Leaderboard
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Denmark
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Rank
Level
3
Erik M. L. Johannesen
Hovedstaden
87
6
Ida Maria Soelje
Hovedstaden
62
7
Jesper Ramsing
Syddanmark
61
9
ole jensen
Hovedstaden
58
10
User
Hovedstaden
56
11
Alexander Mønster
Hovedstaden
51
12
Max Hansen
Syddanmark
51
13
Dyrlund
Midtjylland
49
14
User
Midtjylland
49
15
Hannesbo
Hovedstaden
49
16
Magnus Kanstrup
Sjælland
48
17
Christian Alexander Yabar Mejer 2018e
Sjælland
46
18
Laura Gutiérrez
Hovedstaden
45
19
User
Nordjylland
45
20
User
Nordjylland
44
21
User
Hovedstaden
44
22
User
Hovedstaden
44
23
Laura Turner
Hovedstaden
39
24
User
Hovedstaden
39
25
User
Midtjylland
39
26
User
Hovedstaden
39
27
User
Hovedstaden
38
28
User
Hovedstaden
38
29
User
Midtjylland
37
30
User
Hovedstaden
36
31
User
Midtjylland
36
32
Asmus Rosendal
Midtjylland
36
33
User
Hovedstaden
36
34
Iulia Prundurel
Hovedstaden
35
35
User
Midtjylland
34
36
User
Hovedstaden
33
37
Christian Mejer
Sjælland
32
38
User
Hovedstaden
32
39
User
Midtjylland
31
40
User
Hovedstaden
30
41
User
Syddanmark
30
42
User
Midtjylland
30
43
Danny Nygård Hansen
Midtjylland
30
44
User
Hovedstaden
29
45
User
Nordjylland
28
46
User
Hovedstaden
28
47
User
Hovedstaden
27
48
User
Hovedstaden
27
49
User
Region
27
50
User
Region
27
51
User
Hovedstaden
26
52
User
Hovedstaden
26
53
Marin Jeppesen
Region
26
54
User
Hovedstaden
25
55
User
Hovedstaden
25
56
User
Hovedstaden
25
57
User
Region
25
58
User
Hovedstaden
24
59
User
Hovedstaden
24
60
User
Region
24
61
Teodor Andersen
Hovedstaden
23
62
User
Hovedstaden
23
63
User
Syddanmark
23
64
User
Midtjylland
23
65
User
Hovedstaden
22
66
Gustav Haugan
Hovedstaden
22
67
User
Syddanmark
22
68
User
Sjælland
22
69
User
Region
22
70
Foxylock
Nordjylland
21
71
User
Syddanmark
21
72
User
Hovedstaden
21
73
User
Midtjylland
21
74
User
Hovedstaden
21
75
Ida Marie Soelje
Hovedstaden
21
76
User
Hovedstaden
21
77
Finn Nørgaard-Pedersen
Hovedstaden
21
78
User
Syddanmark
21
79
User
Hovedstaden
21
80
User
Region
21
81
User
Region
21
82
User
Region
21
83
User
Hovedstaden
20
84
Rina
Hovedstaden
20
85
Lucazzz
Hovedstaden
20
86
User
Hovedstaden
20
87
User
Hovedstaden
20
88
User
Region
20
89
User
Region
20
90
User
Hovedstaden
19
91
Mikkel Risgaard
Syddanmark
19
92
User
Hovedstaden
19
93
User
Hovedstaden
19
94
User
Region
19
95
User
Nordjylland
18
96
User
Hovedstaden
18
97
User
Hovedstaden
18
98
User
Hovedstaden
18
99
User
Hovedstaden
18
100
User
Hovedstaden
18
101
User
Midtjylland
18
102
User
Nordjylland
18
103
User
Region
18
104
User
Region
18
105
User
Hovedstaden
17
106
User
Hovedstaden
17
107
User
Syddanmark
17
108
User
Hovedstaden
17
109
User
Hovedstaden
17
110
User
Region
17
111
User
Region
17
112
User
Region
17
113
August Soelje
Hovedstaden
16
114
User
Hovedstaden
16
115
User
Hovedstaden
16
116
User
Hovedstaden
16
117
User
Hovedstaden
15
118
User
Midtjylland
15
119
User
Nordjylland
15
120
User
Nordjylland
15
121
User
Hovedstaden
15
122
User
Midtjylland
15
123
User
Syddanmark
15
124
User
Region
15
125
User
Sjælland
14
126
fishcannon gaming
Hovedstaden
14
127
User
Hovedstaden
14
128
User
Midtjylland
14
129
User
Hovedstaden
14
130
User
Syddanmark
14
131
User
Midtjylland
14
132
Logan
Midtjylland
13
133
User
Syddanmark
13
134
User
Hovedstaden
13
135
Caroline CC
Hovedstaden
13
136
User
Hovedstaden
13
137
User
Hovedstaden
13
138
User
Midtjylland
13
139
User
Hovedstaden
13
140
User
Syddanmark
13
141
User
Nordjylland
13
142
User
Region
13
143
User
Hovedstaden
12
144
User
Hovedstaden
12
145
User
Sjælland
12
146
User
Hovedstaden
12
147
Mergus
Syddanmark
12
148
User
Hovedstaden
12
149
User
Hovedstaden
12
150
User
Hovedstaden
12
151
User
Hovedstaden
12
152
User
Hovedstaden
12
153
User
Hovedstaden
12
154
User
Hovedstaden
12
155
User
Midtjylland
12
156
User
Midtjylland
12
157
User
Syddanmark
12
158
User
Hovedstaden
12
159
Lasse Andersen
Syddanmark
11
160
Johan Sørensen
Hovedstaden
11
161
User
Midtjylland
11
162
User
Hovedstaden
11
163
User
Hovedstaden
11
164
User
Hovedstaden
11
165
User
Region
11
166
User
Nordjylland
10
167
User
Hovedstaden
10
168
User
Hovedstaden
10
169
User
Hovedstaden
10
170
User
Hovedstaden
10
171
User
Hovedstaden
10
172
User
Hovedstaden
10
173
User
Hovedstaden
10
174
User
Syddanmark
10
175
User
Hovedstaden
10
176
User
Hovedstaden
10
177
User
Region
10
178
User
Region
10
179
User
Midtjylland
9
180
User
Hovedstaden
9
181
User
Hovedstaden
9
182
User
Hovedstaden
9
183
User
Syddanmark
9
184
mikkel.vigel@hotmail.com
Hovedstaden
9
185
User
Hovedstaden
9
186
User
Sjælland
9
187
User
Hovedstaden
9
188
User
Hovedstaden
9
189
User
Midtjylland
9
190
User
Midtjylland
9
191
User
Region
9
192
User
Region
9
193
User
Syddanmark
8
194
User
Hovedstaden
8
195
User
Midtjylland
8
196
User
Hovedstaden
8
197
User
Hovedstaden
8
198
User
Hovedstaden
8
199
User
Hovedstaden
8
200
User
Hovedstaden
8
201
User
Hovedstaden
8
202
User
Hovedstaden
8
203
User
Hovedstaden
8
204
User
Nordjylland
8
205
User
Region
8
206
User
Midtjylland
7
207
User
Hovedstaden
7
208
User
Hovedstaden
7
209
User
Midtjylland
7
210
User
Hovedstaden
7
211
User
Hovedstaden
7
212
User
Hovedstaden
7
213
User
Hovedstaden
7
214
User
Hovedstaden
7
215
User
Syddanmark
7
216
User
Hovedstaden
7
217
User
Hovedstaden
7
218
User
Midtjylland
7
219
User
Hovedstaden
7
220
Philip Olsson
Hovedstaden
7
221
User
Hovedstaden
7
222
User
Hovedstaden
7
223
User
Hovedstaden
7
224
User
Region
7
225
User
Region
7
226
User
Region
7
227
User
Nordjylland
6
228
User
Hovedstaden
6
229
User
Nordjylland
6
230
User
Midtjylland
6
231
User
Midtjylland
6
232
User
Sjælland
6
233
User
Hovedstaden
6
234
User
Syddanmark
6
235
User
Hovedstaden
6
236
User
Hovedstaden
6
237
User
Region
6
238
User
Region
6
239
User
Region
6
240
User
Region
6
241
User
Midtjylland
5
242
User
Midtjylland
5
243
User
Hovedstaden
5
244
User
Nordjylland
5
245
User
Midtjylland
5
246
User
Hovedstaden
5
247
User
Hovedstaden
5
248
User
Syddanmark
5
249
User
Sjælland
5
250
User
Syddanmark
5
251
User
Midtjylland
5
252
User
Hovedstaden
5
253
User
Midtjylland
5
254
User
Midtjylland
5
255
User
Hovedstaden
5
256
User
Midtjylland
5
257
User
Hovedstaden
5
258
User
Syddanmark
5
259
User
Syddanmark
5
260
User
Midtjylland
5
