Leaderboard
Portugal
Portugal
Worldwide
Rank
Level
1
User
Lisboa
93
2
User
Aveiro
86
3
User
Aveiro
80
4
Fernando Bacelar de Sousa
Lisboa
65
5
BichodoMato
Porto
62
6
User
Lisboa
62
7
User
Santarém
60
8
User
Faro
60
9
João Tiago Bairras Gorgulho
Porto
54
10
User
Porto
53
11
User
Faro
51
12
Pedro Caeiro
Lisboa
51
13
User
Lisboa
49
14
Tiago Morais
Porto
47
15
User
Porto
43
16
User
Lisboa
42
17
User
Lisboa
42
18
User
Lisboa
42
19
User
Lisboa
42
20
Vilgeforte Águas-Santas
Lisboa
41
21
Solange Silva
Lisboa
41
22
Joaquim Silva
Lisboa
40
23
User
Lisboa
39
24
User
Porto
39
25
joao.miguel
Setúbal
39
26
User
Lisboa
38
27
User
Lisboa
37
28
Shahrukh khan
Lisboa
36
29
User
Coimbra
35
30
User
Lisboa
35
31
User
Lisboa
35
32
User
Lisboa
35
33
User
Lisboa
34
34
User
Porto
34
35
Paulo Pesqueira
Lisboa
34
36
User
Porto
34
37
User
Porto
33
38
User
Porto
33
39
User
Porto
33
40
User
Porto
32
41
User
Vila Real
32
42
User
Santarém
32
43
User
Lisboa
32
44
User
Lisboa
32
45
User
Porto
31
46
User
Porto
31
47
User
Porto
31
48
NM
Lisboa
31
49
User
Porto
31
50
User
Lisboa
31
51
User
Santarém
31
52
Tiago Cabo
Porto
31
53
User
Lisboa
31
54
Andreia Nogueira
Porto
31
55
User
Lisboa
30
56
User
Porto
30
57
User
Aveiro
30
58
User
Lisboa
30
59
User
Lisboa
30
60
edmond turquieh
Santarém
30
61
User
Coimbra
30
62
User
Porto
30
63
User
Lisboa
30
64
User
Lisboa
29
65
User
Porto
29
66
User
Faro
29
67
User
Porto
29
68
User
Porto
29
69
User
Porto
28
70
User
Porto
28
71
User
Porto
28
72
User
Lisboa
28
73
User
Lisboa
28
74
User
Faro
28
75
User
Lisboa
28
76
User
Porto
28
77
User
Porto
27
78
User
Lisboa
27
79
User
Coimbra
27
80
User
Porto
27
81
User
Porto
27
82
User
Lisboa
27
83
User
Porto
27
84
User
Porto
27
85
User
Porto
27
86
Iara Serbaneci
Faro
27
87
User
Porto
27
88
User
Viseu
27
89
User
Porto
26
90
User
Porto
26
91
User
Lisboa
26
92
User
Porto
26
93
User
Porto
26
94
User
Lisboa
26
95
User
Porto
26
96
User
Porto
25
97
User
Porto
25
98
User
Porto
25
99
User
Porto
25
100
User
Lisboa
25
101
User
Porto
25
102
User
Porto
25
103
User
Porto
25
104
User
Porto
25
105
User
Porto
25
106
User
Porto
25
107
User
Porto
25
108
Matthew Brews
Faro
25
109
User
Lisboa
25
110
User
Porto
25
111
User
Porto
25
112
User
Santarém
25
113
User
Porto
25
114
User
Porto
25
115
User
Lisboa
25
116
User
Porto
25
117
User
Beja
25
118
User
Faro
24
119
User
Lisboa
24
120
User
Porto
24
121
User
Porto
24
122
User
Porto
24
123
User
Porto
24
124
User
Porto
24
125
User
Porto
24
126
User
Porto
24
127
User
Porto
24
128
User
Porto
24
129
User
Porto
24
130
User
Porto
24
131
User
Porto
24
132
User
Porto
24
133
User
Porto
24
134
adr
Lisboa
23
135
User
Porto
23
136
User
Porto
23
137
User
Porto
23
138
Teresa Sa
Lisboa
