Leaderboard
Georgia
Rank
Level
1
Peter Andersson
Atlanta
87
2
Blaziken Boi
Ringgold
86
3
camden
Atlanta
82
4
User
Marietta
64
5
User
Ringgold
62
6
mishmash
Atlanta
58
7
User
Moultrie
57
8
User
Lilburn
56
9
User
East Cobb
56
10
User
Atlanta
52
11
User
Roswell
52
12
User
North Druid Hills
51
13
Dustin
Dunwoody
50
14
Abhishek Birhade
Atlanta
49
15
User
Atlanta
48
16
User
Atlanta
48
17
Jake Hoffman
Atlanta
48
18
User
Atlanta
46
19
Terpski624
Atlanta
45
20
User
Johns Creek
44
21
User
Richmond Hill
40
22
User
Atlanta
40
23
User
Alpharetta
40
24
User
Fort Valley
38
25
User
East Cobb
37
26
User
Atlanta
37
27
GURU PRASAD IYER.V
Atlanta
37
28
Yuan Yin
Atlanta
36
29
Chase Brooks
Atlanta
36
30
User
Marietta
36
31
User
Ranburne
35
32
User
Alpharetta
35
33
User
Alpharetta
35
34
User
Sandy Springs
34
35
User
Kennesaw
34
36
User
Athens
34
37
User
Atlanta
34
38
User
Roswell
33
39
User
Norcross
33
40
User
Columbus
33
41
User
Atlanta
32
42
User
Druid Hills
32
43
User
Atlanta
31
44
User
Atlanta
31
45
User
Mcdonough
31
46
User
Forsyth
30
47
User
East Point
30
48
User
Columbus
30
49
User
Atlanta
30
50
Pedro Rossello
Sandy Springs
29
51
User
Atlanta
29
52
User
Atlanta
29
53
User
Albany
29
54
User
Athens
28
55
User
Atlanta
28
56
User
Warner Robins
28
57
Stephen
Atlanta
28
58
Michael Jurado
Athens
28
59
User
Atlanta
28
60
User
Atlanta
27
61
User
Atlanta
27
62
User
North Druid Hills
27
63
User
Atlanta
27
64
User
Atlanta
27
65
Garret Gallion
Atlanta
26
66
User
Holly Springs
26
67
User
Druid Hills
26
68
User
Norcross
26
69
User
Athens
25
70
User
Atlanta
25
71
User
Fort Valley
25
72
User
Macon
25
73
hollists
Atlanta
25
74
User
Alpharetta
25
75
anwesha banerjee
Druid Hills
24
76
User
Tifton
24
77
User
Doraville
24
78
User
Atlanta
24
79
User
Atlanta
23
80
User
Dacula
23
81
User
Atlanta
23
82
User
Macon
23
83
User
Fort Valley
23
84
User
Atlanta
23
85
User
Dekalb County
23
86
User
Brookhaven
22
87
User
Johns Creek
22
88
User
Athens
22
89
User
Decatur
22
90
User
Macon
22
91
User
Atlanta
22
92
User
Atlanta
22
93
User
Atlanta
22
94
User
Druid Hills
22
95
Yvo
Martinez
22
96
User
Atlanta
22
97
Ariana Morgan
Grovetown
22
98
User
Atlanta
22
99
User
Atlanta
22
100
User
Athens
21
101
User
Milledgeville
21
102
Kirby Cyber
Woodstock
21
103
User
Fort Valley
21
104
Noah Davis
Stockbridge
21
105
User
Atlanta
21
106
User
North Druid Hills
21
107
User
Douglasville
21
108
User
Snellville
21
109
User
Norcross
21
110
User
Doraville
21
111
User
Atlanta
21
112
User
Atlanta
21
113
User
Atlanta
21
114
Taylor Lawson
Atlanta
21
115
User
Atlanta
21
116
User
Atlanta
21
117
KeNorian Davis
Mcintyre
21
118
Pigmilk Man
Lilburn
21
119
User
Columbus
21
120
User
Suwanee
21
121
User
Atlanta
20
122
User
Johns Creek
20
123
User
Alpharetta
20
124
User
Atlanta
20
125
User
Macon
20
126
User
Woodstock
20
127
User
Dunwoody
20
128
User
Atlanta
20
129
User
Atlanta
20
130
User
Atlanta
20
131
User
Atlanta
20
132
User
Atlanta
