Leaderboard
Florida
Rank
Level
1
RobDogLovesYou
Siesta Key
92
2
SuperRobDog
Siesta Key
92
3
SeeRobDogRun
Siesta Key
92
4
GoRobDogGo
Siesta Key
92
5
RobDogRocks
Siesta Key
92
6
RobDogSharkDoDo
Siesta Key
92
7
RobCoughDog
Siesta Key
91
8
RobbieBobbie
Siesta Key
86
9
RobOhMyOhMy
Siesta Key
86
10
SenorRobDof
Siesta Key
84
11
MrRobDoggy
Siesta Key
82
12
RobbieMcDoggie
Siesta Key
80
13
PapaRobDog
Siesta Key
80
14
RobbieDoggie
Siesta Key
80
15
SirRobDog
Siesta Key
79
16
MrRobDog
Siesta Key
79
17
RobDog
Siesta Key
79
18
RobDoggy
Siesta Key
78
19
User
Siesta Key
78
20
Florida
Siesta Key
78
21
User
Siesta Key
78
22
RobDogLog
Siesta Key
78
23
Octavius
Orlando
77
24
User
Siesta Key
77
25
User
Siesta Key
76
26
User
Siesta Key
75
27
User
Siesta Key
75
28
Pogo
Siesta Key
75
29
User
Siesta Key
75
30
Jeremy Griffin
Gainesville
74
31
User
Siesta Key
73
32
User
Miramar
72
33
User
Boca Raton
72
34
Max Anderson
Goldenrod
71
35
User
Siesta Key
71
36
User
Siesta Key
70
37
User
Siesta Key
67
38
User
Siesta Key
67
39
User
Siesta Key
62
40
User
Siesta Key
62
41
SOPHIE LI
Oviedo
62
42
Cameron Allen
Wellington
62
43
Adub
Orlando
62
44
Tim Zheng
Villas
61
45
User
Siesta Key
60
46
User
Siesta Key
59
47
Daniel Benayoun
Weston
58
48
Stlove24@gmail.com
Orlando
57
49
User
Jacksonville
57
50
User
North Miami Beach
53
51
User
Siesta Key
51
52
User
Siesta Key
51
53
TJ Cubing
Orlando
50
54
Ling Ling Eggroll
Town N Country
49
55
Ryan H
Royal Palm Beach
48
56
User
Siesta Key
48
57
before I die I’m going to get back at you
Sandalfoot Cove
48
58
User
Clearwater
45
59
Chris Rodriguez
Tamiami
45
60
Jonathan Tibi
Miami Beach
45
61
User
Ormond Beach
44
62
User
Clearwater
42
63
User
Miami
42
64
User
Orlando
41
65
User
Sorrento
41
66
Golliourus
Apopka
40
67
Randall Whitlock
Clearwater
40
68
User
Largo
40
69
User
Tallahassee
39
70
Lauren A
Lehigh Acres
38
71
User
Apopka
38
72
User
Clearwater
37
73
User
Tampa
36
74
User
Gulf Gate Estates
36
75
User
Clearwater
36
76
User
Clearwater
35
77
User
Orlando
35
78
User
Pensacola
35
79
User
Tallahassee
34
80
Hector Orea
Weston
34
81
Nicolas Rodriguez
Miami
34
82
User
Tampa
33
83
Aaron
Coral Gables
33
84
User
Ormond Beach
33
85
Lou
Miami
33
86
User
East Lake
32
87
User
Fort Lauderdale
32
88
Pedro Arruda
Tampa
32
89
User
Orlando
32
90
User
Wellington
32
91
User
Miami Beach
31
92
Christian Tang
North Naples
31
93
User
Clearwater
31
94
User
Orlando
30
95
User
Doral
30
96
User
Cutler Bay
30
97
User
Greenacres
30
98
bhaskar mishra
Pembroke Pines
30
99
User
Miami
30
100
User
Clearwater
29
101
User
Celebration
29
102
Lyykkn
Ormond Beach
28
103
User
Belleair
28
104
User
Panama City Beach
28
105
User
Clearwater
28
106
User
Miami
27
107
User
Miami
27
108
User
Fort Myers
27
109
User
Crystal River
27
110
User
Oviedo
27
111
User
North Miami Beach
27
112
User
Aventura
27
113
Sabrina Noborikawa
Miami
27
114
User
Mango
27
115
Emilie Schmidt
Gainesville
27
116
User
Hialeah
26
117
Tabbitha
Citrus Park
26
118
MizkifEgg
Margate
26
119
User
Orlando
26
120
User
North Miami
25
121
User
Bradenton
25
122
User
Miami
25
123
User
Miami
25
124
User
Weston
25
125
User
Miami Beach
25
126
User
Kissimmee
23
127
User
Jacksonville
23
128
User
Ellenton
23
129
User
Key Largo
23
130
User
North Miami Beach
23
131
User
Tamiami
23
132
User
Gainesville
23
133
User
Siesta Key
23
134
User
Tampa
22
135
Kiki Patel
Celebration
22
136
User
Fern Park
