Leaderboard
Russia
Russia
Worldwide
Rank
Level
1
Cyril Guzeev
Moskva
100
2
Karen Davtyan
Moskva
95
3
Julian Vidal Polania
Moskva
87
4
User
Moskva
87
6
Regard Attentif
Nižegorodskaja oblast\'
74
7
User
Moskva
72
8
Victor
Moskva
69
9
User
Moskva
68
10
User
Moskva
66
13
User
Moskva
63
14
Марк Бондарь
Moskovskaja oblast\'
63
16
Vanilla D
Moskva
62
21
Elisei Stakovskii
Sankt-Peterburg
56
22
Gena Bragin
Vladimirskaja oblast\'
53
23
Alisher Mukhametzhanov
Moskovskaja oblast\'
53
25
Jotaro Kujo
Komi
52
26
User
Moskva
52
27
Anastasia Aaa
Moskva
52
28
Osman Akhonov
Moskva
51
29
Eyedropping
Moskva
51
30
User
Moskva
51
31
Павел Перманганатов
Udmurtskaja Respublika
51
36
User
Moskva
49
37
Archanfel
Moskva
49
38
Demopticon Expo
Moskovskaja oblast\'
49
40
Beardie YOLO
Moskva
48
42
User
Moskva
48
43
User
Moskva
47
46
Semen Orekhov
Sankt-Peterburg
47
48
Даниил Лазарев
Penzenskaja oblast\'
46
50
Иван Осадчиков
Moskva
45
51
Petr Lavrov
Moskva
45
52
Анастасия Петрова
Moskva
44
53
Алексей Суханов
Ivanovskaja oblast\'
44
55
Андрей Машкин
Moskva
43
57
Александр Мелентьев
Moskovskaja oblast\'
43
59
User
Moskva
42
60
ecohigh
Moskva
42
61
User
Moskva
42
63
B T
Moskva
42
64
JLC Master Calendar
Moskva
42
68
Yury Badalian
Moskva
41
70
Пэш Кэш
Permskij kraj
40
72
User
Tyva
40
74
Sadeteen
Moskva
40
75
Serge Spiridonov
Moskva
39
76
Kseniya
Sankt-Peterburg
39
77
User
Moskva
39
78
chemspirit_live
Krasnojarskij kraj
39
79
Elijah
Permskij kraj
39
80
User
Moskva
39
81
User
Moskva
38
82
Olyasailor
Moskva
38
83
Никита Александров
Moskva
36
84
User
Moskva
36
86
User
Moskva
36
87
User
Moskva
35
91
User
Moskva
35
93
Van
Moskva
34
94
ayzerbadjanec
Čečenskaja Respublika
34
96
Timofey Bakunin
Moskva
34
97
User
Moskva
34
98
Khazbi Sugarov
Stavropol\'skij kraj
33
99
Alexey Zhila
Moskva
33
100
Evgeniy Egorov
Moskva
33
102
User
Bashkortostan
33
104
User
Moskva
32
105
User
Moskva
32
107
User
Moskva
31
108
User
Moskva
30
109
User
Moskva
30
110
User
Moskva
30
111
feddoa feddoa
Sankt-Peterburg
29
113
User
Moskva
28
115
User
Burjatija
28
116
Adam Smith
Bashkortostan
27
117
User
Moskva
27
118
User
Region
26
123
User
Moskva
25
124
Максим Некрасов
Novosibirskaja oblast\'
24
125
Иван Смолко
Moskva
24
128
User
Moskva
24
129
User
Moskva
23
130
Вячеслав
Burjatija
23
133
Roza Kutubaeva
Moskva
23
134
Andrey
Moskva
23
137
User
Moskva
22
138
Alisher
Moskva
22
139
User
Moskva
22
141
Mag Larsan
Moskva
22
142
Анжелика Котович
Sverdlovskaja oblast\'
22
143
User
Moskva
22
144
User
Moskva
22
145
Владимир
Moskovskaja oblast\'
22
147
Hendrik Vermaak
Moskva
22
148
Nikita Babich
Moskva
22
149
Данил Семин
Sverdlovskaja oblast\'
22
150
Наталия Бирюкова
Novosibirskaja oblast\'
21
152
Alex Fox
Moskva
21
153
User
Moskva
21
155
User
Moskva
21
156
User
Moskva
21
157
User
Moskva
21
159
Bochkarev
Sankt-Peterburg
21
161
Afan
Moskva
20
165
User
Moskva
20
167
User
Komi
20
