Leaderboard
Netherlands
Netherlands
Worldwide
Rank
Level
2
Gerd Wichers
Noord-Brabant
98
3
Balazs
Zuid-Holland
98
4
User
Overijssel
96
5
User
Overijssel
96
9
Wouter Huisman
Zuid-Holland
91
10
Kyle
Zuid-Holland
91
12
ReynaertPJ
Noord-Holland
88
13
Yannick Vels
Utrecht
87
14
User
Region
87
15
Abhiraj
Noord-Holland
86
16
User
Overijssel
82
17
User
Overijssel
82
19
User
Utrecht
78
20
Justin Leemburg
Noord-Holland
77
21
User
Groningen
77
22
Robin David
Overijssel
76
23
Lars Holtappels
Noord-Brabant
75
25
Tolga Celebi
Noord-Holland
73
26
Sven Polak
Noord-Holland
73
28
Benjamin Oosterom
Noord-Holland
71
30
User
Drenthe
68
31
User
Groningen
67
33
Floris
Zuid-Holland
66
34
Rambo
Zuid-Holland
66
36
User
Gelderland
65
37
Pim Kouwenhoven
Zuid-Holland
65
38
Anano Basilaia
Utrecht
65
39
Nimona Workneh
Noord-Holland
65
40
DaHood
Zuid-Holland
64
41
Olivier van der Vet
Zuid-Holland
64
42
Mitchell Borst
Zuid-Holland
64
43
Ernst
Region
63
44
User
Zuid-Holland
63
47
User
Zuid-Holland
61
48
Rik Noij
Noord-Brabant
61
50
User
Groningen
60
51
Joël Kuyper
Zuid-Holland
59
53
Xinyu Hu
Zuid-Holland
58
54
User
Utrecht
58
55
User
Region
57
56
User
Region
57
57
Alvin
Gelderland
57
58
Ivan Ivanov
Groningen
57
59
Jeroen van der Does de Willebois
Noord-Holland
57
60
User
Gelderland
56
61
Babba babs
Noord-Holland
55
63
User
Zuid-Holland
55
64
User
Flevoland
55
65
User
Zuid-Holland
55
66
Brenno Baas
Zuid-Holland
53
67
Darkmenhigh
Noord-Holland
53
68
Trung Dũng
Noord-Brabant
53
70
User
Zuid-Holland
52
71
kenzo eulink
Gelderland
52
72
Jeffrey Rietveld
Zuid-Holland
51
73
User
Overijssel
51
74
Stijn
Zuid-Holland
51
76
Eline
Zuid-Holland
51
77
Pie pie
Zuid-Holland
50
79
Johnson Mok
Zuid-Holland
50
80
Sakboy TB
Noord-Holland
50
81
Maarten Markering
Gelderland
49
82
User
Utrecht
49
83
Mart van Zon
Noord-Brabant
49
84
Fritsie boiker
Utrecht
49
85
Yal Gnoj
Utrecht
48
86
User
Overijssel
48
87
User
Overijssel
48
88
User
Utrecht
48
89
User
Overijssel
48
90
N. F.
Zuid-Holland
48
91
User
Utrecht
48
92
Dominique Langeslag
Noord-Holland
48
93
User
Zuid-Holland
47
94
User
Region
47
95
Ruben Bieze
Noord-Holland
46
97
User
Gelderland
46
99
User
Utrecht
46
100
User
Region
46
101
User
Gelderland
45
102
User
Noord-Holland
45
103
User
Groningen
45
104
David de Jong
Zuid-Holland
45
105
User
Noord-Holland
45
106
User
Noord-Holland
44
107
Jordy Top
Noord-Holland
44
108
User
Noord-Holland
44
109
Coen Sonneveld
Noord-Brabant
44
110
User
Gelderland
44
111
Max Dijkstra
Noord-Holland
44
112
fedde hop
Overijssel
44
113
Bram Sjaak
Gelderland
44
114
John Doe
Noord-Holland
44
115
Jur Tasseron
Gelderland
44
116
User
Zuid-Holland
43
117
User
Zuid-Holland
43
118
User
Zuid-Holland
43
119
ingmar Heikens
Groningen
43
120
User
Zuid-Holland
43
121
User
Zuid-Holland
43
122
Nick Timmer
Noord-Brabant
43
123
User
Gelderland
43
124
User
Zuid-Holland
43
125
Remmie
Noord-Holland
42
126
Rishab Khandelwal
Noord-Brabant
42
127
User
Zuid-Holland
42
128
User
Zuid-Holland
42
129
User
Utrecht
42
130
User
Groningen
42
131
User
Zuid-Holland
42
132
User
Region
42
133
User
Gelderland
41
134
User
Gelderland
41
135
User
Noord-Brabant
41
136
User
Noord-Brabant
41
137
User
Noord-Holland
41
138
User
Gelderland
41
139
User
Noord-Holland
41
140
Lukas Bieliauskas
Noord-Holland
40
141
User
Zuid-Holland
40
142
User
Utrecht
40
143
Sergio Tam
Zuid-Holland
40
144
faze up
Noord-Holland
40
145
Piet
Noord-Holland
40
146
User
Noord-Holland
39
147
User
Zuid-Holland
39
148
User
Zuid-Holland
39
149
User
Noord-Holland
38
151
User
Zuid-Holland
38
152
User
Zuid-Holland
38
153
Maureen Drijver
Zuid-Holland
38
154
User
Noord-Holland
38
155
User
Zuid-Holland
38
156
User
Utrecht
38
157
User
Zuid-Holland
37
158
User
Region
37
159
User
Zuid-Holland
37
160
User
Zuid-Holland
37
161
User
Utrecht
37
162
Erik J.
