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Russia
Russia
Worldwide
Rank
Level
1
Pserg
Moskva
92
2
Даниил Лазарев
Penzenskaja oblast\'
90
4
Максим Федосеев
Orenburgskaja oblast\'
84
5
chemspirit_live
Krasnojarskij kraj
83
8
Александр Мелентьев
Moskovskaja oblast\'
81
10
Eyedropping
Moskva
80
11
Archanfel
Moskva
75
13
User
Moskva
74
15
User
Moskva
73
18
Марк Бондарь
Moskva
70
19
User
Moskva
68
20
User
Burjatija
68
21
Petr Lavrov
Moskva
67
22
Никита Александров
Moskva
67
24
Beardie YOLO
Moskva
66
25
Alisher Mukhametzhanov
Moskovskaja oblast\'
65
27
Olyasailor
Moskva
65
28
User
Moskva
65
29
Максим Некрасов
Novosibirskaja oblast\'
65
30
User
Moskva
64
34
Demopticon Expo
Moskovskaja oblast\'
62
36
Semen Orekhov
Sankt-Peterburg
61
37
Иван Осадчиков
Moskva
61
38
Yury Badalian
Moskva
61
41
Alexey Zhila
Moskva
59
43
User
Tyva
58
45
User
Moskva
58
46
User
Moskva
58
47
User
Moskva
57
48
Irina
Moskva
57
50
User
Moskva
56
52
Вячеслав
Burjatija
56
53
JLC Master Calendar
Moskva
55
54
User
Moskva
55
57
User
Moskva
54
59
User
Moskva
54
62
Kseniya
Sankt-Peterburg
53
63
User
Moskva
53
64
User
Moskva
51
65
User
Moskva
51
67
User
Moskva
50
68
Павел Перманганатов
Udmurtskaja Respublika
50
70
Khazbi Sugarov
Stavropol\'skij kraj
50
71
User
Moskva
50
72
Serge Osipov
Moskovskaja oblast\'
50
73
User
Moskva
50
74
Elena Omnomnom
Moskva
50
75
Simon Kotler
Moskovskaja oblast\'
49
78
Алексей Суханов
Ivanovskaja oblast\'
47
80
User
Moskva
47
81
Van
Moskva
47
82
Timofey Bakunin
Moskva
47
84
User
Moskva
47
85
Costia Zaytsev
Moskva
47
86
User
Moskva
47
87
Nikita Beknel
Sankt-Peterburg
46
88
Evgeniy Egorov
Moskva
45
94
User
Moskva
45
95
Osman Akhonov
Moskva
44
98
User
Moskva
44
100
User
Moskva
44
102
ALEJANDRO
Moskva
44
104
Анжелика Котович
Sverdlovskaja oblast\'
43
105
Chernyaevg
Moskva
43
106
Alexandr Ilyshev
Moskovskaja oblast\'
43
107
User
Bashkortostan
42
108
Roza Kutubaeva
Moskva
42
109
Наталия Бирюкова
Novosibirskaja oblast\'
42
110
User
Moskva
42
111
Nikita Babich
Moskva
41
114
feddoa feddoa
Sankt-Peterburg
40
115
User
Moskva
40
116
User
Moskva
40
118
User
Moskva
40
119
Иван Смолко
Moskva
39
120
User
Moskva
39
121
User
Komi
39
124
Alisher
Moskva
38
125
User
Moskva
38
126
Bochkarev
Sankt-Peterburg
38
129
Afan
Moskva
37
133
User
Moskva
37
134
Hendrik Vermaak
Moskva
36
135
User
Moskva
36
136
Roman
Moskva
36
138
Geek Spirit
Moskva
36
139
User
Moskva
35
140
Анастасия Петрова
Moskva
35
143
User
Moskva
35
144
User
Moskva
35
148
User
Tatarstan
35
149
User
Moskva
35
150
User
Moskva
35
152
Владимир
Moskovskaja oblast\'
34
153
Kirill
Moskva
34
157
ArtZubkov
Moskva
34
160
User
Moskva
33
161
Паша
Permskij kraj
33
162
User
Moskva
33
163
Al Valkova
Moskva
33
164
User
Tatarstan
33
165
User
Moskva
33
170
User
Moskva
31
173
User
Moskva
31
176
User
Moskva
31
177
Татьяна Антонова
Moskva
31
178
Mag Larsan
Moskva
30
183
User
Moskva
30
189
User
Moskva
29
190
User
Moskva
29
191
Владимир Чехин
Altajskij kraj
29
194
User
Adygeja
29
202
Алексей Сальников
Moskva
28
203
User
Moskva
28
206
User
Tatarstan
28
209
Yulia Isakova
Moskva
28
210
Alex Fox
Moskva
27
212
User
Moskva
27
213
Alexandr Sofronov
Moskovskaja oblast\'
27
214
User
Moskva
27
215
User
Moskva
27
218
User
Moskva
27
219
User
Moskva
27
220
User
Mordovija
26
222
User
Moskva
26
223
User
Bashkortostan
26
224
User
Bashkortostan
26
229
User
Moskva
26
241
User
Moskva
25
243
егор адиятов
Krasnojarskij kraj
24
245
User
Moskva
24
247
User
Permskij kraj
24
249
User
Moskva
24
251
User
Moskva
23
252
User
Mordovija
23
260
User
Moskva
23
268
User
Moskva
22
272
Audrey
Moskva
21
273
User
Mordovija
21
275
David Craven
Rostovskaja oblast\'
21
283
Jovialamigo
Moskovskaja oblast\'
21
286
eminoradd9
Krasnodarskij kraj
21
287
User
Moskva
21
289
User
Moskva
21
290
User
Moskva
21
292
User
Moskva
20
294
User
