Leaderboard
United Kingdom
United Kingdom
Worldwide
Rank
Level
1
User
England
94
2
User
England
94
3
Queen of England
Scotland
93
4
WhiteFalcon
England
92
5
Yellow Ninja
England
91
6
User
England
89
7
劉健聰Kenny
England
87
8
User
England
85
9
Prof Lishkov
England
85
10
G
England
84
11
Tony
England
83
12
Stephen Mellor
England
83
13
James TSANG
Scotland
82
14
Achintya Singh
England
82
15
User
England
82
16
Freddy Fan
England
82
17
George K
England
81
18
P McC
England
81
19
User
England
81
20
User
England
81
21
Tayip
England
80
22
User
England
80
23
User
England
79
24
Morgan
England
79
25
Frankburton
England
78
26
User
England
78
27
User
England
78
28
Hanh
England
77
29
User
England
77
30
User
England
76
31
User
England
76
32
Mark
England
75
33
User
England
75
34
Reuben Mason
England
75
35
Epsilon Delta
England
74
36
Kenny Yuan
England
74
37
ontop
England
74
38
User
England
74
39
User
England
73
40
User
England
73
41
Nikolay Momchev
Scotland
73
42
User
England
72
43
Abs Arosi
England
72
44
Kush Patel
England
72
45
User
England
71
46
Frank Burton
England
70
47
买了否冷
England
69
48
User
England
69
49
Jacob BJ
England
69
50
The Master Procrastinator
England
68
51
George
England
67
52
User
England
67
53
User
England
67
54
User
England
67
55
User
England
66
56
Anastasia
England
65
57
wilma6993
England
65
58
Dominic Hillier
England
65
59
Vibowie
England
65
60
stephen Allison
England
64
61
User
England
64
62
User
England
64
63
User
England
64
64
User
England
63
65
User
England
63
67
George Sarson
England
63
68
User
England
62
69
User
England
62
70
gautham ravisankar
England
62
71
Iona Ffrench-Adam
England
62
72
William Sadler
England
62
73
User
England
62
74
User
England
62
76
Dasha P.
England
61
77
User
England
61
78
Mike Diplock
England
61
79
User
England
61
80
User
England
61
81
User
England
61
82
J T
England
61
83
Michael Driesen
England
61
84
Gav N
England
60
85
User
Scotland
60
86
User
England
60
87
User
England
60
88
User
England
60
89
Joseph Hickie
England
59
90
Elect Akalonu
England
59
91
User
England
59
92
User
England
58
93
candaon
England
58
94
User
England
57
95
abcde
England
57
96
Gaganjit Tandon
England
57
97
User
England
56
98
User
England
56
99
Simon
England
56
100
User
England
56
101
User
England
55
102
Ken Lee
England
55
103
User
England
55
104
eep
England
55
105
Kev Telford
England
55
106
User
England
55
107
L T
England
54
108
User
England
54
109
User
England
54
110
User
England
54
111
User
England
54
112
User
England
54
113
User
England
54
114
User
England
53
115
User
England
53
116
User
Scotland
53
117
User
England
53
118
User
England
53
119
User
England
53
120
User
England
53
121
User
England
53
122
User
England
53
123
User
England
53
124
User
England
52
125
User
England
52
126
User
England
52
127
User
England
52
128
Louis A
England
52
129
Joseph Nathan
England
52
130
User
England
52
131
User
England
52
132
User
England
51
133
User
England
51
134
User
England
51
135
User
England
51
136
User
England
51
137
Nikolas Motsis
England
51
138
Tobbles
England
51
139
shoddyboi
Scotland
51
140
User
England
51
141
User
England
51
142
User
England
51
143
Louis Thackray
England
50
144
Marjorie Torrance
Scotland
50
145
Nathan Lisgo
England
50
146
User
England
50
147
Cat
England
50
148
User
England
50
149
User
England
50
150
User
England
50
151
User
England
50
152
User
England
50
153
User
England
50
154
User
England
50
155
User
England
50
156
User
England
50
157
Alison Lewis
Isle of Man
50
158
User
England
49
159
Sa
England