20
133
User
Atlanta
20
134
cedric
Fort Valley
20
135
User
Holly Springs
20
136
User
East Cobb
20
137
User
Marietta
19
138
User
Dunwoody
19
139
User
Calhoun
19
140
User
Doraville
19
141
User
Duluth
19
142
User
Conyers
19
143
User
Atlanta
19
144
User
Conyers
19
145
User
East Cobb
19
146
User
Atlanta
19
147
User
Fort Valley
19
148
User
Mcintyre
19
149
User
Marietta
18
150
User
Warner Robins
18
151
User
East Cobb
18
152
User
Decatur
18
153
User
Marietta
18
154
Allen Gonzalez
Doraville
18
155
User
Atlanta
18
156
User
Atlanta
18
157
User
Atlanta
18
158
User
Atlanta
18
159
User
Atlanta
18
160
User
East Point
18
161
User
Marietta
18
162
User
Stockbridge
17
163
User
Bremen
17
164
User
Atlanta
17
165
User
Doraville
17
166
User
Atlanta
17
167
User
Atlanta
17
168
User
Atlanta
17
169
User
Atlanta
17
170
User
Duluth
17
171
User
Byron
17
172
User
Sandy Springs
17
173
User
Stockbridge
17
174
Bas Weijerman
Atlanta
17
175
User
Atlanta
17
176
User
Atlanta
17
177
Matthew Wise
Augusta
16
178
User
Lilburn
16
179
User
Atlanta
16
180
User
Atlanta
16
181
User
Atlanta
16
182
User
Atlanta
16
183
User
Atlanta
16
184
Cheronda Reynolds
Irwinton
16
185
User
Cumming
15
186
User
Atlanta
15
187
User
Doraville
15
188
User
North Decatur
15
189
User
Atlanta
15
190
User
Atlanta
15
191
User
Atlanta
15
192
User
Fort Valley
15
193
User
Atlanta
15
194
User
Buford
15
195
User
Atlanta
15
196
User
Lawrenceville
15
197
User
Marietta
15
198
User
Atlanta
15
199
User
Atlanta
14
200
User
Fort Valley
14
201
User
Fort Valley
14
202
Irving
Conyers
14
203
User
Conyers
14
204
User
Atlanta
14
205
User
Atlanta
14
206
User
Atlanta
14
207
User
Pooler
14
208
User
Atlanta
14
209
User
Cumming
14
210
User
Statesboro
14
211
User
Byron
14
212
User
Vinings
14
213
User
Brookhaven
14
214
User
Alpharetta
14
215
User
Marietta
14
216
User
Atlanta
13
217
Mark Simmons
Woodstock
13
218
User
Athens
13
219
User
Marietta
13
220
User
Atlanta
13
221
User
Macon
13
222
User
Atlanta
13
223
User
Atlanta
13
224
User
Atlanta
13
225
User
Atlanta
13
226
User
Atlanta
13
227
User
Atlanta
13
228
User
Atlanta
13
229
User
Fort Valley
13
230
User
City
13
231
User
Druid Hills
13
232
User
Augusta
13
233
User
Conyers
13
234
User
Atlanta
13
235
User
Atlanta
13
236
User
Druid Hills
13
237
Guillermo Reynoso-Gonzalez
Irwinton
13
238
User
Atlanta
12
239
User
Rome
12
240
User
Fort Valley
12
241
Trent Davis
Atlanta
12
242
User
Macon
12
243
User
Atlanta
12
244
User
Atlanta
12
245
User
Atlanta
12
246
User
Atlanta
12
247
User
Fort Valley
12
248
User
East Cobb
12
249
User
Atlanta
12
250
User
Demorest
12
251
User
Jonesboro
12
252
User
Columbus
11
253
User
Conyers
11
254
User
Woodstock
11
255
User
Druid Hills
11
256
User
Atlanta
11
257
User
Macon
11
258
User
Roswell
11
259
User
Atlanta
11
260
User
Atlanta
11
261
User
Atlanta
11
262
User
Atlanta
11
263
User
Atlanta
11
264
User
Atlanta
11
265
User
Atlanta
11
266
User
Atlanta
11
267
User
Alpharetta
11
268
User