Moskva
20
295
User
Moskva
20
303
User
Moskva
20
308
User
Moskva
20
311
User
Moskva
20
314
User
Moskva
19
316
User
Moskva
19
317
User
Moskva
19
319
Георгий Шиллеров
Moskva
19
328
User
Moskva
18
329
Fedor Abaev
Moskva
18
331
User
Moskva
18
334
User
Moskva
18
335
User
Moskva
18
336
User
Moskva
18
337
User
Moskva
17
338
User
Moskva
17
339
User
Moskva
17
341
User
Moskva
17
346
User
Moskva
17
351
User
Moskva
16
352
User
Moskva
16
353
User
Moskva
16
354
User
Moskva
16
355
User
Moskva
16
356
User
Moskva
16
357
User
Moskva
16
358
User
Moskva
16
360
Arman
Moskva
16
366
User
Moskva
16
370
User
Moskva
15
372
User
Moskva
15
375
Evgeniy
Kurskaja oblast\'
15
376
User
Moskva
15
379
User
Moskva
14
382
User
Moskva
14
383
User
Moskva
14
384
Kirill Smirnov
Moskovskaja oblast\'
14
387
User
Moskva
14
388
Никита Володарский
Moskva
14
389
Graftek
Moskva
14
390
User
Moskva
14
394
User
Moskva
14
395
User
Moskva
14
396
User
Moskva
14
397
User
Moskva
14
398
User
Moskva
14
399
User
Moskva
13
400
User
Moskva
13
401
User
Mordovija
13
402
User
Mordovija
13
403
User
Moskva
13
404
User
Moskva
13
406
Aleksei Kalimullin
Moskovskaja oblast\'
13
411
User
Bashkortostan
12
412
User
Moskva
12
414
User
Moskva
12
415
dbsn
Moskva
12
416
Nikolay Laptev
Region
12
420
Pierre Picaud
Tatarstan
12
421
User
Moskva
12
423
Manni Truong
Moskva
11
426
User
Moskva
11
427
User
Mordovija
11
428
User
Moskva
11
429
User
Moskva
11
430
User
Moskva
11
431
User
Moskva
11
432
User
Moskva
11
434
Алексей Лаврухин
Moskva
11
436
User
Moskva
11
437
User
Moskva
11
438
User
Moskva
11
440
User
Moskva
11
442
User
Moskva
11
443
User
Moskva
11
444
User
Moskva
11
447
User
Permskij kraj
10
448
Bioloopy
Moskva
10
452
Сергей Евгеньевич Осипов
Moskva
10
454
User
Moskva
10
455
User
Moskva
10
457
User
Moskva
10
460
User
Moskva
9
461
User
Moskva
9
463
User
Moskva
9
464
User
Moskva
9
465
User
Moskva
9
467
User
Moskva
9
468
User
Moskva
9
469
User
Tatarstan
9
472
Isami Wind
Moskva
9
473
User
Moskva
9
475
User
Moskva
9
476
User
Moskva
9
477
User
Moskva
8
479
User
Moskva
8
483
markwicked
Bashkortostan
8
486
Max Bonici
Moskva
8
487
User
Moskva
8
488
Тихон Клунный
Krasnodarskij kraj
8
494
User
Moskva
8
497
User
Moskva
8
498
Svyatoslav Feofanov
Moskovskaja oblast\'
7
500
User
Moskva
7
501
Inna Timonina
Moskva
7
503
Daniil Korbut
Jaroslavskaja oblast\'
7
504
Alexandra Menshina
Sankt-Peterburg
7
506
User
Moskva
7
510
User
Moskva
7
512
User
Moskva
7
515
User
Moskva
6
517
User
Moskva
6
518
User
Moskva
6
520
User
Moskva
6
523
User
Moskva
6
526
User
Moskva
5
527
User
Moskva
5
528
User
Moskva
5
532
User
Moskva
5
534
User
Komi
5
538
User
Moskva
4
539
User
Moskva
4
541
User
Moskva
4
543
Аня Медведева
Moskva
4
548
User
Moskva
4
553
User
Moskva
4
556
User
Moskva
4
558
User
Moskva
3
562
User
Moskva
3
564
User
Burjatija
3
566
User
Mordovija
3
568
User
Moskva
3
570
User
Moskva
3
583
User
Moskva
3
584
User
Moskva
3
591
Blackmur
Moskva
3
594
User
Moskva
2
598
User
Dagestan
2
601
User
Moskva
2
606
User
Moskva
2
608
User
Moskva
2
609
User
Moskva
2
614
User
Moskva
2
616
User
Moskva
2
620
User
Moskva
2
621
User
Moskva
2
625
User
Moskva
2
627
User
Moskva
2
628
Mila Koren
Sankt-Peterburg
2
629
User
Moskva
2
630
User
Moskva
2
631
User
Moskva
2
635
User
Moskva
2
636
Маргарита Вячеславовна Гаврилова
Moskovskaja oblast\'
2
641
Andrei Timoshenko
Moskva
1
642
User
Moskva
1
644
User
Moskva
1
645
User
Moskva
1
646
User
Moskva
1
653
User
Moskva
1
654
User
Moskva
1
655
User
Dagestan
1
658
User
Moskva
1
660
User
Dagestan
1
661
User
Moskva
1
665
User
Moskva
1
667
User
Mordovija
1
669
User
Moskva
1
671
User
Moskva
1
672
User
Moskva
1
673
Матвей Тетерин
Sverdlovskaja oblast\'
1
674
Илья Печеньков
Jaroslavskaja oblast\'
1
675
silenttikeus
Krasnodarskij kraj
1
676
niksah
Sankt-Peterburg
1
677
Дмитрий
Krasnojarskij kraj
1