49
160
User
England
49
161
julia sink
England
49
162
User
England
49
163
User
England
49
164
Max
England
49
165
User
England
49
166
User
England
49
167
User
England
48
168
User
Wales
48
169
Kavi
England
48
170
Sazidul Hoque
England
48
171
AABB
Wales
48
172
User
England
48
173
User
England
48
174
Ed Jellylegs
England
48
175
Shaz
England
48
176
User
England
48
177
User
Scotland
47
178
User
England
47
179
User
England
47
180
User
England
47
181
User
England
47
182
User
England
47
183
Kowtham
England
47
184
User
England
47
185
bhumin
England
47
186
User
England
47
187
User
England
47
188
User
England
47
189
Hi There
England
47
190
User
Wales
47
191
User
England
47
192
User
England
47
193
Anthony Johnson
England
46
194
User
England
46
195
User
England
46
196
Shah
England
46
197
User
England
46
198
Jeffrey Chan
England
46
199
User
England
46
200
Peter Ashley
England
46
201
User
England
46
202
User
England
45
203
User
Wales
45
204
User
England
45
205
User
England
45
206
User
England
45
207
User
England
45
208
User
England
45
209
User
England
45
210
User
England
45
211
User
England
45
212
Marcus Hodgart
England
45
213
User
Scotland
45
214
User
Region
44
215
User
Scotland
44
216
User
England
44
217
User
England
44
218
User
England
44
219
User
England
44
220
User
England
44
221
User
England
44
222
Phil Davies
England
44
223
User
England
44
224
User
England
44
225
alex
England
44
226
User
England
44
227
User
England
44
228
User
England
44
229
User
England
44
230
User
Scotland
44
231
User
England
44
232
User
England
44
233
User
England
44
234
Rachel Stephanie van den Broek
England
43
235
User
England
43
237
XdFamSquadDabLittyFireDabXD
England
43
238
User
England
43
239
User
Scotland
43
240
Aleksander Keatings
Scotland
43
241
reggie bains
England
43
242
User
England
43
243
Gordon
England
43
244
User
England
43
245
User
England
43
246
User
England
43
247
User
England
43
248
User
England
43
249
User
England
43
250
User
England
43
251
User
England
42
252
User
England
42
253
User
England
42
254
User
England
42
255
User
England
42
256
User
England
42
257
Donalf tumpdf
England
42
258
User
England
42
259
User
England
42
260
User
England
42
261
JAAFAR
England
42
262
User
England
42
263
Saswata Chatterjee
England
42
264
User
England
42
265
Dennis Dinkelmeyer
England
42
266
User
England
42
267
User
England
42
268
User
England
42
269
User
England
42
270
Belo Beleus
England
42
271
User
England
42
272
Thanat
England
42
273
User
England
42
274
Amy Szarvas
England
42
275
User
England
42
276
User
England
41
278
User
England
41
279
User
England
41
280
User
England
41
281
Ponnochio
England
41
282
User
England
41
283
User
England
41
284
User
Wales
41
285
User
England
41
286
User
England
41
287
User
England
41
288
User
England
41
289
User
England
41
290
User
England
41
291
Connie Cheung
England
41
292
User
England
41
293
User
England
41
294
User
England
41
295
User
England
41
296
yayayaya
England
41
297
Harriet
England
41
298
User
England
41
299
Freddie Farmer
England
41
300
Vincenz Heidenreich
England
41
301
User
England
41
302
a s
England
41
303
User
England
41
304
Tom Draper
England
41
305
User
England
40
306
User
England
40
307
User
England
40
308
User
England
40
309
User
England
40
310
User
England
40
311
User
England
40
312
User
England
40
313
User
England
40
314
Javier Melo
England
40
315
User
England
40
316
User
England
40
317
Kenny Stevens
England
40
318
User
England
40
319
User
England
40
320
User
England
40
321
Phoenix Wright
England
40
322