Savannah
11
269
User
Atlanta
11
270
User
Atlanta
11
271
Adriana Garcia Ceja
Atlanta
11
272
User
Warner Robins
11
273
MJ
Dekalb County
11
274
User
Athens
10
275
User
Atlanta
10
276
User
Atlanta
10
277
User
Atlanta
10
278
User
Dunwoody
10
279
User
Atlanta
10
280
User
Atlanta
10
281
User
Atlanta
10
282
User
Atlanta
10
283
User
Atlanta
10
284
User
Watkinsville
10
285
User
Holly Springs
10
286
User
Atlanta
10
287
User
Acworth
10
288
User
Johns Creek
10
289
User
Atlanta
10
290
User
Atlanta
10
291
User
Savannah
10
292
User
Johns Creek
9
293
User
Milton
9
294
Bobby J
Gainesville
9
295
Aaliyah McDowell
Hiram
9
296
User
Atlanta
9
297
User
Atlanta
9
298
User
Macon
9
299
User
Duluth
9
300
User
Atlanta
9
301
User
Atlanta
9
302
User
Atlanta
9
303
User
Atlanta
9
304
User
Atlanta
9
305
edward
Fort Valley
9
306
User
Fort Valley
9
307
User
Conyers
9
308
User
Statesboro
9
309
User
Statesboro
9
310
User
Roswell
9
311
User
Carrollton
9
312
User
Jefferson
9
313
User
Fayetteville
9
314
User
Roswell
9
315
User
Johns Creek
8
316
User
Atlanta
8
317
User
Woodstock
8
318
User
Powder Springs
8
319
User
Roswell
8
320
User
Dunwoody
8
321
User
Atlanta
8
322
User
Atlanta
8
323
User
Atlanta
8
324
User
Atlanta
8
325
User
Atlanta
8
326
User
Atlanta
8
327
User
Atlanta
8
328
User
Statesboro
8
329
User
Atlanta
8
330
User
Atlanta
8
331
User
Peachtree Corners
8
332
User
East Cobb
7
333
User
Atlanta
7
334
User
Roswell
7
335
User
Atlanta
7
336
User
Atlanta
7
337
User
Athens
7
338
User
Druid Hills
7
339
User
North High Shoals
7
340
User
Atlanta
7
341
Janine Jasmin
Mcdonough
7
342
User
Dunwoody
7
343
User
Macon
7
344
User
Moultrie
7
345
User
Atlanta
7
346
User
Holly Springs
7
347
User
Statesboro
7
348
User
Alpharetta
7
349
User
Stockbridge
7
350
User
Druid Hills
7
351
User
Atlanta
7
352
User
Atlanta
7
353
User
Evans
7
354
joshua wood
Irwinton
7
355
User
Cumming
7
356
User
Demorest
6
357
User
Palmetto
6
358
User
Dunwoody
6
359
User
Atlanta
6
360
User
Woodstock
6
361
User
Duluth
6
362
User
Atlanta
6
363
User
Atlanta
6
364
User
Atlanta
6
365
User
Augusta
6
366
User
Moultrie
6
367
User
Atlanta
6
368
User
Atlanta
6
369
User
Atlanta
6
370
User
Atlanta
6
371
User
Cumming
6
372
User
Fort Valley
6
373
User
Atlanta
6
374
d j
Fort Valley
6
375
User
Conyers
6
376
User
Atlanta
6
377
User
Atlanta
6
378
User
Fort Valley
6
379
User
Dacula
6
380
User
Statesboro
6
381
User
Lilburn
6
382
User
Johns Creek
6
383
User
Conyers
6
384
User
Atlanta
6
385
User
Atlanta
5
386
Michelle Li
Athens
5
387
User
Johns Creek
5
388
User
Atlanta
5
389
User
Acworth
5
390
User
Woodstock
5
391
User
Union City
5
392
User
Riverdale
5
393
User
Atlanta
5
394
User
Fort Valley
5
395
User
Brookhaven
5
396
User
Canton
5
397
User
Mableton
5
398
User
Riverdale
5
399
User
Atlanta
5
400
User
Dunwoody
5
401
User
Porterdale
5
402
User
Savannah
5
403
User
Atlanta
5
404
User
Atlanta
5
405
User
Atlanta
5
406
User
Atlanta
5
407
User
Atlanta
5
408
User