Zuid-Holland
37
163
Victor Harmsen
Zuid-Holland
37
164
User
Noord-Brabant
37
165
User
Zuid-Holland
36
166
User
Zuid-Holland
36
167
User
Gelderland
36
168
User
Overijssel
36
169
User
Noord-Holland
36
170
Bas Nijman
Noord-Holland
36
171
User
Zuid-Holland
36
172
Radmir Leushuis
Utrecht
36
173
Danique
Utrecht
36
175
Sven Witteveen
Zuid-Holland
35
176
Freek
Zuid-Holland
35
177
Mark
Zuid-Holland
35
178
User
Overijssel
35
179
User
Overijssel
35
180
User
Overijssel
35
181
User
Zuid-Holland
35
182
User
Noord-Holland
34
183
Jan Hoekman
Zuid-Holland
34
184
User
Noord-Holland
34
185
Dwarrel
Noord-Holland
34
186
User
Zuid-Holland
34
187
User
Noord-Holland
34
188
User
Noord-Brabant
34
189
User
Utrecht
34
190
Johan Loots
Groningen
34
191
User
Zuid-Holland
34
192
User
Zuid-Holland
34
193
User
Zuid-Holland
34
194
User
Noord-Holland
34
195
User
Zuid-Holland
34
196
gamer
Region
34
197
Powerslider
Zuid-Holland
34
198
Doodle
Noord-Brabant
34
199
User
Overijssel
33
200
Casper Steenbergen
Noord-Holland
33
201
User
Noord-Holland
33
202
User
Noord-Brabant
33
203
User
Noord-Holland
33
204
User
Zuid-Holland
33
205
User
Zuid-Holland
33
206
finnley
Noord-Holland
32
207
User
Zuid-Holland
32
208
User
Zuid-Holland
32
209
User
Zuid-Holland
32
210
User
Zuid-Holland
32
211
User
Zuid-Holland
32
212
Michael Wijtzes
Zuid-Holland
32
213
User
Region
32
214
Olivier Kuijpers
Zuid-Holland
32
215
User
Noord-Holland
32
216
User
Noord-Brabant
32
218
Prashanth Neelakantan
Zuid-Holland
32
219
User
Noord-Holland
32
220
Stevan Jevremov
Zuid-Holland
31
221
User
Noord-Brabant
31
222
Austin Menzies
Noord-Holland
31
223
User
Zuid-Holland
31
224
David
Noord-Holland
31
225
User
Utrecht
31
226
Titus Pellegrom
Noord-Holland
31
227
User
Noord-Holland
31
228
sky sky
Zuid-Holland
31
229
User
Zuid-Holland
31
230
User
Noord-Holland
31
231
User
Zuid-Holland
31
232
User
Utrecht
30
233
User
Zuid-Holland
30
234
User
Region
30
235
User
Overijssel
30
236
User
Utrecht
30
237
User
Gelderland
30
238
User
Noord-Holland
30
239
User
Zuid-Holland
30
240
User
Zuid-Holland
30
241
User
Gelderland
30
242
User
Overijssel
30
243
Empty Suit
Noord-Brabant
30
244
User
Noord-Holland
30
245
Daan Klaver
Zuid-Holland
30
246
User
Zuid-Holland
30
247
Giovanni Scheepers
Flevoland
29
248
User
Noord-Holland
29
249
User
Limburg
29
250
User
Zuid-Holland
29
251
User
Gelderland
29
252
User
Noord-Holland
29
253
User
Overijssel
29
254
User
Noord-Holland
29
255
User
Noord-Brabant
29
256
User
Zuid-Holland
29
257
Wisse
Zuid-Holland
28
258
User
Zuid-Holland
28
259
Bas bakker
Gelderland
28
260
User
Zuid-Holland
28
261
User
Zuid-Holland
28
262
User
Noord-Holland
28
263
User
Noord-Holland
28
264
User
Noord-Holland
28
265
Carlos Alberto Neto
Zuid-Holland
28
266
User
Overijssel
28
267
Bram
Noord-Holland
28
268
User
Region
28
269
User
Zuid-Holland
28
270
User
Noord-Holland
27
271
User
Zuid-Holland
27
272
User
Noord-Brabant
27
273
User
Noord-Holland
27
274
Stan Schalij
Noord-Holland
27
275
User
Zuid-Holland
27
276
User
Zuid-Holland
27
277
Sci Sil
Region
27
278
User
Gelderland
26
279
User
Utrecht
26
280
User
Noord-Holland
26
281
Daan Wimmers
Noord-Brabant
26
282
User
Noord-Holland
26
283
els mus
Zuid-Holland
26
284
User
Noord-Holland