23
139
User
Lisboa
23
140
User
Porto
23
141
User
Porto
22
142
User
Lisboa
22
143
User
Porto
22
144
User
Porto
22
145
User
Porto
22
146
User
Coimbra
22
147
User
Porto
22
148
User
Porto
22
149
User
Porto
22
150
User
Porto
22
151
User
Porto
22
152
User
Porto
22
153
User
Porto
22
154
User
Porto
22
155
User
Porto
22
156
User
Porto
22
157
User
Porto
22
158
User
Porto
22
159
User
Porto
22
160
User
Porto
22
161
User
Lisboa
21
162
User
Porto
21
163
User
Porto
21
164
User
Porto
21
165
User
Porto
21
166
User
Porto
21
167
User
Porto
21
168
User
Lisboa
21
169
User
Lisboa
21
170
User
Porto
21
171
null
Lisboa
21
172
User
Porto
20
173
User
Porto
20
174
User
Lisboa
20
175
User
Porto
20
176
User
Porto
20
177
User
Lisboa
20
178
User
Porto
20
179
User
Lisboa
20
180
User
Porto
20
181
User
Porto
20
182
User
Porto
20
183
User
Porto
20
184
User
Porto
20
185
User
Porto
20
186
User
Lisboa
20
187
User
Lisboa
20
188
User
Setúbal
20
189
User
Porto
20
190
User
Lisboa
20
191
User
Porto
20
192
User
Porto
20
193
User
Lisboa
20
194
User
Lisboa
20
195
User
Porto
20
196
User
Porto
19
197
User
Porto
19
198
User
Porto
19
199
User
Porto
19
200
User
Porto
19
201
User
Porto
19
202
User
Porto
19
203
User
Porto
19
204
User
Porto
19
205
User
Porto
19
206
Vanessa Muteia
Lisboa
19
207
User
Porto
19
208
User
Porto
19
209
User
Porto
19
210
User
Porto
19
211
User
Porto
19
212
User
Porto
19
213
User
Porto
19
214
User
Porto
19
215
User
Porto
19
216
User
Porto
19
217
User
Porto
18
218
User
Lisboa
18
219
User
Porto
18
220
User
Porto
18
221
User
Porto
18
222
User
Porto
18
223
Afonso Elvas
Porto
18
224
User
Porto
18
225
User
Porto
18
226
User
Porto
18
227
User
Porto
18
228
User
Porto
18
229
User
Porto
18
230
User
Porto
18
231
User
Porto
17
232
User
Porto
17
233
User
Porto
17
234
User
Porto
17
235
User
Lisboa
17
236
User
Porto
17
237
User
Porto
17
238
User
Faro
17
239
User
Porto
17
240
User
Porto
17
241
User
Porto
17
242
User
Coimbra
17
243
User
Porto
17
244
User
Lisboa
17
245
User
Lisboa
16
246
User
Porto
16
247
User
Porto
16
248
User
Porto
16
249
User
Porto
16
250
User
Porto
16
251
User
Porto
16
252
User
Porto
16
253
User
Porto
16
254
User
Porto
16
255
User
Porto
16
256
User
Porto
16
257
User
Porto
16
258
User
Lisboa
16
259
User
Porto
16
260
User
Lisboa
16
261
User
Lisboa
16
262
User
Porto
16
263
User
Porto
16
264
User
Porto
16
265
Adam Grey
Porto
16
266
User
Porto
16
267
User
Porto
16
268
User
Porto
16
269
User
Porto
15
270
User
Porto
15
271
User
Porto
15
272
henrique proenca
Lisboa
15
273
User
Lisboa
15
274
User
Braga
15
275
User
Porto
15
276
User
Porto
15
277
User
Porto
15
278
User
Porto
15
279
User
Coimbra
15
280
User
Porto
15
281
Francis M
Bragança
15
282
User
Porto
15