User
England
40
323
Sameer Aiyar-Majeed
England
40
324
User
England
40
325
User
England
40
326
User
England
40
327
User
England
40
328
User
England
40
329
User
England
40
330
User
England
39
331
Maks
England
39
332
User
England
39
333
User
England
39
334
User
England
39
335
User
England
39
336
M K
England
39
337
User
England
39
338
User
England
39
339
User
England
39
340
User
England
39
341
User
England
39
342
User
England
39
343
MrNobody _
England
39
344
Dennis Dinkelmeyer
England
39
345
User
England
39
346
User
England
39
347
James de Salis Young
England
39
348
User
England
39
349
User
Scotland
39
350
User
England
39
351
User
England
39
352
User
England
39
353
Nick Summers
England
39
354
User
England
39
355
Moritz S
England
39
356
User
England
39
357
User
England
39
358
User
England
38
359
User
England
38
360
User
England
38
361
User
England
38
362
User
England
38
363
User
England
38
364
User
England
38
365
User
England
38
366
User
England
38
367
User
England
38
368
User
England
38
369
User
England
38
370
User
England
38
371
User
England
38
372
User
England
38
373
User
England
38
374
User
England
38
375
Bri Borup
England
38
376
Ishita Jainer
England
38
377
User
Scotland
38
378
Leanne Cheng
England
38
379
User
England
38
380
User
England
38
381
Tajri Salek
England
38
382
User
England
38
383
User
England
38
384
User
England
38
385
User
England
38
386
User
England
38
387
User
England
37
388
Maria M
England
37
389
User
England
37
390
User
England
37
391
Nithil Kennedy
England
37
392
User
England
37
393
User
England
37
394
John Cook
England
37
395
User
England
37
396
Jimmy Li
England
37
397
Alex Hill
England
37
398
User
England
37
399
User
England
37
400
JUN ALI
England
37
401
User
England
37
402
Martin Smith
England
37
403
User
England
37
404
Beth Ca
England
37
405
User
England
37
406
User
England
37
407
User
England
37
408
User
England
37
409
User
England
37
410
User
England
37
411
Boris
England
37
412
User
England
37
413
User
England
37
414
User
England
37
415
User
England
37
416
User
England
37
417
caleb
England
37
418
User
England
36
419
User
England
36
420
User
England
36
421
Michael Wielondek
England
36
422
User
England
36
423
User
England
36
424
User
England
36
425
Katy Griffiths
England
36
426
User
England
36
427
Emily Broadhurst
England
36
428
User
England
36
429
User
England
36
430
User
Scotland
36
431
User
England
36
432
Yaseen Al-shawk
England
36
433
User
England
36
434
User
England
36
435
User
England
36
436
Cindy Wu
England
36
437
dan
England
36
438
maths
England
36
439
User
England
36
440
User
England
35
441
Natalie Wall
England
35
442
User
England
35
443
User
England
35
444
User
England
35
445
Kevin Ledda
England
35
446
User
England
35
447
User
England
35
448
User
England
35
449
User
England
35
450
Tom
England
35
451
User
England
35
452
User
England
35
453
User
England
35
454
Alishba K
England
35
455
User
England
35
456
User
England
35
457
User
England
35
458
User
England
35
459
User
England
35
460
User
England
35
461
YAHIA
Region
35
463
User
England
35
464
User
England
35
465
User
Scotland
35
466
User
England
35
467
User
England
35
468
User
England
35
469
Beemore
England
34
470
User
England
34
472
User
England
34
473
User
England
34
474
User
England
34
475
Gabriel Ng
England
34
476
User
England
34
477
Juan garcia
England
34
478
User
England
34
479
User
England
34
480
User
England
34
481
User
England
34
482
User
England
34
483
User
England
34
484
User
England
34
485
Elijah Lisgo
England
34
486
User
England