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A Web App for Mathematics Training

Do you want to be fast at mental math? Many people do, but the options for doing the necessary exercises are simply too cumbersome for all but the most dedicated of trainees. In physical fitness, many people are interested in training their bodies but allocating the time, energy, and money for it is a significant obstacle. Likewise, lugging around books and whatnot for math practice is a threshold that just doesn't meet the standards of modern life.

Training yourself to be skilled at mental math needs to be quick and convenient. mathtrainer.org is a web app that works in your browser rather than a program you have to download and install on your computer or phone. This allows users to try and use the app without having to install new software. As a web app, updates are also much simpler. There is no need to download endless updates—the website will always be the most current version.

You can access a web app from any device connected to the internet and equipped with a web browser, including smartphones, tablets, and desktop computers. Moreover, you are free to use whichever browser you prefer, including Google Chrome, Safari, Firefox, and others. Google Chrome is the recommended browser for the best maths training since it tends to lead the pack in supporting the latest web technologies.

Math Trainer is designed to offer a similar experience regardless of what you’re using to access it, whether it be Android, iOS, Windows, or another operating system. Though an on-screen touch keyboard will appear on mobile devices, you may prefer to use the app on a desktop with a keyboard. Hopefully the advantages of a web app for convenient mathematics training are apparent.

Another part of making the app easy to use is eliminating the need for signing up and logging in. Users can get started with their math training as soon as they click the start button on this page. After progressing to higher levels in the app, your progress is automatically saved so long as your return to the site through the same browser.