22
137
User
New Smyrna Beach
22
138
Michelle Paul
Orlando
22
139
User
Miami
22
140
User
Pinellas Park
22
141
Michael Marcotte
Largo
22
142
User
Weston
22
143
Victor Manuel Bellera
Lake Butler
22
144
User
Coral Terrace
22
145
User
Ormond Beach
22
146
Daniel Watson
Pensacola
22
147
User
Riviera Beach
21
148
User
Palm Valley
21
149
User
Clearwater
21
150
User
Clearwater
21
151
Ethan Bingham
Orlando
21
152
User
Spring Hill
21
153
Brittany Skeens
Orlando
21
154
User
Davie
21
155
User
Lake Worth
21
156
User
Cape Coral
21
157
User
Key Largo
21
158
User
Miramar Beach
21
159
User
Melbourne
20
160
User
Clearwater
20
161
User
Wellington
20
162
User
Deland
20
163
User
Gainesville
20
164
User
Pembroke Pines
20
165
User
Altamonte Springs
20
166
User
Plantation
20
167
User
Trinity
20
168
User
Pensacola
20
169
Curtis H
Orlando
20
170
User
Villas
20
171
User
Casselberry
20
172
User
Tampa
20
173
User
Orlando
19
174
J G
Kendall
19
175
User
Pinellas Park
19
176
Gabriel Diraviam
Pembroke Pines
19
177
Eugene Li
Cutler Bay
19
178
Vivi
Bradenton
19
179
User
Gainesville
18
180
User
New Port Richey
18
181
User
Tampa
18
182
User
Bay Lake
18
183
User
Saint Petersburg
18
184
User
North Sarasota
18
185
User
Kendall
18
186
User
Gateway
18
187
User
Golf
17
188
User
Orlando
17
189
User
Clermont
17
190
User
Cheval
17
191
User
Vineyards
17
192
User
Union Park
17
193
User
Sanford
17
194
User
Clearwater
17
195
User
Greenacres
17
196
User
Tallahassee
17
197
User
Tampa
17
198
Valentina Salazar
Kendall West
17
199
User
Deerfield Beach
16
200
Elizabeth Baldor
Tamiami
16
201
User
Oviedo
16
202
User
Pinellas Park
16
203
User
Clermont
16
204
Caroline Wallace
Orlando
16
205
User
Orlando
16
206
User
Melbourne
16
207
User
Tallahassee
16
208
User
Pompano Beach
16
209
User
Palm Beach Gardens
16
210
Handyman
Orlando
16
211
User
Orlando
16
212
User
Kissimmee
16
213
User
Jacksonville
15
214
Starmer
Orlando
15
215
Henry Parker
Gainesville
15
216
User
Jensen Beach
15
217
User
Kendall
15
218
User
Kendall
15
219
User
Eastpoint
15
220
User
Miramar Beach
15
221
User
Gainesville
15
222
User
Miami
15
223
User
Sanford
15
224
User
Orlando
15
225
Andy Chan
Oviedo
15
226
Daniel Gomez
Miami
15
227
Jasmine
Orlando
15
228
User
Tampa
15
229
User
Orlando
15
230
User
Miami
15
231
Michael Irias
Miami
15
232
User
Miami
15
233
User
Miami Beach
15
234
User
Citrus Park
15
235
User
Bay Lake
15
236
User
Jacksonville
15
237
User
St. Augustine
15
238
User
Orlando
15
239
User
Sanford
14
240
User
Orlando
14
241
User
Lakewood Ranch
14
242
Shahneel
St. Cloud
14
243
User
West Palm Beach
14
244
User
Wellington
14
245
User
Fruit Cove
14
246
User
Gateway
14
247
User
Miami
14
248
Romina Doubnia
North Miami
14
249
Tien
Orlando
14
250
User
Miami
14
251
User
Clearwater
13
252
User
Lakewood Ranch
13
253
User
Boca Raton
13
254
User
Fort Myers
13
255
User
Orlando
13
256
User
Tampa
13
257
User
Riviera Beach
13
258
Laís Atilano
Aventura
13
259
User
Port Charlotte
13
260
User
Miami
13
261
marco peric
Wellington
13
262
User
Orlando
13
263
User
Orlando
13
264
User
Jacksonville
13
265
User
Miramar Beach
13
266
Gabriel Diraviam
Davie
13
267
User
Orlando
12
268
User
Sanford
12
269
Dylan Levine
Maitland
12
270
User
Coral Springs
12
271
User
San Carlos Park
12
272
User
Bithlo
12
273
User
Melbourne
12
274
User
Boynton Beach
12
275
Michael
Boca Raton
12
276
User
North Naples
12
277
User
Temple Terrace