283
User
Porto
15
284
User
Coimbra
15
285
User
Porto
15
286
User
Porto
15
287
User
Lisboa
15
288
User
Lisboa
15
289
User
Porto
15
290
User
Porto
15
291
User
Porto
15
292
User
Porto
15
293
User
Aveiro
15
294
User
Porto
15
295
User
Porto
15
296
User
Porto
15
297
User
Lisboa
15
298
User
Porto
15
299
User
Porto
14
300
User
Porto
14
301
User
Lisboa
14
302
User
Porto
14
303
User
Porto
14
304
User
Beja
14
305
User
Porto
14
306
User
Porto
14
307
User
Porto
14
308
User
Porto
14
309
User
Porto
14
310
User
Lisboa
14
311
User
Porto
14
312
User
Porto
14
313
User
Porto
14
314
User
Lisboa
14
315
User
Porto
14
316
User
Porto
14
317
User
Porto
14
318
User
Lisboa
14
319
User
Setúbal
14
320
User
Porto
14
321
User
Porto
13
322
User
Lisboa
13
323
Simao Sarmento
Lisboa
13
324
User
Porto
13
325
User
Porto
13
326
User
Lisboa
13
327
User
Porto
13
328
User
Porto
13
329
User
Lisboa
13
330
User
Porto
13
331
User
Porto
13
332
User
Porto
13
333
User
Porto
13
334
User
Bragança
13
335
User
Porto
13
336
User
Porto
13
337
User
Porto
13
338
User
Lisboa
13
339
User
Porto
13
340
User
Lisboa
13
341
User
Porto
13
342
User
Porto
13
343
User
Lisboa
12
344
User
Porto
12
345
User
Lisboa
12
346
User
Lisboa
12
347
User
Lisboa
12
348
User
Porto
12
349
User
Braga
12
350
User
Porto
12
351
User
Porto
12
352
User
Porto
12
353
User
Porto
12
354
User
Porto
12
355
User
Porto
12
356
User
Porto
12
357
User
Porto
12
358
User
Porto
12
359
User
Lisboa
12
360
User
Porto
12
361
User
Porto
12
362
User
Lisboa
12
363
User
Porto
12
364
User
Porto
12
365
User
Porto
12
366
User
Lisboa
11
367
User
Porto
11
368
User
Porto
11
369
User
Lisboa
11
370
User
Porto
11
371
XGariex
Lisboa
11
372
Ricardo Correia
Aveiro
11
373
User
Porto
11
374
User
Porto
11
375
User
Porto
11
376
User
Porto
11
377
EzYRa
Faro
11
378
User
Porto
11
379
User
Porto
11
380
User
Porto
11
381
User
Porto
11
382
User
Porto
11
383
User
Porto
11
384
User
Porto
11
385
User
Lisboa
11
386
User
Porto
11
387
User
Lisboa
10
388
User
Porto
10
389
User
Vila Real
10
390
User
Lisboa
10
391
User
Lisboa
10
393
User
Porto
10
394
User
Porto
10
395
User
Porto
10
396
User
Porto
10
397
User
Porto
10
398
User
Porto
10
399
Alexandre Romao
Lisboa
10
400
User
Coimbra
10
401
User
Lisboa
10
402
User
Lisboa
10
403
User
Porto
9
404
User
Porto
9
405
Rodrigo Maia da Silva
Região Autónoma dos Açores
9
406
User
Lisboa
9
407
User
Braga
9
408
User
Porto
9
409
User
Setúbal
9
410
User
Porto
9
411
User
Porto
9
412
User
Porto
9
413
User
Lisboa
9
414
User
Braga
9
415
User
Porto
9
416
User
Porto
9
417
User
Porto
9
418
User
Porto
9
419
User
Porto
9
420
User
Porto
9
421
User
Porto
9
422
User
Porto
9
423
User
Porto
9
424
User
Porto
9
425
User
Porto
9
426
User
Porto
9
427
