Leaderboard
United Kingdom
United Kingdom
Worldwide
Rank
Level
1
User
England
98
2
WhiteFalcon
England
96
3
User
England
94
4
User
England
94
5
Queen of England
Scotland
93
6
John Ewart
England
92
7
Yellow Ninja
England
91
8
User
England
89
9
Zohaib
England
87
10
劉健聰Kenny
England
87
11
G
England
85
12
User
England
85
13
Prof Lishkov
England
85
14
Jack Treanor
England
83
15
Tony
England
83
16
Stephen Mellor
England
83
17
Michalis
England
82
18
Achintya Singh
England
82
19
User
England
82
20
Freddy Fan
England
82
21
User
England
81
22
User
England
81
23
P McC
England
81
24
User
England
81
25
User
England
81
26
Tayip
England
80
27
User
England
80
28
User
Region
79
29
User
England
79
30
Morgan
England
79
31
User
England
78
32
Ibrahim Sulaiman
England
78
33
George
England
78
34
Frankburton
England
78
35
User
England
78
36
User
England
78
37
stephen Allison
England
77
38
Hanh
England
77
39
User
England
77
40
User
England
76
41
User
England
76
42
Anastasia
England
75
43
User
England
75
44
Joe
England
75
45
User
England
75
46
Reuben Mason
England
75
47
Fabrizio Lilliu
England
74
48
Bob
England
74
49
User
England
74
50
Epsilon Delta
England
74
51
ontop
England
74
52
User
England
74
53
B l
England
73
54
JJJJ
England
73
55
User
England
73
56
User
England
73
57
Nikolay Momchev
Scotland
73
58
Gav N
England
72
59
User
England
72
60
Abs Arosi
England
72
61
Kush Patel
England
72
62
Max Bridge
England
71
63
User
England
71
64
User
England
71
65
Jonathan
England
70
66
User
Wales
70
67
User
Scotland
70
68
JP
England
70
69
Frank Burton
England
70
70
User
England
69
71
User
England
69
72
买了否冷
England
69
73
User
England
69
74
Jacob BJ
England
69
75
User
England
68
76
User
England
67
77
Nina P
England
67
78
User
England
67
79
User
England
67
80
User
England
67
81
User
England
66
82
isuck@division
England
66
83
User
England
66
84
Sacha
England
65
85
User
Scotland
65
86
F CDN
England
65
87
User
England
65
88
wilma6993
England
65
89
Dominic Hillier
England
65
90
Vibowie
England
65
91
E.P. Thompson
England
64
92
User
England
64
93
User
England
64
94
User
England
64
95
Andrew Koto
England
63
96
User
England
63
98
George Sarson
England
63
99
User
England
62
100
User
England
62
101
User
England
62
102
User
England
62
103
gautham ravisankar
England
62
104
Iona Ffrench-Adam
England
62
105
William Sadler
England
62
106
User
England
62
107
User
England
62
109
User
England
61
110
User
England
61
111
Dasha P.