34
487
User
England
34
488
User
England
34
489
Anjaney M
England
34
490
User
England
34
491
User
Scotland
34
492
User
England
34
493
User
England
34
494
User
England
34
495
User
England
34
496
Ollie Matt
England
34
497
User
England
34
498
User
England
34
499
User
England
34
500
User
England
34
501
User
England
34
502
User
England
34
503
User
England
34
504
User
England
34
505
User
England
34
506
User
Scotland
33
507
User
England
33
508
User
England
33
509
User
England
33
510
Ramleen Pan
England
33
511
User
England
33
512
User
England
33
513
User
England
33
514
User
England
33
515
User
England
33
516
Ben Renton
England
33
517
HazHS
England
33
518
User
England
33
519
MarcoPigna
England
33
520
User
England
33
521
User
England
33
522
User
England
33
523
User
England
33
524
User
England
33
525
User
England
33
526
Federico Romei
England
33
527
User
England
33
528
User
England
33
529
User
England
33
530
User
England
33
531
User
England
33
532
User
England
33
533
User
England
33
534
Sonya G
England
33
535
User
England
33
536
User
England
33
537
Devesteter252101
England
33
538
User
England
33
539
User
England
33
540
User
England
33
541
User
England
33
542
User
England
32
543
User
England
32
544
User
England
32
545
User
England
32
546
User
England
32
547
User
England
32
548
Umar Tariq
England
32
549
Bob
England
32
550
Alberto Dolcetta
England
32
551
User
England
32
552
User
England
32
553
User
England
32
554
User
England
32
555
M R
England
32
556
Nithin Subhakar
England
32
557
User
England
32
558
User
England
32
559
User
England
32
560
User
England
32
561
User
Scotland
32
562
User
England
32
563
User
England
32
564
User
England
32
565
User
England
32
566
User
England
32
567
User
England
32
568
User
England
32
569
User
England
32
570
User
England
32
571
hmsschofield
England
32
572
Maharaja
England
32
573
User
England
32
574
User
England
32
575
User
England
32
576
User
Scotland
32
577
User
England
32
578
User
England
32
579
User
England
32
580
User
England
32
581
User
Scotland
32
582
User
England
32
583
User
England
32
584
User
England
32
585
Gopal Kaverikanth
England
32
586
Sumer Jaitly
England
32
587
User
England
31
588
User
England
31
589
Jaroslav Vohradsky
England
31
590
User
England
31
591
Dylan
England
31
592
User
England
31
593
Nicolas Lefort
England
31
594
User
England
31
595
User
England
31
596
User
Scotland
31
597
User
England
31
598
Felix Pereira
England
31
599
User
England
31
600
User
England
31
601
Mic
England
31
602
User
England
31
603
User
England
31
604
Olivia
Wales
31
605
User
England
31
606
User
England
31
607
User
England
31
608
Ernesta Spathas
England
31
609
User
England
31
610
Kristers
England
31
611
Sam
England
31
612
User
England
31
613
Khawla
England
31
614
User
England
31
615
User
England
31
616
User
England
31
617
User
England
31
618
Kat
England
31
619
User
England
31
620
User
England
31
621
User
England
31
622
User
England
31
623
Tyler Woodstock
England
31
624
User
Wales
31
626
User
England
31
627
User
England
31
628
User
England
31
629
User
England
31
630
Nick Cupit
England
31
631
User
England
31
632
User
England
31
633
User
England
31
634
User
England
31
635
User
England
31
636
User
England
31
637
Frill Seekaz
Region
31
638
User
Wales
31
639
User
England
31
640
User
England
31
641
User
England
31
642
User
Scotland
30
643
Roxana Tsirikhova
England
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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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