Leaderboard
United Arab Emirates
United Arab Emirates
Worldwide
Rank
Level
1
User
Dubayy
92
2
Erkin
Dubayy
77
3
User
Dubayy
69
4
User
Dubayy
68
5
CYPHERCYPHERCYPHER
Dubayy
67
6
Zainab Naveed
Abū Z̧aby
63
7
Rydar
Abū Z̧aby
62
8
User
Dubayy
59
9
User
Dubayy
52
10
User
Abū Z̧aby
51
11
Nithila Rajapakse
Dubayy
50
12
Jad Karam
Dubayy
50
13
User
Dubayy
47
14
User
Dubayy
46
15
User
Dubayy
44
16
User
Dubayy
43
18
Vivek Tomer
Abū Z̧aby
42
19
User
Dubayy
42
20
User
Dubayy
41
22
User
Dubayy
40
23
User
Dubayy
40
24
User
Dubayy
39
25
User
Dubayy
38
27
Aaditya Harikrishnan
Dubayy
35
28
User
Dubayy
35
29
User
Dubayy
34
31
User
Dubayy
31
33
User
Abū Z̧aby
30
34
User
Dubayy
30
35
User
Abū Z̧aby
30
36
Alex Howe
Dubayy
30
38
User
Dubayy
30
39
User
Dubayy
29
40
User
Abū Z̧aby
29
41
Carlos
Dubayy
29
42
savagethuglifelogang
Dubayy
29
43
User
Dubayy
29
44
User
Dubayy
28
45
User
Dubayy
28
46
User
Abū Z̧aby
28
47
Zohaib
Dubayy
28
48
User
Dubayy
27
49
User
Dubayy
27
50
User
Abū Z̧aby
27
51
Hour
Al Fujayrah
26
53
User
Abū Z̧aby
26
54
User
Dubayy
26
55
User
Abū Z̧aby
26
56
User
Dubayy
26
57
User
Abū Z̧aby
26
58
User
Dubayy
26
59
User
Dubayy
25
60
Aadam Karim
Dubayy
25
62
User
Dubayy
25
63
User
Abū Z̧aby
24
64
Amr x killel
Dubayy
24
65
User
Dubayy
24
66
User
Dubayy
23
67
User
Dubayy
23
68
surya pillai
\'Ajmān
23
71
User
Dubayy
23
72
User
Dubayy
22
73
User
Dubayy
22
74
User
Dubayy
22
75
asser khaled
Abū Z̧aby
22
76
noor
Dubayy
22
77
User
Dubayy
22
79
User
Dubayy
22
81
User
Dubayy
22
82
User
Dubayy
21
83
Nikhil Balaji
Dubayy
21
84
User
Dubayy
21
85
User
Abū Z̧aby
21
86
Maysa Sedeek
Dubayy
21
88
User
Dubayy
21
89
User
Abū Z̧aby
20
90
User
Dubayy
20
91
User
Dubayy
20
92
User
Dubayy
20
94
Ammar
Ash Shāriqah
20
95
User
Dubayy
20
96
User
Dubayy
20
97
User
Dubayy
19
98
Charlene
Abū Z̧aby
19
100
User
Dubayy
19
101
Dhani
Dubayy
19
102
User
Dubayy
19
103
User
Ash Shāriqah
19
104
User
Dubayy
19
105
Zakhar
Dubayy
18
106
User
Dubayy
18
107
User
Abū Z̧aby
18
108
User
Dubayy
18
109
Youssef too pro for you
Abū Z̧aby
18
110
User
Abū Z̧aby
18
111
User
Ash Shāriqah
18
112
User
Dubayy
18
113
Your Name
Ash Shāriqah
18
114
User
Dubayy
18
115
User
Dubayy
18
116
User
Ash Shāriqah
17
117
User
Dubayy
17
118
Haneya
Dubayy
17
119
User
Dubayy
17
120
User
Dubayy
17
121
User
Ash Shāriqah
17
122
User
Ash Shāriqah
17
123
User
Dubayy
17
124
User
Dubayy
17
125
User
Dubayy
17
126
User
Dubayy
17
127
User
Dubayy
17
128
User
Abū Z̧aby
17
129
Ray zayed
Dubayy
16
130
User
Dubayy
16
131
User
Dubayy
16
132
User
Abū Z̧aby
16
133
i feel gooooooooood
Dubayy
16
134
player two
\'Ajmān
16
135
User
Dubayy
16
136
User
Dubayy
16
137
User
Ash Shāriqah
16
138
User
\'Ajmān
16
139
User
Dubayy