England
61
112
Mike Diplock
England
61
113
User
England
61
114
User
England
61
115
User
England
61
116
J T
England
61
117
Michael Driesen
England
61
118
User
England
60
119
User
Scotland
60
120
User
England
60
121
User
England
60
122
User
England
60
123
User
England
60
124
User
England
60
125
User
England
60
126
User
Scotland
60
127
User
England
60
128
User
England
60
129
User
England
60
130
Jahan14
England
59
131
Joseph Hickie
England
59
132
Elect Akalonu
England
59
133
User
England
59
134
User
England
58
135
User
England
58
136
Bk
England
58
137
Ulrich Hornheimer
England
58
138
candaon
England
58
139
User
England
57
140
User
England
57
141
User
England
57
142
Gaganjit Tandon
England
57
143
User
England
56
144
User
England
56
145
User
England
56
146
User
England
56
147
Bruce Boutell
England
56
148
User
England
56
149
User
England
56
150
User
England
56
151
User
England
56
152
User
England
56
153
User
England
56
154
User
England
56
155
User
England
56
156
Simon
England
56
157
User
England
56
158
User
England
55
159
Jiahung Li
England
55
160
viggy
England
55
161
User
England
55
162
User
England
55
163
User
England
55
164
User
England
55
165
User
England
55
166
User
Scotland
55
167
User
England
55
168
eep
England
55
169
Kev Telford
England
55
170
User
England
55
171
User
England
54
172
User
England
54
173
Marc P
England
54
174
User
England
54
175
L T
England
54
176
User
England
54
177
User
England
54
178
User
England
54
179
User
England
54
180
User
England
54
181
User
England
54
182
User
England
53
183
User
England
53
184
User
England
53
185
User
England
53
186
User
England
53
187
Aliya boiiii get off meh account mate
England
53
188
User
England
53
189
User
England
53
190
User
Scotland
53
191
User
England
53
192
User
England
53
193
User
England
53
194
User
England
53
195
User
England
53
196
User
England
53
197
Gayle
England
52
198
User
Isle of Man
52
199
User
England
52
200
User
England
52
201
User
England
52
202
User
England
52
203
User
England
52
204
User
England
52
205
User
England
52
206
Louis A
England
52
207
Joseph Nathan
England
52
208
User
England
52
209
User
England
52
210
User
England
51
211
User
England
51
212
User
England
51
213
Yo jam
England
51
214
User
England
51
215
User
England
51
216
User
England
51
217
User
England
51
218
User
England
51
219
Nikolas Motsis
England
51
220
shoddyboi
Scotland
51
221
User
England
51
222
User
England
51
223
User
England
51
224
User
England
50
225
Vinicius Fernandes
England
50
226
Georgia Brown
England
50
227
Louis Thackray
England
50
228
Marjorie Torrance
Scotland
50
229
Nathan Lisgo
England
50
230
User
England
50
231
Cat
England
50
232
User
England
50
233
User
England
50
234
User
England
50
235
User
England
50
236
User
England
50
237
User
England
50
238
User
England
50
239
User
England
50
240
User
England
50
241
Alison Lewis
Isle of Man
50
242
amir jarada
England
49
243
Sara
England
49
244
User
England
49
245
User
England
49
246
User
England
49
247
Ricky Green
England
49
248
User
Scotland
49
249
User
England
49
250
User
England
49
251
Sam Geracitano
England
49
252
Jonny Dowe
England
49
253
User
England
49
254
User
England
49
255
Sa
England
49
256
User
England
49
257
julia sink
England
49
258
User
England
49
259
User
England
49
260
Max
England
49
261
User
England
49
262
User
England
49
263
Chris
England
48
264
Richard Clouter
Scotland
48
265
User
England
48
266
User
England
48
267
User
England
48
268
bexgravell
England
48
269
User
England
48
270
User
England
48
271
Alex Bor
England
48
272
User
England
48
273
anonymous anonymous
England
48
274
Nick Thomson
England
48
275
User
England
48
276
User
Wales
48
277
Kavi
England
48
278
Sazidul Hoque
England
48
279
AABB
Wales
48
280
User
England
48
281
Ed Jellylegs
England
48
282
Shaz
England
48
283
User
England
48
284
Nick
England
47
285
User
England
47
286
Benjamin Irwin
England
47
287
User
