Leaderboard
Switzerland
Switzerland
Worldwide
Rank
Level
1
Xingyu Yang
Zürich
85
2
Phoomraphee Luenam
Zürich
84
3
User
Zürich
79
4
andy
Vaud
77
5
User
Zug
76
6
User
Zürich
75
7
RetoCH
Solothurn
70
8
User
Vaud
65
9
Amanda Margo
Valais
63
10
Joshua Rohrer
Genève
62
11
User
Vaud
62
12
User
Zürich
61
13
Bramart
Zürich
59
14
Hönzger
Zürich
58
15
Aashrit
Valais
56
16
User
Sankt Gallen
54
17
User
Zürich
50
18
Kirill Elson
Zürich
50
19
User
Valais
49
20
Georg Felber
Thurgau
49
21
User
Zürich
49
22
SRA
Zürich
48
23
ChessKing
Genève
48
24
Mohamed Belguendouz
Zürich
48
25
Mathias Blarer
Zürich
46
26
Lo Dro
Genève
45
27
User
Graubünden
45
28
tty 1
Zürich
45
29
User
Vaud
44
30
User
Zürich
43
31
User
Basel-Stadt
43
32
knuddelbaer
Zürich
42
33
User
Vaud
42
34
User
Vaud
42
35
User
Vaud
41
36
User
Zürich
41
37
User
Zürich
41
38
User
Genève
41
39
User
Genève
41
40
User
Genève
40
41
User
Bern
40
42
User
Vaud
40
43
Mark (Yu-Cheng) Cheng
Vaud
40
44
User
Zürich
40
45
Oscar Björklund
Vaud
39
46
Louisa
Bern
39
47
User
Luzern
39
48
User
Zürich
39
49
SeaDiamond
Vaud
38
50
User
Zürich
38
51
Andy Bahou
Zürich
38
52
User
Zürich
37
53
User
Vaud
36
54
User
Vaud
36
55
User
Thurgau
35
56
User
Zürich
35
57
User
Zürich
34
58
Jeton
Zürich
34
59
User
Zürich
33
60
jojo13
Zürich
33
61
User
Zürich
32
62
User
Bern
32
63
User
Neuchâtel
32
64
User
Vaud
32
65
Sandro Lindenmann
Sankt Gallen
31
66
User
Vaud
31
67
User
Vaud
31
68
User
Obwalden
31
69
Mal sar
Zürich
31
70
User
Zürich
30
71
User
Zürich
30
72
User
Zürich
30
73
User
Genève
30
74
User
Neuchâtel
30
75
User
Solothurn
30
76
User
Vaud
29
77
User
Bern
29
78
User
Aargau
29
79
Lou
Vaud
29
80
User
Aargau
28
81
User
Zürich
28
82
dcdavid84
Zürich
28
83
User
Vaud
28
84
User
Vaud
28
85
User
Vaud
28
86
User
Zürich
28
87
User
Zürich
27
88
User
Vaud
27
89
User
Zürich
27
90
User
Vaud
27
91
User
Zürich
27
92
User
Zürich
27
93
User
Zürich
26
94
User
Bern
26
95
User
Vaud
26
96
User
Sankt Gallen
26
97
User
Zürich
25
98
User
Zürich
25
99
User
Genève
25
100
User
Basel-Stadt
25
101
User
Zürich
24
102
Charlotte Sertic
Zürich
24
103
User
Ticino
24
104
User
Sankt Gallen
24
105
User
Zürich
24
106
User
Zürich
23
107
User
Sankt Gallen
23
108
User
Vaud
23
109
User
Solothurn
23
110
Joona Soratie
Vaud
22
111
User
Valais
22
112
User
Zürich
22
113
User
Genève
22
114
User
Vaud
22
115
User
Sankt Gallen
22
116
Raphaël Cardinaux
Vaud
22
117
User
Zürich
22
118
User
Genève
21
119
Harry Tuttle
Basel-Landschaft
21
120
jean-mickael nounahon
Zürich
21
121
User
Bern
21
122
User
Sankt Gallen
21
123
User
Vaud
21
124
User
Zürich
21
125
User
Sankt Gallen
21
126
User
Zürich
20
127
User