What's a Mental Math Tip?

A mental math tip is a sequence of steps that can be taken to solve a math problem in your head. Click the arrow below to see an example for the following problem:

÷
984
3
328

A tip like this one is available for every problem in Math Trainer, so there's always help if you get stuck. With enough practice, you'll be able to predict what the tips will say—you'll have learned mental math!


Get Better at Mental Math

The ability to quickly perform mental calculations offers advantages in certain circumstances. But even without applications, getting better at mental math is a great way to stimulate one’s mind. It develops better number sense and intuition for quantifying the world around us. Practicing mental calculation will strengthen your foundation for learning more advanced maths topics.

Nonetheless, the tangible benefits of improving at mental math are many. It is certainly expected that educated people are able to do simple arithmetic without having to pull out a calculator. An inability to do so may reflect poorly on you, while being well-practiced in mental calculation will leave your contemporaries impressed. In many scientific and technical circles, mental math ability is even more highly regarded.

For students, mental calculation speed will often have a direct impact on math and science test scores. At all grade levels, it is not sufficient to know how to solve math problems when tests have a time limit on them. The highest-scoring test takers are able to answer questions both correctly and efficiently. Improving mental math skills will only benefit a student’s academic career.

Calculating the solution to an arithmetic problem in your head is often faster than pulling out a device to tell you the answer. For example, figuring out how much to tip a server at a restaurant is a straightforward arithmetic problem that many people are unable to perform without a calculator. By training your brain to solve basic math problems, you can save time in situations like these.

Mental math can also be relied upon when calculation devices are not available. Even with the conveniences of modern life, we occasionally find ourselves without access to our cell phones or other capable devices. A mind skilled in mental math is always available to you.

Finally, getting better at mental math enables a quick estimate and sanity check on results obtained from calculators. While computers are extremely reliable at solving math problems, there is always the risk of incorrectly inputting the problem to the computer. By getting better at mental mathematics, you will develop an intuition for whether the results of calculators make sense.

In fact, the ability to estimate is often sufficient to avoid using calculators altogether. While the use of computers is widespread, estimation is an increasingly valued skill in many industries. There are many situations where complex math will eventually be required, but a preliminary estimate is needed quickly. A major boost to productivity!


Use a Math Trainer

Mental math ability is a lot like physical fitness training. You may be out of shape in the beginning, but with diligent training you can and will improve. Initially you might not enjoy the exercise, but you will reap significant rewards for your effort. As you become more fit, you’ll begin to enjoy the activity much more. If you are serious about it, your mental calculation fitness could become a source of energy, galvanizing you to face the challenges of life with enthusiasm.

In physical training, you break down the fibers in your muscles during a workout session. Your muscles actually sustain tiny tears during resistance training exercises. While you rest afterwards, your body repairs the damage, rebuilding the fibers thicker and stronger.

A similar process is believed to occur for cognitive tasks. A 2016 study found "extensive evidence that brain-training interventions improve performance on the trained tasks".1 Therefore you can expect training your brain to answer mental math questions will lead to improved performance over time.

In the context of physical fitness, a "trainer" often refers to a trained professional who guides the workout and recovery process. Personal trainers are tasked with assessing a trainee's level of ability, prescribing an exercise regimen, and offering feedback as the training goes along. The word "trainer" could also refer to a system that automates the role of a personal trainer. Many aerobic exercise machines today offer interactive training programs with feedback and analysis of a user's performance.

A math trainer is needed for optimal math fitness. Like in physical fitness, the trainer should be compatible with users at a variety of skill levels and should guide them to the next level. It should give an accurate assessment of a user's strengths and weakness, as well as offer helpful feedback on where to focus one's efforts. Learning the ropes of mental maths with a math trainer should be a seamless, rewarding journey to ever-greater abilities.


Mental Calculation

Mental calculation, or mental math, is performing arithmetical calculations without the aid of tools or supplies. As opposed to using a calculator or pencil and paper, mental math is performed entirely in one’s head.

People use mental calculation when computation aides are not available, when it is faster to do so, or when they wish to practice, show off, or participate in mental math competitions. Most people perform basic mental calculation using elementary arithmetic on a daily basis. An inability to calculate mentally is a serious obstacle to many common tasks.