England
47
288
User
England
47
289
User
Scotland
47
290
User
England
47
291
User
England
47
292
User
England
47
293
User
England
47
294
User
England
47
295
Kowtham
England
47
296
User
England
47
297
bhumin
England
47
298
User
England
47
299
User
England
47
300
User
England
47
301
Hi There
England
47
302
User
Wales
47
303
User
England
47
304
User
England
47
305
Salman Hussain
England
46
306
Amy Szarvas
England
46
307
Charles Siu
England
46
308
User
England
46
309
User
England
46
310
Tobbles
England
46
311
Anthony Johnson
England
46
312
User
England
46
313
Shah
England
46
314
User
England
46
315
Jeffrey Chan
England
46
316
User
England
46
317
Peter Ashley
England
46
318
User
England
46
319
User
England
45
320
ifu05444
England
45
321
User
England
45
322
User
England
45
323
Paul Joseph
England
45
324
Rachel Stephanie van den Broek
England
45
325
User
England
45
326
User
Wales
45
327
User
England
45
328
User
England
45
329
User
England
45
330
User
England
45
331
User
England
45
332
User
England
45
333
User
England
45
334
User
England
45
335
Marcus Hodgart
England
45
336
User
Scotland
45
337
George K
England
44
338
Omeed
Region
44
339
User
England
44
340
User
England
44
341
User
England
44
342
Toby
England
44
343
andrew
England
44
344
User
England
44
345
User
England
44
346
User
England
44
347
User
Scotland
44
348
User
England
44
349
User
England
44
350
User
England
44
351
User
England
44
352
User
England
44
353
User
England
44
354
Phil Davies
England
44
355
User
England
44
356
User
England
44
357
User
England
44
358
User
England
44
359
User
England
44
360
User
England
44
361
User
Scotland
44
362
User
England
44
363
User
England
44
364
User
England
44
365
User
England
43
366
Ella Barnes
England
43
367
Tahmid Rahman
England
43
368
User
England
43
369
User
England
43
370
User
England
43
371
User
England
43
372
User
England
43
373
User
England
43
374
Josh Paul
England
43
375
User
England
43
377
User
England
43
378
Aleksander Keatings
Scotland
43
379
reggie bains
England
43
380
User
England
43
381
Gordon
England
43
382
User
England
43
383
User
England
43
384
User
England
43
385
User
England
43
386
User
England
43
387
User
England
43
388
User
England
43
389
User
England
42
390
User
Scotland
42
391
User
England
42
392
User
England
42
393
User
England
42
394
Davide Uccello
Scotland
42
395
User
Scotland
42
396
User
England
42
397
User
England
42
398
User
England
42
399
User
England
42
400
User
England
42
401
User
England
42
402
User
England
42
403
User
England
42
404
User
England
42
405
User
England
42
406
User
England
42
407
Donalf tumpdf
England
42
408
User
England
42
409
User
England
42
410
User
England
42
411
JAAFAR
England
42
412
User
England
42
413
Saswata Chatterjee
England
42
414
User
England
42
415
User
England
42
416
User
England
42
417
User
England
42
418
User
England
42
419
Belo Beleus
England
42
420
User
England
42
421
Thanat
England
42
422
User
England
42
423
User
England
41
424
User
England
41
425
User
England
41
426
User
England
41
427
Alex Hanrahan
England
41
428
Jen Furmston
England
41
429
User
England
41
430
User
England
41
431
User
England
41
433
User
England
41
434
User
England
41
435
User
England
41
436
Ponnochio
England
41
437
User
England
41
438
User
England
41
439
User
Wales
41
440
User
England
41
441
User
England
41
442
User
England
41
443
User
England
41
444
User
England
41
445
Connie Cheung
England
41
446
User
England
41
447
User
England
41
448
User
England
41
449
User
England
41
450
yayayaya
England
41
451
Harriet
England
41
452
User
England
41
453
Freddie Farmer
England
41
454
Vincenz Heidenreich
England
41
455
User
England
41
456
a s
England
41
457
User
England
41
458
Tom Draper
England
41
459
User
Scotland
40
460
User
England
40
461
User
England
40
462
User
England
40
463
User
England
40
464
Zana Osmani
England
40
465
User
England
40
466
User
Region
40
467
User
England