16
140
User
Dubayy
16
141
User
Dubayy
16
142
User
Dubayy
16
143
User
Dubayy
15
144
User
Abū Z̧aby
15
145
User
Al Fujayrah
15
146
User
Dubayy
15
147
User
Dubayy
15
148
Aimee
Dubayy
15
149
Marvi Islam
Dubayy
15
150
User
Dubayy
15
151
User
Dubayy
15
152
User
Ash Shāriqah
15
153
User
Dubayy
15
154
User
Dubayy
15
155
User
Abū Z̧aby
15
156
User
Dubayy
15
157
User
Ash Shāriqah
14
158
User
Abū Z̧aby
14
159
User
Abū Z̧aby
14
160
User
Ash Shāriqah
14
161
Ahmed Alnaqbi
Dubayy
14
162
User
Al Fujayrah
14
163
Abida El Kiuch
Dubayy
14
164
User
Dubayy
14
165
User
Abū Z̧aby
13
166
User
Abū Z̧aby
13
167
User
Ash Shāriqah
13
168
User
Al Fujayrah
13
169
User
Dubayy
13
170
User
Ash Shāriqah
13
171
User
Dubayy
13
172
User
Ash Shāriqah
13
173
User
Dubayy
13
174
Syed Omar Haleem
Dubayy
13
175
User
Abū Z̧aby
12
176
User
Dubayy
12
177
User
Dubayy
12
178
User
Dubayy
12
179
User
Ash Shāriqah
12
180
User
Abū Z̧aby
12
181
User
Dubayy
12
182
Naveed SHah
Dubayy
12
183
Ary Tg
Dubayy
11
184
User
Dubayy
11
185
User
Abū Z̧aby
11
186
User
Abū Z̧aby
11
187
User
Ash Shāriqah
11
188
User
Dubayy
11
189
User
Dubayy
11
190
Anjalee
Ash Shāriqah
11
191
User
Ash Shāriqah
11
192
User
Dubayy
11
193
User
Abū Z̧aby
11
194
Ali Ahmed
Dubayy
11
195
User
Abū Z̧aby
11
196
User
Dubayy
11
197
User
Ash Shāriqah
11
198
User
Ash Shāriqah
11
199
User
Dubayy
10
200
User
Dubayy
10
201
User
Dubayy
10
202
User
Abū Z̧aby
10
203
User
Dubayy
10
204
Rayan Sultani
Dubayy
10
205
User
Dubayy
10
206
User
Dubayy
10
207
User
Ash Shāriqah
10
208
User
Abū Z̧aby
10
209
User
Dubayy
10
210
User
Dubayy
10
211
Shazina
Ash Shāriqah
10
212
User
Dubayy
10
213
User
Dubayy
10
214
User
Abū Z̧aby
10
215
User
Dubayy
10
216
User
Dubayy
10
217
User
Abū Z̧aby
9
218
User
Dubayy
9
220
User
Abū Z̧aby
9
221
User
Dubayy
9
222
User
Dubayy
9
225
User
Dubayy
9
226
User
Dubayy
9
229
User
Dubayy
9
230
User
Dubayy
9
231
User
Dubayy
8
232
User
Abū Z̧aby
8
234
Mouza Rashed
Al Fujayrah
8
235
User
Dubayy
8
236
User
Dubayy
8
237
User
Dubayy
8
238
User
Dubayy
8
240
User
Dubayy
8
241
User
Dubayy
8
242
User
Dubayy
8
243
User
Dubayy
8
247
User
Abū Z̧aby
8
249
Omar Alali
Dubayy
8
250
User
Abū Z̧aby
8
251
User
Dubayy
8
252
User
Dubayy
8
253
User
Dubayy
8
254
User
Dubayy
7
255
User
Abū Z̧aby
7
256
User
Dubayy
7
257
User
Dubayy
7
258
User
Dubayy
7
260
Tibor Paluch
Ra\'s al Khaymah
7
263
User
Abū Z̧aby
7
265
User
Al Fujayrah
7
266
User
Al Fujayrah
7
267
User
Al Fujayrah
7
268
User
Dubayy
7
270
User
Dubayy
7
271
User
Dubayy
7
272
User
Dubayy
7
273
User
Dubayy
7
275
User
Dubayy
7
276
User
Abū Z̧aby
7
277
User
Dubayy
7
278
User
Dubayy
7
283
Sam A
Dubayy
7
284
User
Abū Z̧aby
7
285
User
Dubayy
7
286
User
Dubayy
6
287
User
Dubayy
