Leaderboard
Russia
Russia
Worldwide
Rank
Level
1
Pserg
Moskva
92
2
Даниил Лазарев
Penzenskaja oblast\'
90
3
Максим Федосеев
Orenburgskaja oblast\'
84
4
chemspirit_live
Krasnojarskij kraj
83
5
Александр Мелентьев
Moskovskaja oblast\'
81
6
Eyedropping
Moskva
80
8
Archanfel
Moskva
75
9
User
Moskva
74
11
User
Moskva
68
12
User
Burjatija
68
13
Никита Александров
Moskva
67
14
Olyasailor
Moskva
65
15
User
Moskva
65
16
Максим Некрасов
Novosibirskaja oblast\'
65
19
Petr Lavrov
Moskva
61
21
Alexey Zhila
Moskva
59
23
User
Moskva
58
24
User
Moskva
58
25
Yury Badalian
Moskva
57
26
Irina
Moskva
57
27
Kseniya
Moskva
56
29
Вячеслав
Burjatija
56
30
User
Moskva
55
32
User
Moskva
54
33
Demopticon
Moskovskaja oblast\'
54
35
User
Moskva
54
36
User
Moskva
53
37
User
Moskva
52
38
User
Moskva
51
40
Serge Osipov
Moskovskaja oblast\'
50
41
User
Moskva
50
42
Elena Omnomnom
Moskva
50
43
Simon Kotler
Moskovskaja oblast\'
49
45
User
Moskva
47
46
Costia Zaytsev
Moskva
47
47
User
Moskva
47
48
Nikita Beknel
Sankt-Peterburg
46
53
User
Moskva
45
54
User
Moskva
44
56
User
Moskva
44
58
ALEJANDRO
Moskva
44
59
Анжелика Котович
Sverdlovskaja oblast\'
43
60
Chernyaevg
Moskva
43
61
Alexandr Ilyshev
Moskovskaja oblast\'
43
62
Roza Kutubaeva
Moskva
42
63
Наталия Бирюкова
Novosibirskaja oblast\'
42
64
User
Moskva
42
66
User
Moskva
41
67
Nikita Babich
Moskva
41
68
User
Moskva
41
70
User
Moskva
40
72
User
Moskva
40
74
Иван Смолко
Moskva
39
75
User
Moskva
39
76
User
Komi
39
77
Alex Fox
Moskva
39
80
Alisher
Moskva
38
81
User
Moskva
38
82
Bochkarev
Sankt-Peterburg
38
85
Afan
Moskva
37
89
User
Moskva
37
90
Hendrik Vermaak
Moskva
36
91
Иван Осадчиков
Moskva
36
92
User
Moskva
36
93
Roman
Moskva
36
95
Geek Spirit
Moskva
36
98
User
Moskva
35
99
User
Moskva
35
103
User
Tatarstan
35
104
User
Moskva
35
105
User
Moskva
35
107
Владимир
Moskovskaja oblast\'
34
108
Kirill
Moskva
34
112
ArtZubkov
Moskva
34
114
Паша
Permskij kraj
33
115
User
Moskva
33
116
Al Valkova
Moskva
33
117
User
Tatarstan
33
118
User
Moskva
33
125
User
Moskva
31
128
User
Moskva
31
129
Татьяна Антонова
Moskva
31
134
User
Moskva
30
141
Владимир Чехин
Altajskij kraj
29
144
User
Adygeja
29
151
Алексей Сальников
Moskva
28
152
User
Moskva
28
155
User
Tatarstan
28
158
Yulia Isakova
Moskva
28
159
Alexandr Sofronov
Moskovskaja oblast\'
27
160
User
Moskva
27
161
User
Moskva
27
164
User
Moskva
27
165
User
Moskva
27
166
User
Mordovija
26
168
User
Moskva
26
169
User
Bashkortostan
26
170
User
Bashkortostan
26
175
User
Moskva
26
183
User
Moskva
25
184
егор адиятов
Krasnojarskij kraj
24
186
User
Moskva
24
188
User
Permskij kraj
24
190
User
Moskva
24
192
Meloman Cool
Samarskaja oblast\'
24
193
JustBucket
Sankt-Peterburg
24
194
User
Mordovija
23
202
User
Moskva
23
209
User
Moskva
22
212
User
Mordovija
21
214
David Craven
Rostovskaja oblast\'
21
222
Jovialamigo
Moskovskaja oblast\'
21
225
eminoradd9
Krasnodarskij kraj
21
226
User
Moskva
21
228
User
Moskva
21
229
User
Moskva
21
231
User
Moskva
20
233
User
Moskva
20
234
User
Moskva
20
242
User
Region
20
243
User
Moskva
20
248
User
Moskva
20
251
User
Moskva
20
252
Анастасия Петрова
Moskva
