confusion on holding intermediate numbers lessens.

I suspect that if you want to start doing things that appear more magical then you may want to explore some of the other skills.

If you are trying to practice numeracy that’s a little bit different question and in which case the tricks may just distract you learning your numbers.

There is a lot to say for having facts available. Having your first 99 squares at your fingertips extends your range dramatically. Having your double-digit multiplication table nailed would let you wow them at your Fields Medal acceptance speech.


Definitely familiarity with the numbers helps. It makes them easier to hold on to. I think left to right is the way to go. Especially for practical math - usually you only need 1.5 digits - rarely more than 3.

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My first step would be to simplify. For example, I’d find it easier to work with 5600 than with 5595, so I’d take 5 from 3742 and add it to 5595. Now I’m adding 5600 and 3737, and I don’t find it hard to turn that into 5600 + 3700 + 37. This is two-digit addition, and it’s not as hard as four-digit addition. And speaking just for myself, I’d find the inclusion of an elaborate mnemonic system needlessly complex.

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So true and very important.
Every step in simplification makes the calculation easier on the brain.

This is how I work, too!
I told about my current way of actively trying to find out how my brain calculates.

Most of the time I present numbers to my brain (don’t know how else to describe it) and my brain either goes to work or immediately presents a number.
If I give it 35 and 45, 80 immediately pops up. No calculation.
However; if I give it 175 and 85, then it immediately gets changed to 180 and 80.
Never to 170 and 90. My mind seems to prefer even numbers instead of odd ones.

Only after 180 and 80, 260 comes up.

However; if I force my brain to focus on 17 and 8 (still in the calculation of 175 + 85), then 25 immediately comes up and I know I have to add one to get 26.

How many digits can you keep in your head?
Try to mentally calculate:
1: 7 + 8
2: 16 + 23
3: 16 + 26
4: 103 + 15
5: 108 + 18
6: 103 + 205
7: 108 + 118
8: 188 + 288

Let us know which ones you can and cannot do.
We can help you at any level!

I haven’t found a use for mnemonics in addition or subraction either.

Just starting in mental math, myself. Using the Ofpad system.

I haven’t developed a system for memorizing the numbers, yet. I use a Dominic system with PAO for memorizing numbers, and a variation of that to memorize cards. But, for numbers, I’m looking at a PAO image and translating that into a six digit number. It makes recall easy, but seems like I’m adding too many steps for calculating those numbers.

Currently, I’m repeating the numbers and just holding them in my head. In the meantime, I’m considering a shape system for calculations, with a Palace that I can see locations that line up like a math problem.

Not sure if it will work, but that’s my current approach. In the meantime, as I’m learning the methods to calculate mentally, I’m also looking at the problem to begin. That’s where the calculations are really fast.