In U.S. schools, mental calculation is taught only for the most elementary arithmetic, such as single-digit addition and multiplication of two numbers between 0 and 12. To solve addition problems involving multiple digits, you are taught to add columns of digits from right to left, carrying the tens digit if the column sum exceeds 9. For example, how would you approach this addition problem?

Example of two-digit
addition problem

If you were trained like many of us were, you’d add the right column to obtain 12. Since that’s two digits, you’d write the 2 under the right column and carry the 10 by writing a 1 above the left column. Finally, you’d add the two tens digits and the carried 1 to obtain the answer, 52.

To solve an addition problem mentally, it’s best to add the columns from left to right. In our example, you could add the tens digit of the second number, 30, to the first number, 14, to obtain 44. This is easier than the full problem because you’re just doing one mental calculation and tacking on the 4 from the 14 as the singles digit. Then you’d add the remaining ones digit of the second number, 8, to 44 to arrive at the answer, 52.

Which approach seems simpler to you? Can you do the first approach without pulling out a pencil and paper? It turns out the same advantages of left-to-right addition apply to much larger numbers as well. It’s unlikely that difficult addition problems can be solved right to left without needing to write it all out, which of course is more time consuming.

Mental math should be distinguished from the memorization of math facts such as multiplication tables. A foundation of memorized answers to simple math problems will make mental math easier, but performing maths in your head requires both memorized facts and the manipulation of numbers and operations to solve problems. This combination of skill and memory allows us to solve far more complex math questions than can be answered with readily-memorized math facts.

Many mental math tricks are specific to particular numbers or types of problems, usually dependent on the base of the number system used. In the decimal numeral system, for example, it is trivially easy to multiply by 10—just add a 0 to the end of the number. This mental math trick wouldn’t work in the hexadecimal numeral system, though, because the base is 16 instead of 10.

Therefore mental calculation is the ability to manipulate complex arithmetic problems in such a way that they can be resolved using simple memorized math facts.


Arithmetic

Arithmetic is the branch of mathematics concerning basic number operations: addition, subtraction, multiplication, and division. As kids, we are taught to do arithmetic because real-world math problems depend on a mastery of elementary arithmetic. Higher-level study of arithmetic and the integers, or whole numbers, is known as number theory.

Though the math kids initially study is arithmetic, the word is rarely used in this context anymore. Originally it comes from the Greek arithmos, meaning “number”. It has however been included in the “three Rs” of elementary Western education: reading, writing, and arithmetic.

There is evidence prehistoric humans were using arithmetic as hunter-gatherers. Archaeologists have uncovered a tally stick, believed to be over 20,000 years old, which may exhibit the earliest known sequences of prime numbers. An understanding of prime numbers, which are only divisible by themselves and the number 1, requires knowledge of the operation in arithmetic known as division.

From tally marks came base-10 numerals such as those used in Egypt over 5,000 years ago. Number systems based on 10 probably arose because humans have ten “digits” as fingers on their hands (or toes on their feet). A later advance in arithmetic was positional notation, which allowed the same symbols to represent different magnitudes depending on their position in the written number. These numeral systems allowed complex arithmetic to be communicated, recorded, and applied to the challenges faced by our ancestors.

The basic operation of arithmetic is addition. It combines two or more numbers into one, the sum of the terms. The terms can be added in any order, which is known as the commutative property of arithmetic. On a number line, the sum of two numbers is the total distance from zero covered by both numbers.

The inverse arithmetical operation of addition is subtraction. It finds the difference between two numbers. Subtraction is not commutative because the order of the numbers determines whether the answer is positive or negative. On a number line, the difference between two numbers is the distance between their positions.

A second basic operation of arithmetic is multiplication, which scales a number by another number. This second number is called a factor. Like addition, multiplication is commutative—you can change the order of the factors and still get the same answer. Multiplication on a number line can be viewed as adding the first number a total number of times equal to the second factor.

Finally, division is an arithmetical operation that is essentially the inverse of multiplication. Rather than scaling a number, it is divided into a number of pieces equal to the second number. Dividing by the number 0 is not defined in arithmetic because dividing something into zero pieces is impossible.

Basic arithmetic allows us to evaluate the answers to an unlimited number of mathematical expressions. Arithmetical expressions can be purely mathematical, as in 2 + 2, or they can represent quantities in the physical world, such as two items plus two more. Understanding the laws of arithmetic is tremendously powerful.


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