6
289
sinan sarafudheen
Al Fujayrah
6
290
Jegatheesh M
Dubayy
6
291
User
Abū Z̧aby
6
293
User
Dubayy
6
294
User
Dubayy
6
295
User
Dubayy
6
296
User
Dubayy
6
297
User
Abū Z̧aby
6
298
User
Abū Z̧aby
6
299
User
Dubayy
6
300
User
Al Fujayrah
6
301
User
Dubayy
6
302
User
Al Fujayrah
6
303
User
Al Fujayrah
6
307
Omar Elsayed
Dubayy
6
310
User
Dubayy
6
312
User
\'Ajmān
6
313
User
Dubayy
6
314
User
Abū Z̧aby
6
315
User
Dubayy
6
316
User
Dubayy
6
317
User
\'Ajmān
6
319
User
Dubayy
6
320
Evan Issa
Dubayy
6
321
User
Abū Z̧aby
6
322
User
Dubayy
6
323
User
Abū Z̧aby
6
324
User
Dubayy
6
325
User
Al Fujayrah
6
326
Maryam
Abū Z̧aby
6
327
User
Abū Z̧aby
6
328
ibrahim alhammadi
Dubayy
6
329
khalifa aljanahi
Dubayy
6
330
User
Dubayy
6
332
User
Dubayy
6
333
User
Dubayy
6
334
User
Dubayy
6
335
User
Al Fujayrah
5
336
User
Abū Z̧aby
5
337
Abdullah
Dubayy
5
338
User
Abū Z̧aby
5
339
User
Dubayy
5
340
User
Dubayy
5
341
Webb Jack
Abū Z̧aby
5
342
User
Abū Z̧aby
5
344
User
Dubayy
5
345
User
Dubayy
5
346
User
Abū Z̧aby
5
347
Aswin Kumar
Abū Z̧aby
5
348
User
Abū Z̧aby
5
351
User
Dubayy
5
352
User
Dubayy
5
353
User
Al Fujayrah
5
354
User
Al Fujayrah
5
356
User
Dubayy
5
357
Afra Aln
Dubayy
5
358
User
Dubayy
5
359
User
Dubayy
5
361
User
Dubayy
5
362
User
Abū Z̧aby
5
363
User
Dubayy
5
364
User
Dubayy
5
369
User
Abū Z̧aby
5
374
Saud Abdulla
Dubayy
5
375
User
Abū Z̧aby
5
376
User
Abū Z̧aby
5
378
User
Abū Z̧aby
5
379
User
Dubayy
5
380
User
Dubayy
5
381
User
Dubayy
5
382
User
Dubayy
5
383
User
Dubayy
5
384
User
Dubayy
5
385
User
Dubayy
4
386
User
Abū Z̧aby
4
387
User
Dubayy
4
388
User
Dubayy
4
389
User
Dubayy
4
390
User
Abū Z̧aby
4
391
User
Abū Z̧aby
4
393
User
Abū Z̧aby
4
394
User
Abū Z̧aby
4
395
Burhanuddin
Dubayy
4
396
User
Dubayy
4
397
User
Al Fujayrah
4
398
User
Al Fujayrah
4
399
User
Dubayy
4
400
User
Al Fujayrah
4
401
User
Dubayy
4
402
User
Dubayy
4
403
User
Dubayy
4
404
User
Abū Z̧aby
4
405
User
Dubayy
4
406
Asiya syed
Dubayy
4
407
hina nowfel
Dubayy
4
408
Jellybean
\'Ajmān
4
410
User
Dubayy
4
411
User
Dubayy
4
412
User
Dubayy
4
417
User
Dubayy
4
418
User
Dubayy
4
428
User
Dubayy
4
429
Mariam Abdelazim
Dubayy
4
430
User
Dubayy
4
431
User
Dubayy
4
432
User
Abū Z̧aby
4
433
User
Dubayy
4
434
User
Dubayy
4
435
User
Dubayy
4
441
User
\'Ajmān
4
442
User
Dubayy
4
443
User
Dubayy
4
444
User
Dubayy
4
445
User
Abū Z̧aby
4
446
User
Dubayy
3
447
User
Dubayy
3
448
User
Dubayy
3
449
User
Dubayy
3
450
User
Dubayy
3
451
AITA PAVANI
Abū Z̧aby
3
452
User
\'Ajmān
3
453
User
Dubayy
3
455
User
Dubayy
3
456
User
Dubayy
3
457
User
Dubayy
3
459
User
Dubayy
3
460
User
Dubayy
3
461
User
Dubayy
3
462
User
Dubayy
3
463
User
Dubayy
3
464
User
Abū Z̧aby
3
466
User
Abū Z̧aby