19
254
User
Moskva
19
255
User
Moskva
19
257
Георгий Шиллеров
Moskva
19
263
User
Moskva
18
264
Fedor Abaev
Moskva
18
266
User
Moskva
18
269
User
Moskva
18
270
User
Moskva
18
271
User
Moskva
18
272
User
Moskva
17
274
User
Moskva
17
279
User
Moskva
17
284
User
Moskva
16
285
User
Moskva
16
286
User
Moskva
16
288
Arman
Moskva
16
294
User
Moskva
16
296
User
Moskva
15
298
User
Moskva
15
301
Evgeniy
Kurskaja oblast\'
15
302
User
Moskva
15
304
User
Moskva
14
307
User
Moskva
14
308
User
Moskva
14
309
Kirill Smirnov
Moskovskaja oblast\'
14
312
User
Moskva
14
313
Никита Володарский
Moskva
14
314
Graftek
Moskva
14
315
User
Moskva
14
319
User
Moskva
14
320
User
Moskva
14
321
User
Moskva
14
322
User
Moskva
14
323
User
Moskva
14
324
User
Moskva
13
325
User
Mordovija
13
326
User
Mordovija
13
327
User
Moskva
13
328
User
Moskva
13
330
Aleksei Kalimullin
Moskovskaja oblast\'
13
335
User
Moskva
12
336
dbsn
Moskva
12
337
Nikolay Laptev
Region
12
341
Pierre Picaud
Tatarstan
12
342
User
Moskva
12
344
User
Moskva
11
345
User
Mordovija
11
346
User
Moskva
11
347
User
Moskva
11
348
User
Moskva
11
349
User
Moskva
11
350
User
Moskva
11
352
Алексей Лаврухин
Moskva
11
354
User
Moskva
11
355
User
Moskva
11
356
User
Moskva
11
358
User
Moskva
11
360
User
Moskva
11
361
User
Moskva
11
362
User
Moskva
11
363
User
Permskij kraj
10
364
Bioloopy
Moskva
10
368
Сергей Евгеньевич Осипов
Moskva
10
370
User
Moskva
10
371
User
Moskva
10
373
User
Moskva
10
376
User
Moskva
9
377
User
Moskva
9
378
User
Moskva
9
380
User
Moskva
9
381
User
Moskva
9
382
User
Tatarstan
9
385
Isami Wind
Moskva
9
386
User
Moskva
9
388
User
Moskva
9
389
User
Moskva
9
391
markwicked
Bashkortostan
8
394
Max Bonici
Moskva
8
395
User
Moskva
8
396
Тихон Клунный
Krasnodarskij kraj
8
402
User
Moskva
8
405
User
Moskva
8
407
User
Moskva
7
408
Inna Timonina
Moskva
7
410
Daniil Korbut
Jaroslavskaja oblast\'
7
411
Alexandra Menshina
Sankt-Peterburg
7
413
User
Moskva
7
417
User
Moskva
7
419
User
Moskva
7
422
User
Moskva
6
425
User
Moskva
6
426
User
Moskva
6
428
User
Moskva
6
431
User
Moskva
6
432
User
Moskva
5
433
User
Moskva
5
437
User
Moskva
5
439
User
Komi
5
443
User
Komi
5
446
User
Moskva
4
448
User
Moskva
4
450
Аня Медведева
Moskva
4
455
User
Moskva
4
460
User
Moskva
4
463
User
Moskva
4
465
User
Burjatija
3
467
User
Mordovija
3
469
User
Moskva
3
471
User
Moskva
3
485
User
Moskva
3
486
User
Moskva
3
493
Blackmur
Moskva
3
496
User
Moskva
2
501
User
Moskva
2
503
User
Moskva
2
504
User
Moskva
2
509
User
Moskva
2
511
User
Moskva
2
515
User
Moskva
2
516
User
Moskva
2
520
User
Moskva
2
522
User
Moskva
2
523
Mila Koren
Sankt-Peterburg
2
524
User
Moskva
2
525
User
Moskva
2
526
User
Moskva
2
530
User
Moskva
2
531
Маргарита Вячеславовна Гаврилова
Moskovskaja oblast\'
2
537
User
Moskva
1
539
User
Mordovija
1
541
User
Moskva
1
543
User
Moskva
1
544
User
Moskva
1
545
Матвей Тетерин
Sverdlovskaja oblast\'
1
546
Илья Печеньков
Jaroslavskaja oblast\'
1
547
silenttikeus
Krasnodarskij kraj
1
548
niksah
Sankt-Peterburg
1
549
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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