26
285
User
Noord-Holland
26
286
User
Noord-Holland
25
287
User
Zuid-Holland
25
288
User
Zuid-Holland
25
289
Tom Bour
Limburg
25
290
User
Noord-Holland
25
291
Tartagnan
Utrecht
25
292
User
Overijssel
25
293
User
Utrecht
25
294
User
Noord-Holland
25
295
User
Noord-Holland
25
296
User
Noord-Brabant
25
297
User
Zuid-Holland
25
298
User
Noord-Holland
25
301
User
Noord-Holland
24
302
User
Noord-Holland
24
303
User
Noord-Holland
24
304
User
Noord-Holland
24
305
User
Noord-Holland
24
306
User
Zuid-Holland
24
307
User
Noord-Brabant
24
308
Mátyás Tóth
Noord-Holland
24
309
User
Utrecht
24
310
User
Noord-Holland
24
311
User
Gelderland
24
312
User
Zuid-Holland
24
313
Anner
Zuid-Holland
23
315
User
Zuid-Holland
23
317
User
Zuid-Holland
23
318
User
Noord-Holland
23
319
Tim
Overijssel
23
320
User
Noord-Holland
23
321
User
Gelderland
23
322
User
Zuid-Holland
23
323
User
Zuid-Holland
23
324
User
Zuid-Holland
23
325
User
Zuid-Holland
23
326
User
Gelderland
23
327
User
Zuid-Holland
23
328
Paul Vergouwe
Zuid-Holland
23
329
User
Utrecht
23
330
User
Noord-Holland
23
331
User
Noord-Holland
23
332
User
Zuid-Holland
22
333
User
Zuid-Holland
22
334
Matt Tee
Zuid-Holland
22
335
DJ Bread
Zuid-Holland
22
336
User
Noord-Holland
22
337
User
Gelderland
22
338
User
Utrecht
22
339
User
Utrecht
22
340
User
Noord-Holland
22
341
User
Noord-Holland
22
342
User
Noord-Holland
22
343
dddd
Noord-Brabant
22
344
User
Noord-Holland
22
345
User
Zuid-Holland
22
346
User
Noord-Holland
22
347
User
Noord-Holland
22
348
User
Zuid-Holland
21
349
User
Noord-Brabant
21
350
User
Noord-Holland
21
351
User
Gelderland
21
352
User
Noord-Holland
21
353
User
Noord-Holland
21
354
User
Noord-Holland
21
355
User
Region
21
356
User
Groningen
21
357
User
Zuid-Holland
21
358
User
Zuid-Holland
21
359
User
Utrecht
21
360
User
Overijssel
21
361
User
Zuid-Holland
21
362
User
Zuid-Holland
21
363
John Doe
Zuid-Holland
21
364
User
Utrecht
21
365
User
Zuid-Holland
20
366
User
Noord-Holland
20
367
User
Gelderland
20
368
User
Noord-Brabant
20
369
User
Utrecht
20
370
User
Gelderland
20
371
User
Noord-Holland
20
372
User
Overijssel
20
374
User
Noord-Holland
20
375
User
Noord-Holland
20
376
User
Overijssel
20
377
P.R. Keus
Zuid-Holland
20
378
Dániel Erdélyi
Zuid-Holland
20
379
User
Noord-Holland
20
380
User
Utrecht
20
381
User
Limburg
20
382
User
Gelderland
20
383
User
Noord-Holland
20
384
Bram Klein Kranenbarg
Noord-Holland
20
385
User
Noord-Holland
19
386
User
Zuid-Holland
19
387
User
Overijssel
19
388
User
Noord-Holland
19
389
User
Noord-Holland
19
390
User
Noord-Holland
19
391
User
Noord-Holland
19
392
User
Noord-Holland
19
393
Rowan Mommers
Utrecht
19
394
User
Noord-Holland
19
395
User
Noord-Brabant
19
396
User
Overijssel
19
397
Rabea Semmler
Limburg
19
398
User
Noord-Holland
19
399
User
Noord-Holland
19
400
MvGulik
Noord-Holland
19
401
User
Noord-Holland
19
402
User
Zuid-Holland
19
403
User
Overijssel
19
404
User
Noord-Holland
19
405
User
Zuid-Holland
19
406
Sebastiaan Vaz
Noord-Holland
18
407
Thomas
Zuid-Holland
18
408
User
Gelderland
18
409
Hajime Sasaki
Limburg
18
410
User
Noord-Holland
18
411
User
Noord-Holland
18
412
User
Utrecht
18
413
User
Zuid-Holland
18
414
User
Noord-Brabant
18
415