12
278
User
Orlando
12
279
User
Aventura
12
280
User
Palm Beach Gardens
12
281
User
Saint Petersburg
12
282
User
Pensacola
12
283
User
North Miami
12
284
User
Miami
12
285
User
Sanford
12
286
User
Davie
12
287
User
Royal Palm Beach
12
288
User
Oviedo
12
289
Samuel Norey
Pompano Beach
12
290
User
Plantation
12
291
User
Orlando
12
292
User
Weston
12
293
User
Hialeah Gardens
12
294
User
Miami
12
295
User
Tampa
11
296
User
Coral Gables
11
297
User
Coral Gables
11
298
User
Lake Magdalene
11
299
User
Tampa
11
300
User
Orlando
11
301
User
Sanford
11
302
User
Miami
11
303
User
Forest City
11
304
User
Wellington
11
305
User
The Hammocks
11
306
User
Saint Cloud
11
307
User
Florida Ridge
11
308
User
Pace
11
309
User
Orlando
11
310
User
Largo
11
311
Larry Johnson
Safety Harbor
11
312
User
Miami
11
313
User
Bay Lake
11
314
User
Palm Beach Gardens
11
315
User
Port Saint Joe
11
316
User
Union Park
11
317
User
Oviedo
11
318
User
Orlando
10
319
MRMFade
Sanford
10
320
User
Tampa
10
321
User
Greenacres
10
322
User
Miami Lakes
10
323
User
Orlando
10
324
User
Bay Lake
10
325
User
Bay Lake
10
326
User
Bay Lake
10
327
User
Plantation
10
328
User
Safety Harbor
10
329
User
Tampa
10
330
User
Goldenrod
10
331
User
Oviedo
10
332
Hart Doan
Largo
10
333
User
Villas
10
334
User
Orlando
10
335
User
Villas
10
336
User
Miami
10
337
User
Sandalfoot Cove
10
338
User
Orlando
10
339
User
Cape Coral
10
340
User
South Miami
10
341
User
Kendall
10
342
User
North Sarasota
10
343
User
Gateway
10
344
User
Gainesville
10
345
User
Tampa
10
346
User
Cutler Bay
10
347
InterTalks 1908
Saint Petersburg
10
348
User
Tampa
10
349
User
Celebration
10
350
User
Davie
10
351
User
Miami Beach
10
352
User
Orlando
10
353
User
Apopka
10
354
User
Hialeah Gardens
10
355
Renzo Baez
Coral Springs
9
356
User
Gainesville
9
357
User
Orlando
9
358
User
Sanford
9
359
User
Pinecrest
9
360
User
Fort Myers
9
361
Pablo
Miami
9
362
DanielaF
Coral Springs
9
363
User
Jacksonville
9
364
User
Hallandale Beach
9
365
User
Yulee
9
366
User
Tallahassee
9
367
User
Bay Lake
9
368
User
Orlando
9
369
User
Orlando
9
370
User
Palatka
9
371
User
Greenacres
9
372
User
Gainesville
9
373
User
Hobe Sound
9
374
Jeremy Hoffman
Ocala
9
375
User
Winter Garden
9
376
User
East Lake-Orient Park
9
377
User
Plantation
9
378
User
Plantation
9
379
Scott Farwell
Leesburg
9
380
User
Coral Gables
9
381
User
Miami
9
382
User
Myrtle Grove
9
383
Aqueel Majied
Jacksonville
9
384
User
Union Park
9
385
Obviouslyniyah
Richmond West
9
386
User
Sanford
9
387
User
Gainesville
9
388
User
North Naples
9
389
User
Fort Lauderdale
9
390
User
Melbourne
9
391
Rio Torres
Winter Garden
9
392
User
Orlando
9
393
User
Orlando
9
394
User
Pompano Beach
9
395
User
Davie
9
396
Brian Loftus
Brandon
9
397
User
Riverview
9
398
User
Fort Lauderdale
9
399
User
Jacksonville
9
400
User
Sanford
9
401
Chambers
Quincy
9
402
User
Palm Coast
9
403
User
Tampa
9
404
User
Orlando
9
405
User
Largo
9
406
User
Hialeah
9
407
Scaarlett Luis
Tamiami
9
408
User
Oviedo
8
409
User
Bay Lake
8
410
A Evans
Oviedo
8
411
User
Tamiami
8
412
User
Kings Point
8
413
User
Miami
8
414
User
The Hammocks
8
415
User
Siesta Key
8
416
User
Tallahassee
8
417
User
Sanford
8
418
User
Bradenton
8
419
User
Port St. Lucie
8
420
User
Goldenrod
8
421
User
Tallahassee
8
422
User
Cape Coral
8
423
User
Cutler Bay
8
424
Krista
Myakka City
8
425
User
Miami
8
426
User
Lutz