169
Roman
Moskva
20
171
User
Moskva
20
176
User
Moskva
19
177
User
Moskva
19
179
User
Moskva
19
182
User
Moskva
19
183
Kirill
Moskva
19
185
Serge Osipov
Moskovskaja oblast\'
18
186
User
Moskva
18
187
User
Moskva
18
188
Владимир Чехин
Altajskij kraj
18
189
User
Moskva
18
194
User
Moskva
18
196
Alexandr Sofronov
Moskovskaja oblast\'
17
197
Chernyaevg
Moskva
17
202
User
Moskva
16
204
Алексей Сальников
Moskva
16
205
User
Mordovija
16
207
User
Moskva
16
208
User
Moskva
16
213
Costia Zaytsev
Moskva
16
214
User
Moskva
15
216
Киреев Александр
Krasnodarskij kraj
15
217
User
Moskva
15
218
User
Tatarstan
15
221
User
Moskva
15
223
User
Tatarstan
15
224
User
Moskva
15
225
User
Moskva
15
227
Audrey
Moskva
15
228
User
Moskva
15
230
User
Adygeja
15
231
User
Moskva
15
236
Nikita Beknel
Sankt-Peterburg
14
238
User
Moskva
14
239
User
Mordovija
14
241
User
Moskva
14
244
User
Tatarstan
14
246
егор адиятов
Krasnojarskij kraj
14
249
User
Moskva
14
250
User
Moskva
13
252
User
Moskva
13
255
User
Moskva
13
256
User
Moskva
13
258
User
Moskva
13
260
User
Mordovija
13
264
User
Moskva
13
265
User
Moskva
13
266
User
Moskva
13
269
User
Moskva
13
272
Geek Spirit
Moskva
12
276
User
Moskva
12
278
User
Moskva
12
285
User
Moskva
12
287
User
Moskva
12
289
User
Tatarstan
12
291
User
Moskva
12
292
User
Moskva
11
294
User
Moskva
11
295
Александр Чабин
Sverdlovskaja oblast\'
11
296
User
Moskva
11
298
User
Moskva
11
299
User
Moskva
11
303
User
Moskva
11
305
User
Bashkortostan
11
307
User
Moskva
11
310
User
Bashkortostan
11
313
ArtZubkov
Moskva
11
315
User
Moskva
11
318
User
Moskva
11
323
User
Moskva
10
324
User
Moskva
10
325
User
Moskva
10
328
David Craven
Rostovskaja oblast\'
10
329
User
Bashkortostan
10
334
Fedor Abaev
Moskva
10
343
User
Moskva
10
344
User
Moskva
10
349
Jovialamigo
Moskovskaja oblast\'
10
350
User
Tatarstan
9
351
User
Moskva
9
352
Manni Truong
Moskva
9
356
User
Moskva
9
358
User
Moskva
9
363
User
Moskva
9
365
User
Moskva
9
366
User
Moskva
9
369
User
Moskva
9
370
User
Moskva
9
371
User
Moskva
9
372
User
Moskva
9
374
User
Moskva
8
384
User
Moskva
8
385
eminoradd9
Krasnodarskij kraj
8
387
User
Moskva
8
388
User
Moskva
8
392
User
Mordovija
8
393
User
Mordovija
8
396
User
Moskva
8
399
User
Mordovija
8
401
Георгий Шиллеров
Moskva
8
402
Kirill Smirnov
Moskovskaja oblast\'
8
404
User
Moskva
8
405
User
Moskva
8
406
User
Moskva
8
410
dbsn
Moskva
7
411
User
Moskva
7
415
User
Moskva
7
418
User
Moskva
7
420
User
Moskva
7
422
User
Moskva
7
423
User
Moskva
7
426
User
Moskva
7
428
Bioloopy
Moskva
7
431
User
Moskva
7
432
User
Moskva
7
433
User
Moskva
7
437
User
Moskva
7
438
User
Moskva
7
440
Никита Володарский
Moskva
7
442
User
Moskva
7
443
Nikolay Laptev
Region
7
447
Graftek
Moskva
6
452
Arman
Moskva
6
453
Сергей Евгеньевич Осипов
Moskva
6
454
User
Moskva
6
456
User
Moskva
6
458
User
Moskva
6
461
User
Moskva
6
464
User
Moskva