alain faddegon
Zuid-Holland
18
416
User
Noord-Holland
18
417
Ketchup
Noord-Holland
18
418
User
Zuid-Holland
18
419
Andrej N
Zuid-Holland
18
420
Jeroen van der Gevel
Utrecht
18
421
User
Utrecht
18
422
User
Noord-Holland
18
423
User
Noord-Holland
18
424
Jantine Boomsma
Zuid-Holland
17
425
User
Zuid-Holland
17
426
User
Noord-Holland
17
427
Loredana Lenghel
Noord-Holland
17
428
Susan Harris
Utrecht
17
429
User
Zuid-Holland
17
430
User
Overijssel
17
431
User
Noord-Holland
17
432
User
Noord-Brabant
17
433
User
Zuid-Holland
17
434
User
Zuid-Holland
17
435
vicc
Utrecht
17
436
User
Overijssel
17
437
User
Noord-Holland
17
438
User
Zuid-Holland
17
439
User
Utrecht
17
440
User
Overijssel
17
441
User
Noord-Holland
17
442
User
Noord-Holland
17
443
User
Limburg
17
444
Nicolette Bosch
Zuid-Holland
17
445
User
Zuid-Holland
17
446
User
Noord-Holland
17
447
User
Zuid-Holland
17
448
User
Noord-Holland
17
449
User
Zuid-Holland
17
450
Anna
Zuid-Holland
17
451
User
Zuid-Holland
16
452
User
Zuid-Holland
16
453
Jelmer
Utrecht
16
454
User
Noord-Holland
16
455
Guus
Noord-Holland
16
456
User
Utrecht
16
457
User
Noord-Brabant
16
458
User
Overijssel
16
459
User
Region
16
460
sg
Gelderland
16
461
User
Zuid-Holland
16
462
User
Zuid-Holland
16
463
User
Noord-Holland
16
464
Wouter Janssen
Overijssel
16
465
User
Utrecht
16
466
User
Noord-Holland
16
467
User
Noord-Holland
16
468
User
Noord-Holland
16
469
User
Zuid-Holland
16
470
User
Zuid-Holland
16
471
User
Noord-Holland
16
472
User
Gelderland
16
473
User
Noord-Brabant
15
474
User
Noord-Holland
15
475
User
Zuid-Holland
15
476
Clint
Noord-Brabant
15
477
User
Gelderland
15
478
User
Noord-Holland
15
479
User
Utrecht
15
480
User
Zuid-Holland
15
481
Igor Quint
Noord-Holland
15
482
User
Noord-Holland
15
483
User
Noord-Holland
15
484
Nick Hennen
Noord-Holland
15
485
User
Noord-Holland
15
486
User
Noord-Holland
15
487
User
Noord-Holland
15
488
User
Groningen
15
489
User
Noord-Holland
15
490
User
Noord-Holland
15
491
User
Overijssel
15
492
User
Zuid-Holland
15
493
User
Zuid-Holland
15
494
User
Overijssel
15
495
User
Noord-Holland
15
496
User
Noord-Holland
15
497
User
Noord-Holland
15
498
User
Noord-Brabant
15
499
User
Zuid-Holland
15
500
User
Noord-Brabant
15
501
Jojo
Limburg
15
502
User
Noord-Holland
15
503
Vince
Limburg
15
504
Ronald Schotman
Zuid-Holland
15
505
User
Utrecht
15
506
Gert
Gelderland
15
507
User
Gelderland
15
508
User
Overijssel
14
509
User
Noord-Brabant
14
510
User
Zuid-Holland
14
511
User
Noord-Holland
14
512
User
Noord-Holland
14
513
Anniek van Eijkern
Zuid-Holland
14
514
User
Overijssel
14
515
User
Noord-Brabant
14
516
User
Zuid-Holland
14
517
User
Zuid-Holland
14
518
User
Noord-Holland
14
519
User
Noord-Holland
14
520
User
Zuid-Holland
14
521
User
Noord-Holland
14
522
User
Zuid-Holland
14
523
User
Zuid-Holland
14
524
User
Noord-Holland
14
525
Marco Rodriguez
Noord-Brabant
14
526
User
Zuid-Holland
14
527
User
Zuid-Holland
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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 math 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 math, 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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