261
hbrds B
Hovedstaden
5
262
User
Nordjylland
5
263
User
Hovedstaden
5
264
User
Hovedstaden
5
265
Marco Simmini
Hovedstaden
5
266
User
Hovedstaden
5
267
User
Hovedstaden
5
268
User
Hovedstaden
5
269
User
Syddanmark
5
270
User
Region
5
271
User
Region
5
272
User
Nordjylland
4
273
User
Hovedstaden
4
274
User
Midtjylland
4
275
User
Syddanmark
4
276
User
Hovedstaden
4
277
User
Midtjylland
4
278
User
Syddanmark
4
279
User
Hovedstaden
4
280
User
Hovedstaden
4
281
User
Hovedstaden
4
282
User
Hovedstaden
4
283
User
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4
284
User
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4
285
User
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4
286
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4
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User
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4
288
User
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4
289
User
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4
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User
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4
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User
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4
292
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4
293
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4
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4
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4
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4
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User
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4
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User
Midtjylland
3
301
User
Hovedstaden
3
302
User
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3
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3
304
User
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3
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User
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3
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3
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User
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3
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User
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3
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User
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3
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User
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3
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User
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3
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3
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3
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3
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3
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3
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3
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3
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3
321
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3
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KIm Lungay
Region
3
323
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Hovedstaden
2
324
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2
325
User
Hovedstaden
2
326
User
Nordjylland
2
327
User
Nordjylland
2
328
User
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2
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User
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2
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2
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2
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2
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2
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2
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2
344
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2
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2
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2
347
User
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2
348
User
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2
349
User
Hovedstaden
2
350
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2
351
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2
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2
353
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2
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User
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2
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User
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2
356
User
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2
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2
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2
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2
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2
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2
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2
365
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1
374
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1
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User
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1
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User
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1
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User
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1
378
User
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1
379
User
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1
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User
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1
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User
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1
382
User
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1
383
User
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1
384
jrk
Syddanmark
1
385
Emil Lykke Grann
Midtjylland
1
386
Helga correia
Sjælland
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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