6
465
User
Moskva
6
466
User
Moskva
6
468
User
Moskva
6
473
Алексей Лаврухин
Moskva
6
474
User
Moskva
6
476
User
Moskva
6
477
User
Moskva
6
478
User
Moskva
6
481
Svyatoslav Feofanov
Moskovskaja oblast\'
6
483
User
Moskva
6
484
User
Moskva
6
485
markwicked
Bashkortostan
5
487
Elena Omnomnom
Moskva
5
493
User
Moskva
5
495
Max Bonici
Moskva
5
496
User
Moskva
5
497
User
Moskva
5
498
Pierre Picaud
Tatarstan
5
499
User
Moskva
5
500
User
Moskva
5
501
User
Moskva
5
503
User
Moskva
5
504
User
Moskva
5
508
User
Moskva
5
509
User
Tatarstan
5
510
User
Moskva
5
512
User
Moskva
5
513
Тихон Клунный
Krasnodarskij kraj
5
519
Aleksei Kalimullin
Moskovskaja oblast\'
5
520
User
Moskva
5
525
Isami Wind
Moskva
5
526
Inna Timonina
Moskva
5
527
User
Moskva
5
528
User
Moskva
4
531
Herbert West
Sankt-Peterburg
4
532
User
Moskva
4
537
User
Moskva
4
540
User
Moskva
4
545
Daniil Korbut
Jaroslavskaja oblast\'
4
546
Alexandra Menshina
Sankt-Peterburg
4
547
User
Moskva
4
549
User
Moskva
4
550
User
Moskva
4
554
User
Moskva
4
555
User
Moskva
4
557
User
Moskva
3
558
User
Moskva
3
561
User
Moskva
3
562
User
Moskva
3
568
User
Moskva
3
570
User
Moskva
3
571
User
Moskva
3
575
User
Moskva
3
576
User
Komi
3
577
User
Moskva
3
578
User
Moskva
3
580
User
Moskva
3
581
User
Moskva
3
582
User
Moskva
3
586
User
Moskva
2
588
User
Moskva
2
591
User
Moskva
2
593
Аня Медведева
Moskva
2
594
User
Moskva
2
597
User
Moskva
2
603
User
Moskva
2
607
User
Burjatija
2
611
User
Mordovija
2
613
User
Moskva
2
615
User
Moskva
2
622
Simon Kotler
Moskovskaja oblast\'
2
624
User
Moskva
2
628
User
Moskva
2
643
User
Moskva
1
645
User
Dagestan
1
650
User
Moskva
1
651
User
Moskva
1
653
Ilya Vasilyev
Moskva
1
654
User
Moskva
1
655
User
Moskva
1
660
User
Moskva
1
667
elijah
Permskij kraj
1
668
User
Moskva
1
669
User
Moskva
1
671
User
Moskva
1
672
User
Moskva
1
677
User
Moskva
1
679
User
Moskva
1
683
User
Moskva
1
684
User
Moskva
1
686
User
Tatarstan
1
689
User
Moskva
1
692
User
Moskva
1
693
User
Moskva
1
698
User
Moskva
1
699
Mila Koren
Sankt-Peterburg
1
700
User
Moskva
1
701
User
Moskva
1
702
Andrei Timoshenko
Moskva
1
703
User
Moskva
1
704
User
Moskva
1
706
User
Moskva
1
708
User
Moskva
1
710
User
Moskva
1
717
User
Moskva
1
718
User
Moskva
1
719
User
Dagestan
1
722
User
Moskva
1
725
User
Moskva
1
726
User
Dagestan
1
727
User
Moskva
1
729
Маргарита Вячеславовна Гаврилова
Moskovskaja oblast\'
1
732
User
Moskva
1
734
User
Mordovija
1
737
User
Moskva
1
739
User
Moskva
1
740
User
Moskva
1
741
Матвей Тетерин
Sverdlovskaja oblast\'
1
742
Илья Печеньков
Jaroslavskaja oblast\'
1
743
silenttikeus
Krasnodarskij kraj
1
744
niksah
Sankt-Peterburg
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 math 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 math, 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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