Zürich
20
128
User
Aargau
20
129
User
Genève
20
130
SneakyRobot
Basel-Landschaft
19
131
User
Genève
19
132
User
Vaud
19
133
User
Zürich
19
134
User
Vaud
19
135
User
Genève
19
136
User
Genève
19
137
User
Zürich
19
138
User
Vaud
18
139
User
Basel-Stadt
18
140
User
Zürich
18
141
Mònica Morera Ruocco
Basel-Stadt
18
142
Marius Furter
Zürich
18
143
Tomas Carbo Medem
Vaud
17
144
User
Zürich
17
145
User
Genève
17
146
User
Vaud
17
147
User
Zürich
17
148
User
Vaud
17
149
User
Genève
17
150
User
Aargau
17
151
User
Vaud
16
152
User
Genève
16
153
User
Vaud
16
154
User
Vaud
16
155
Mingjie Ma
Vaud
16
156
User
Vaud
16
157
User
Vaud
16
158
User
Zürich
16
159
TheMaster
Luzern
15
160
Alex M
Zürich
15
161
Priscilla
Sankt Gallen
15
162
User
Genève
15
163
User
Basel-Stadt
15
164
User
Aargau
15
165
User
Genève
15
166
User
Aargau
15
167
User
Zürich
14
168
User
Valais
14
169
User
Vaud
14
170
User
Zürich
14
171
User
Genève
14
172
User
Aargau
13
173
Michal Grabowski
Vaud
13
174
User
Vaud
13
175
User
Genève
13
176
User
Aargau
13
177
User
Vaud
13
178
User
Vaud
13
179
User
Zürich
13
180
User
Aargau
13
181
Honzger
Zürich
12
182
User
Vaud
12
183
User
Zürich
12
184
User
Luzern
12
185
User
Genève
12
186
User
Vaud
12
187
User
Zürich
12
188
User
Zürich
12
189
User
Zürich
12
190
User
Zürich
11
191
User
Valais
11
192
User
Vaud
11
193
User
Vaud
11
194
User
Vaud
11
195
User
Vaud
11
196
Jackson Jackson
Vaud
11
197
User
Vaud
11
198
User
Zürich
11
199
Jannat
Zürich
11
200
User
Zürich
10
201
User
Genève
10
202
User
Freiburg
10
203
User
Bern
10
204
User
Vaud
10
205
User
Zürich
10
206
User
Solothurn
9
207
Owen Gibbs
Genève
9
208
User
Zürich
9
209
Matt
Vaud
9
210
User
Genève
9
211
User
Vaud
9
212
virgil
Zürich
8
213
User
Zürich
8
214
User
Genève
8
215
User
Basel-Stadt
8
216
User
Vaud
8
217
User
Basel-Stadt
8
218
User
Bern
8
219
User
Genève
8
220
User
Genève
8
221
User
Zürich
8
222
User
Luzern
8
223
User
Vaud
8
224
User
Basel-Stadt
8
225
User
Sankt Gallen
7
226
User
Vaud
7
227
User
Vaud
7
228
User
Vaud
7
229
User
Sankt Gallen
7
230
User
Zürich
7
231
User
Zürich
7
232
User
Zürich
7
233
User
Vaud
7
234
User
Vaud
6
235
User
Zürich
6
236
Jerry (Yudingkun) Tan
Vaud
6
237
User
Zürich
6
238
Andrey Tolkachev
Zürich
6
239
User
Vaud
6
240
User
Zürich
6
241
User
Sankt Gallen
6
242
User
Zürich
6
243
User
Zürich
6
244
User
Aargau
6
245
Daniel Bucher
Luzern
6
246
User
Vaud
6
247
User
Vaud
6
248
User
Zürich
6
249
User
Zürich
6
250
User
Vaud
6
251
User
Zug
6
252
User
Zürich
6
253
User
Genève
6
254
User
Ticino
6
255
User
Zürich
6
256
User
Sankt Gallen
5
257
User
Zürich
5
258
User
Zürich
5
259
User
Vaud
5
260
User