40
468
User
England
40
469
User
England
40
470
User
England
40
471
User
England
40
472
User
England
40
473
User
England
40
474
User
England
40
475
Javier Melo
England
40
476
User
England
40
477
User
England
40
478
Kenny Stevens
England
40
479
User
England
40
480
User
England
40
481
Phoenix Wright
England
40
482
User
England
40
483
Sameer Aiyar-Majeed
England
40
484
User
England
40
485
User
England
40
486
User
England
40
487
User
England
40
488
User
England
40
489
User
England
39
490
Mari Gravell
England
39
491
Abi
Wales
39
492
User
England
39
493
User
England
39
494
User
Wales
39
495
winky
England
39
496
User
England
39
497
User
England
39
498
User
England
39
499
User
England
39
500
Pak
England
39
501
Maks
England
39
502
User
England
39
503
User
England
39
504
User
England
39
505
User
England
39
506
M K
England
39
507
User
England
39
508
User
England
39
509
User
England
39
510
User
England
39
511
User
England
39
512
User
England
39
513
MrNobody _
England
39
514
Dennis Dinkelmeyer
England
39
515
User
England
39
516
User
England
39
517
James de Salis Young
England
39
518
User
England
39
519
User
Scotland
39
520
User
England
39
521
User
England
39
522
User
England
39
523
Nick Summers
England
39
524
User
England
39
525
Moritz S
England
39
526
User
England
39
527
User
England
39
528
User
England
38
529
User
England
38
530
User
England
38
531
Ernie T
England
38
532
User
England
38
533
User
England
38
534
User
England
38
535
DC
England
38
536
User
England
38
537
User
Scotland
38
538
User
England
38
539
User
England
38
540
User
England
38
541
User
England
38
542
User
England
38
543
User
England
38
544
User
England
38
545
User
England
38
546
User
England
38
547
User
England
38
548
User
England
38
549
User
England
38
550
User
England
38
551
User
England
38
552
User
England
38
553
User
England
38
554
User
England
38
555
Bri Borup
England
38
556
Ishita Jainer
England
38
557
User
Scotland
38
558
Leanne Cheng
England
38
559
User
England
38
560
User
England
38
561
Tajri Salek
England
38
562
User
England
38
563
User
England
38
564
User
England
38
565
User
England
38
566
User
England
38
567
User
England
37
568
User
England
37
569
User
England
37
570
User
England
37
571
edward stubbs
England
37
572
mb8993
England
37
573
User
England
37
574
Radek
England
37
575
User
England
37
576
User
England
37
577
User
England
37
578
JahrhysG
England
37
579
User
England
37
580
User
England
37
581
Nithil Kennedy
England
37
582
User
England
37
583
User
England
37
584
John Cook
England
37
585
User
England
37
586
Alex Hill
England
37
587
User
England
37
588
JUN ALI
England
37
589
User
England
37
590
Martin Smith
England
37
591
User
England
37
592
Beth Ca
England
37
593
User
England
37
594
User
England
37
595
User
England
37
596
User
England
37
597
User
England
37
598
User
England
37
599
Boris
England
37
600
User
England
37
601
User
England
37
602
User
England
37
603
User
England
37
604
User
England
37
605
caleb
England
37
606
Okyere
England
36
607
Ben Alfert
England
36
608
User
England
36
609
Asvigaa Ganesh
England
36
610
User
England
36
611
Beemore
England
36
612
User
England
36
613
User
England
36
614
User
England
36
615
User
England
36
616
User
England
36
617
Michael Wielondek
England
36
618
User
England
36
619
User
England
36
620
User
England
36
621
Katy Griffiths
England
36
622
User
England
36
623
Emily Broadhurst
England
36
624
User
England
36
625
User
England
36
626
User
Scotland
36
627
User
England
36
628
Yaseen Al-shawk
England
36
629
User
England
36
630
User
England
36
631
User
England
36
632
Cindy Wu
England
36
633
dan
England
36
634
maths
England
36
635
User
Scotland
35
636
User
England
35
637
User
England
35
638
User
England
35
639
User
England
35
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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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