Atlanta
5
409
User
Conyers
5
410
User
Atlanta
5
411
User
Dock Junction
5
412
User
Conyers
5
413
User
Statesboro
5
414
hunter
Statesboro
5
415
User
Statesboro
5
416
Anne Jean
Atlanta
5
417
User
Warner Robins
5
418
User
Augusta
5
419
User
Johns Creek
5
420
User
Columbus
5
421
User
Atlanta
5
422
User
Snellville
5
423
User
Albany
5
424
User
Marietta
5
425
User
Atlanta
5
426
User
Alpharetta
5
427
User
Dacula
5
428
User
Atlanta
4
429
User
Conyers
4
430
User
Statesboro
4
431
User
Atlanta
4
432
User
Conyers
4
433
User
Conyers
4
434
User
Macon
4
435
User
Lawrenceville
4
436
User
Atlanta
4
437
DongJun Kim
Atlanta
4
438
User
Atlanta
4
439
User
East Cobb
4
440
User
Atlanta
4
441
User
Dunwoody
4
442
User
Buford
4
443
User
Moultrie
4
444
User
Dalton
4
445
User
Suwanee
4
446
User
Atlanta
4
447
User
Atlanta
4
448
User
Atlanta
4
449
User
Atlanta
4
450
User
Atlanta
4
451
User
Atlanta
4
452
User
Atlanta
4
453
User
Lawrenceville
4
454
User
Atlanta
4
455
User
Fort Valley
4
456
User
Atlanta
4
457
User
Conyers
4
458
User
Grayson
4
459
User
Statesboro
4
460
User
Statesboro
4
461
User
Suwanee
4
462
User
Atlanta
4
463
User
Statesboro
4
464
User
Suwanee
4
465
User
East Cobb
4
466
User
Duluth
4
467
User
Tucker
4
468
User
Atlanta
4
469
User
Cumming
4
470
User
Atlanta
4
471
User
Atlanta
4
472
User
Fort Valley
4
473
User
Irwinton
4
474
User
Irwinton
4
475
User
Union City
4
476
User
Marietta
4
477
User
Waycross
4
478
User
Alpharetta
4
479
User
Conyers
3
480
User
Dahlonega
3
481
User
Atlanta
3
482
Lothania Roberts
Statesboro
3
483
User
Athens
3
484
User
Atlanta
3
485
Dax
Smyrna
3
486
User
Woodstock
3
487
User
Atlanta
3
488
User
Atlanta
3
489
User
Duluth
3
490
User
Atlanta
3
491
User
Augusta
3
492
User
Atlanta
3
493
User
Stockbridge
3
494
User
Atlanta
3
495
User
Atlanta
3
496
User
Conyers
3
497
User
Atlanta
3
498
User
Atlanta
3
499
User
Atlanta
3
500
User
Johns Creek
3
501
User
Dunwoody
3
502
User
Conyers
3
503
User
Atlanta
3
504
User
Atlanta
3
505
User
Conyers
3
506
User
Atlanta
3
507
User
Augusta
3
508
User
Fort Valley
3
509
User
Holly Springs
3
510
User
Fort Valley
3
511
User
Fort Valley
3
512
User
Atlanta
3
513
User
Tucker
3
514
User
Fort Valley
3
515
User
Statesboro
3
516
User
Atlanta
3
517
User
Atlanta
3
518
User
Atlanta
3
519
rose
Statesboro
3
520
User
Hartwell
3
521
User
Statesboro
3
522
User
Atlanta
3
523
User
Johns Creek
3
524
Virginia Kump
Irwinton
3
525
Brianna Smith
Irwinton
3
526
User
Atlanta
3
527
User
Lilburn
3
528
User
Johns Creek
2
529
User
Conyers
2
530
User
Conyers
2
531
User
Conyers
2
532
User
Conyers
2
533
User
Atlanta
2
534
User
Snellville
2
535
kmeeks
Statesboro
2
536
User
Kennesaw
2
537
User
Thomasville
2
538
User
Atlanta
2
539
User
Atlanta
2
540
Charles Butler
Tucker
2
541
User
Conyers
2
542
User
Conyers
2
543
User
Atlanta
2
544
User
Morrow
2
545
User
Stonecrest
2
546
User
Fort Valley
2
547
User
Duluth
2
548
User
Athens
2
549
User
Snellville
2
550
User