8
427
User
Orlando
8
428
User
Miramar Beach
8
429
User
Greenacres
8
430
User
Orlando
8
431
User
Union Park
8
432
User
Union Park
8
433
overloadcode
Boynton Beach
8
434
User
Lake Magdalene
8
435
User
Orlando
8
436
travis marciano
Pembroke Pines
8
437
User
Palm Beach Gardens
8
438
k
Fort Lauderdale
8
439
User
Sanford
8
440
User
Coconut Creek
8
441
User
Apopka
8
442
User
Orlando
8
443
User
Buckingham
7
444
User
Tampa
7
445
User
Chipley
7
446
User
Fruitville
7
447
Alexander Diraviam
Pembroke Pines
7
448
User
Largo
7
449
User
Pompano Beach
7
450
User
Orlando
7
451
User
Richmond West
7
452
User
Fort Lauderdale
7
453
User
Saint Cloud
7
454
User
Tampa
7
455
User
Eglin Air Force Base
7
456
User
Saint Petersburg
7
457
User
Tallahassee
7
458
Aggressivemonkey
Spring Hill
7
459
User
Rockledge
7
460
User
Orlando
7
461
michael kadow
Vero Beach South
7
462
User
Orlando
7
463
User
Fontainebleau
7
464
User
Hialeah
7
465
User
Union Park
7
466
User
Temple Terrace
7
467
User
Tampa
7
468
User
Largo
7
469
User
Saint Petersburg
7
470
User
Cape Coral
7
471
User
Boynton Beach
7
472
Jennifer Ivey
The Hammocks
7
473
User
Bay Lake
7
474
Dylan Parker
Gainesville
7
475
User
Miami Beach
7
476
User
Bithlo
7
477
User
San Carlos Park
7
478
User
Town N Country
7
479
User
Miami
7
480
User
Miami
7
481
User
Tarpon Springs
7
482
User
Daytona Beach
7
483
User
Tamarac
7
484
User
Davie
7
485
User
Melbourne
7
486
User
Miami Beach
7
487
User
Tampa
6
488
User
Jacksonville
6
489
User
Maitland
6
490
User
West Palm Beach
6
491
User
Union Park
6
492
User
Coral Gables
6
493
User
Union Park
6
494
User
Sanford
6
495
User
Siesta Key
6
496
User
Apopka
6
497
User
Palm Springs
6
498
User
St. Augustine
6
499
User
Tallahassee
6
500
User
Tampa
6
501
User
Orlando
6
502
User
Orlando
6
503
User
Miami
6
504
User
Tallahassee
6
505
User
Yulee
6
506
User
Lakewood Ranch
6
507
User
Coral Gables
6
508
User
Miami
6
509
User
Palm Bay
6
510
User
North Miami Beach
6
511
Hoxie Ackerman
Fort Lauderdale
6
512
User
Mango
6
513
User
Ferry Pass
6
514
User
University
6
515
User
Nocatee
6
516
User
Miami
6
517
User
Tampa
6
518
User
Orlando
6
519
User
Lauderhill
6
520
User
Orlando
6
521
User
Orlando
6
522
User
Bay Lake
6
523
User
Gainesville
6
524
User
Sanford
6
525
User
Sanford
6
526
User
Sanford
6
527
User
Land O Lakes
6
528
User
Orlando
6
529
User
Lake Magdalene
6
530
Shannon
Tampa
6
531
User
Richmond West
6
532
User
Plantation
6
533
User
Coral Springs
6
534
User
Orlando
6
535
User
Miami
6
536
User
Florida Ridge
6
537
User
Miami
5
538
User
Orlando
5
539
User
Hurlburt Field
5
540
User
Jacksonville
5
541
User
Union Park
5
542
User
Wellington
5
543
User
Jacksonville
5
544
User
Buckingham
5
545
Nickelle Vil
Buena Ventura Lakes
5
546
User
Union Park
5
547
User
Miami
5
548
User
Destin
5
549
User
Boca Del Mar
5
550
User
Orlando
5
551
User
Davie
5
552
User
Plant City
5
553
User
Tampa
5
554
User
Coral Gables
5
555
Court Kreisler
Lake Alfred
5
556
User
Orlando
5
557
User
Palm Coast
5
558
User
Jacksonville
5
559
User
Miami
5
560
User
West Palm Beach
5
561
Shannon
Orlando
5
562
User
Tallahassee
5
563
User
Orlando
5
564
User
Pace
5
565
User
Royal Palm Beach
5
566
Logan
Sanford
5
567
User
Saint Petersburg
5
568
User
Jacksonville
5
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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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