Zürich
5
261
User
Zürich
5
262
User
Zürich
5
263
User
Zug
5
264
User
Vaud
5
265
User
Zürich
5
266
User
Vaud
5
267
User
Vaud
5
268
User
Vaud
5
269
User
Vaud
5
270
User
Sankt Gallen
5
271
User
Zürich
5
272
User
Zürich
5
273
User
Aargau
5
274
User
Zürich
5
275
User
Zürich
5
276
User
Sankt Gallen
4
277
User
Sankt Gallen
4
278
User
Genève
4
279
Radinka Siddiqi
Genève
4
281
User
Zürich
4
282
User
Bern
4
283
User
Solothurn
4
284
User
Aargau
4
285
User
Vaud
4
286
User
Vaud
4
287
User
Zürich
4
288
User
Zürich
4
289
User
Zürich
4
290
User
Zürich
4
291
User
Luzern
4
292
User
Vaud
4
293
User
Zürich
4
294
User
Zürich
4
295
User
Vaud
4
296
User
Luzern
4
297
User
Zürich
4
298
User
Bern
3
299
User
Zürich
3
300
User
Ticino
3
301
User
Zürich
3
302
User
Vaud
3
303
User
Vaud
3
304
User
Zürich
3
305
User
Zürich
3
306
User
Genève
3
307
User
Zürich
3
308
User
Basel-Stadt
3
309
User
Vaud
3
310
User
Thurgau
3
311
User
Aargau
3
312
User
Genève
3
313
User
Obwalden
3
314
User
Zürich
3
315
Laura
Genève
3
316
User
Zürich
3
317
User
Zürich
3
318
User
Zürich
3
319
User
Genève
3
320
User
Zürich
3
321
User
Vaud
3
322
User
Zürich
3
323
User
Vaud
2
324
User
Zürich
2
325
User
Zürich
2
326
HappySquid
Zug
2
327
User
Zürich
2
328
User
Aargau
2
329
User
Vaud
2
330
User
Sankt Gallen
2
331
User
Bern
2
332
User
Vaud
2
333
User
Zürich
2
334
User
Zürich
2
335
User
Vaud
2
336
User
Vaud
2
337
User
Genève
2
338
User
Ticino
2
339
User
Solothurn
2
340
User
Genève
2
341
User
Vaud
2
342
User
Basel-Stadt
2
343
User
Zürich
2
344
User
Vaud
2
345
User
Zürich
2
346
User
Zürich
2
347
User
Sankt Gallen
2
348
User
Vaud
2
349
User
Vaud
2
350
User
Vaud
2
351
User
Vaud
2
352
User
Freiburg
2
353
User
Vaud
2
354
User
Zürich
2
355
User
Vaud
2
356
User
Zug
2
357
User
Thurgau
2
358
User
Sankt Gallen
2
359
User
Vaud
2
360
User
Genève
2
361
User
Freiburg
2
362
User
Vaud
2
363
User
Luzern
2
364
User
Vaud
2
365
User
Bern
2
366
User
Zürich
2
367
User
Sankt Gallen
2
368
User
Zürich
2
369
User
Zürich
2
370
User
Zürich
2
371
User
Zürich
1
372
User
Zürich
1
373
User
Zürich
1
374
User
Genève
1
375
User
Zürich
1
376
User
Zürich
1
377
User
Zürich
1
378
User
Genève
1
379
User
Vaud
1
380
User
Schwyz
1
381
User
Aargau
1
382
User
Vaud
1
383
User
Zürich
1
384
User
Zürich
1
385
User
Valais
1
386
Natalie Tommey
Vaud
1

Free

Free basic access

Login Optional

Progress saved automatically

Students

Works great in classrooms

20,000,000
Response times
650,000
Unique questions
100
Difficulty levels

Cross-Platform

Use any operating system with Chrome, Safari, or Firefox

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.


Privacy Policy