Athens
2
551
User
Kennesaw
2
552
User
Atlanta
2
553
User
Atlanta
2
554
User
Atlanta
2
555
User
Scottdale
2
556
User
Conyers
2
557
User
Conyers
2
558
User
Conyers
2
559
User
Atlanta
2
560
Katie Roberts
Moultrie
2
561
User
Dunwoody
2
562
User
Atlanta
2
563
User
Albany
2
564
User
Atlanta
2
565
User
Savannah
2
566
User
Griffin
2
567
User
Sandy Springs
2
568
User
Conyers
2
569
User
Atlanta
2
570
User
Atlanta
2
571
User
Georgetown
2
572
User
Augusta
2
573
User
Conyers
2
574
christopher
Conyers
2
575
User
Decatur
2
576
User
Atlanta
2
577
User
Atlanta
2
578
User
Atlanta
2
579
User
Atlanta
2
580
User
Atlanta
2
581
User
Atlanta
2
582
User
Atlanta
2
583
User
Atlanta
2
584
User
Atlanta
2
585
User
Atlanta
2
586
User
Atlanta
2
587
User
Atlanta
2
588
User
Cumming
2
589
v
Fort Valley
2
590
User
Warner Robins
2
591
User
Fort Valley
2
592
User
Atlanta
2
593
User
Fort Valley
2
594
User
Conyers
2
595
User
Holly Springs
2
596
User
Conyers
2
597
User
Conyers
2
598
User
Statesboro
2
599
User
Statesboro
2
600
User
Statesboro
2
601
User
Statesboro
2
602
User
Statesboro
2
603
User
Atlanta
2
604
User
Statesboro
2
605
User
Fort Valley
2
606
User
Union City
2
607
User
Jefferson
2
608
User
Mcintyre
2
609
User
Tyrone
2
610
User
East Cobb
2
611
User
Fort Valley
2
612
User
Augusta
2
613
User
Statesboro
2
614
User
Statesboro
2
615
User
Statesboro
2
616
User
Powder Springs
2
617
User
Atlanta
2
618
User
Atlanta
2
619
User
Atlanta
2
620
User
Atlanta
2
621
User
Jefferson
2
622
User
Hamilton
2
623
User
East Point
2
624
User
Atlanta
2
625
User
Columbus
2
626
User
Atlanta
2
627
User
Acworth
2
628
User
Atlanta
2
629
User
Powder Springs
2
630
Tanajah Harris
Irwinton
2
631
User
Powder Springs
2
632
User
Atlanta
2
633
User
Alpharetta
2
634
User
Alpharetta
2
635
User
Tyrone
2
636
User
Marietta
2
637
User
Roswell
2
638
User
Gainesville
2
639
User
Savannah
2
640
User
Duluth
2
641
User
Atlanta
2
642
User
Atlanta
1
643
User
Atlanta
1
644
User
Conyers
1
645
User
Statesboro
1
646
User
Atlanta
1
647
User
Johns Creek
1
648
User
Mcdonough
1
649
User
Union City
1
650
User
Roswell
1
651
User
Atlanta
1
652
User
Columbus
1
653
User
Atlanta
1
654
User
Atlanta
1
655
User
Scottdale
1
656
User
Hapeville
1
657
User
Atlanta
1
658
User
Sandy Springs
1
659
User
North Druid Hills
1
660
User
Athens
1
661
User
Canton
1
662
User
Perry
1
663
Abhishek Birhade
Atlanta
1
664
Janaysha Newell-Reeves
Atlanta
1
665
ELM
Atlanta
1
666
Srithan Rudrangi
Dunwoody
1
667
john swift
Suwanee
1
668
ciani
Conyers
1
669
Guruprasad Venkataraghavan
Sandy Springs
1
670
Orlando Morales
Atlanta
1
671
Timia Corbin
Irwinton
1

Free

Free basic access

Login Optional

Progress saved automatically

Students

Works great in classrooms

20,000,000
Response times
650,000
Unique questions
100
Difficulty levels

Cross-Platform

Use any operating system with Chrome, Safari, or Firefox

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.


Privacy Policy