3
467
User
Dubayy
3
468
User
Dubayy
3
469
TG
Dubayy
3
470
User
Al Fujayrah
3
471
User
Al Fujayrah
3
472
User
Abū Z̧aby
3
473
User
Dubayy
3
474
User
Dubayy
3
475
fred prior
Al Fujayrah
3
476
User
Abū Z̧aby
3
477
User
Abū Z̧aby
3
478
User
Abū Z̧aby
3
479
User
Dubayy
3
480
User
Abū Z̧aby
3
481
User
Dubayy
3
482
User
Abū Z̧aby
3
483
User
Dubayy
3
484
User
Dubayy
3
485
User
Abū Z̧aby
3
486
User
Abū Z̧aby
3
487
User
Abū Z̧aby
3
489
User
Abū Z̧aby
3
490
User
Dubayy
3
491
User
Dubayy
3
492
mariam
Abū Z̧aby
3
496
User
\'Ajmān
3
497
User
Dubayy
3
498
User
\'Ajmān
3
499
User
Abū Z̧aby
3
500
User
\'Ajmān
3
502
User
Dubayy
3
508
User
\'Ajmān
3
509
User
\'Ajmān
3
512
User
Dubayy
3
514
User
Dubayy
3
516
User
Dubayy
3
517
User
Dubayy
3
518
User
Dubayy
3
519
User
Abū Z̧aby
3
524
User
Dubayy
3
525
User
Dubayy
3
526
User
Dubayy
3
527
User
Abū Z̧aby
3
528
User
Dubayy
3
529
User
Dubayy
3
530
User
Dubayy
3
531
User
Dubayy
3
532
User
Abū Z̧aby
3
533
User
Dubayy
3
534
User
Dubayy
3
535
User
Dubayy
3
536
User
Dubayy
3
537
User
Dubayy
2
538
User
Dubayy
2
539
User
Dubayy
2
540
User
Dubayy
2
541
User
Dubayy
2
543
User
Dubayy
2
544
User
Abū Z̧aby
2
545
User
Abū Z̧aby
2
546
User
Dubayy
2
547
Declan Misquitta
Abū Z̧aby
2
548
User
Dubayy
2
550
Mostafa Ahmed
Dubayy
2
552
User
Dubayy
2
553
User
Dubayy
2
554
User
Dubayy
2
555
User
Dubayy
2
556
User
Dubayy
2
557
User
Dubayy
2
558
User
Abū Z̧aby
2
559
Chris Campher
Abū Z̧aby
2
560
User
Abū Z̧aby
2
562
User
\'Ajmān
2
563
User
Dubayy
2
565
User
Dubayy
2
566
User
Dubayy
2
567
User
Dubayy
2
568
User
Dubayy
2
569
User
Dubayy
2
570
User
Dubayy
2
571
User
Abū Z̧aby
2
572
User
Abū Z̧aby
2
573
User
Dubayy
2
574
User
Dubayy
2
575
User
Dubayy
2
576
User
Abū Z̧aby
2
577
User
Al Fujayrah
2
578
User
Abū Z̧aby
2
579
User
Dubayy
2
580
User
Dubayy
2
581
User
Dubayy
2
582
User
Dubayy
2
583
User
Dubayy
2
584
User
Al Fujayrah
2
585
User
Dubayy
2
586
User
Al Fujayrah
2
587
User
Al Fujayrah
2
588
User
Al Fujayrah
2
589
User
Dubayy
2
590
User
Dubayy
2
591
User
Dubayy
2
592
User
Abū Z̧aby
2
593
User
Dubayy
2
594
User
Dubayy
2
595
User
Abū Z̧aby
2
596
User
Dubayy
2
597
User
Dubayy
2
598
User
Dubayy
2
599
User
Dubayy
2
600
User
Dubayy
2
601
User
Dubayy
2
602
User
Dubayy
2
603
User
Abū Z̧aby
2
604
User
Dubayy
2
605
User
Dubayy
2
607
User
Dubayy
2
608
User
Dubayy
2
609
User
Abū Z̧aby
2
610
User
Dubayy
2
611
User
Abū Z̧aby
2
612
User
Abū Z̧aby
2
613
User
Abū Z̧aby
2
614
User
Dubayy
2
615
User
Dubayy
2
616
User
Dubayy
2
617
User
Dubayy
2
618
User
Dubayy
2
619
User
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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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