User
Porto
9
428
User
Porto
8
429
User
Porto
8
430
User
Porto
8
431
User
Lisboa
8
432
User
Lisboa
8
433
User
Lisboa
8
434
User
Lisboa
8
435
User
Lisboa
8
436
User
Setúbal
8
437
User
Porto
8
438
User
Porto
8
439
User
Porto
8
440
User
Porto
8
441
User
Porto
8
442
User
Porto
8
443
User
Porto
8
444
User
Lisboa
8
445
User
Porto
8
446
User
Porto
8
447
User
Porto
8
448
User
Porto
8
449
User
Setúbal
8
450
User
Lisboa
7
451
Calvin Duarte
Lisboa
7
452
User
Porto
7
453
User
Porto
7
454
User
Porto
7
455
User
Porto
7
456
Mary Hopkins
Lisboa
7
457
User
Lisboa
7
458
Filipa Sebastião
Lisboa
7
459
User
Lisboa
7
460
User
Faro
7
461
User
Coimbra
7
462
User
Porto
7
463
User
Porto
7
464
User
Porto
7
465
User
Faro
7
466
User
Aveiro
6
467
User
Porto
6
468
User
Lisboa
6
469
User
Lisboa
6
470
User
Lisboa
6
471
User
Coimbra
6
472
User
Lisboa
6
473
User
Lisboa
6
474
User
Lisboa
6
475
User
Lisboa
6
476
User
Lisboa
6
477
User
Lisboa
6
478
User
Porto
6
479
User
Porto
6
480
User
Lisboa
6
481
User
Lisboa
6
482
User
Porto
6
483
User
Viseu
6
484
User
Porto
6
485
User
Lisboa
6
486
User
Lisboa
5
487
User
Lisboa
5
488
David Marques
Viseu
5
489
User
Setúbal
5
490
User
Porto
5
491
User
Beja
5
492
User
Lisboa
5
493
User
Porto
5
494
User
Porto
5
495
User
Viseu
5
496
User
Porto
5
497
Marta Rolo
Lisboa
5
498
User
Faro
5
499
Maria Fonseca
Lisboa
5
500
User
Porto
4
501
User
Lisboa
4
502
User
Porto
4
503
User
Lisboa
4
504
User
Lisboa
4
505
User
Porto
4
506
User
Lisboa
4
507
User
Lisboa
4
508
User
Lisboa
4
509
User
Lisboa
4
510
User
Braga
4
511
sofs lobo
Porto
3
512
User
Porto
3
513
User
Viseu
3
514
User
Porto
3
515
User
Beja
3
516
User
Lisboa
3
517
User
Setúbal
3
518
User
Lisboa
3
519
User
Braga
3
520
User
Lisboa
3
521
User
Santarém
3
522
User
Porto
3
523
User
Setúbal
3
524
User
Lisboa
3
525
User
Lisboa
2
526
User
Lisboa
2
527
User
Lisboa
2
528
User
Setúbal
2
529
User
Lisboa
2
530
User
Braga
2
531
User
Porto
2
532
User
Lisboa
2
533
User
Lisboa
2
534
Pedro Caeiro
Lisboa
2
535
User
Santarém
2
536
User
Coimbra
2
537
User
Lisboa
2
538
User
Lisboa
2
539
User
Porto
2
540
User
Porto
2
541
User
Porto
2
542
User
Coimbra
2
543
User
Lisboa
2
544
User
Porto
2
545
User
Setúbal
2
546
User
Braga
2
547
User
Porto
2
548
User
Braga
2
549
User
Braga
1
550
User
Lisboa
1
551
User
Setúbal
1
552
User
Viseu
1
553
User
Aveiro
1
554
User
Porto
1
555
User
Porto
1
556
User
Setúbal
1
557
User
Lisboa
1
558
User
Lisboa
1
559
User
Porto
1
560
edmond turquieh
Santarém
1

Free

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Students

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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.


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