Leaderboard
Colombia
Colombia
Worldwide
Rank
Level
1
Sebastian Guevara
Distrito Capital de Bogotá
68
5
Viviana Cardenas
Distrito Capital de Bogotá
50
6
Nicolás Moreno
Distrito Capital de Bogotá
46
11
User
Santander
42
13
User
Santander
40
16
User
Cundinamarca
38
17
Alejandro Piñeros
Distrito Capital de Bogotá
37
18
User
Santander
34
19
User
Risaralda
33
20
User
Santander
32
21
User
Santander
32
22
Cortes el Conquistador
Distrito Capital de Bogotá
32
23
Luis Ardila
Cauca
32
25
User
Santander
31
26
User
Cundinamarca
30
27
sdoekwpekdwpkfpwe
Atlántico
30
30
Laura Bermudez
Distrito Capital de Bogotá
29
31
ISAAC ALEJANDRO JANICA PINEROS
Distrito Capital de Bogotá
28
33
User
Cundinamarca
28
34
User
Santander
28
36
Paulina Hoyos Restrepo
Distrito Capital de Bogotá
27
37
User
Santander
26
38
User
Santander
25
39
Nicolás Tarazona Loaysa
Distrito Capital de Bogotá
25
40
Paul David Becerra Fajardo
Distrito Capital de Bogotá
25
42
User
Santander
24
43
Arsene1412
Norte de Santander
23
44
User
Santander
23
46
User
Santander
22
47
Santiago Alviar
Caldas
22
48
Jorge Tarazona
Distrito Capital de Bogotá
22
49
User
Santander
22
50
ANDREA DOMINGUEZ
Cundinamarca
21
53
User
Santander
20
54
User
Antioquia
20
55
User
Santander
20
56
User
Santander
20
57
User
Santander
20
58
User
Santander
20
59
User
Santander
20
61
User
Cundinamarca
19
63
User
Antioquia
18
65
User
Cundinamarca
18
66
User
Santander
18
68
User
Cauca
17
69
User
Santander
17
71
User
Santander
17
72
User
Cundinamarca
16
78
Santiago Palacino
Distrito Capital de Bogotá
15
80
User
Santander
15
81
Simon Venslauskas
Antioquia
15
82
User
Atlántico
15
83
User
Santander
14
84
Maria camila Garces
Distrito Capital de Bogotá
14
88
User
Antioquia
14
89
User
Santander
14
92
Maria
Cundinamarca
13
96
User
Antioquia
12
97
User
Quindío
12
98
User
Santander
12
101
User
Risaralda
11
102
User
Santander
11
106
User
Santander
11
109
User
Santander
11
110
User
Santander
11
113
User
Quindío
10
115
User
Antioquia
10
117
User
Santander
10
118
User
Santander
10
119
alejandra prada
Distrito Capital de Bogotá
10
120
User
Cundinamarca
10
123
User
Santander
10
124
User
Santander
10
125
User
Santander
10
127
User
Bolívar
10
128
User
Atlántico
9
130
User
Magdalena
9
132
User
Antioquia
9
134
User
Cundinamarca
9
136
User
Santander
8
137
User
Santander
8
141
User
Santander
8
143
User
Santander
8
144
User
Antioquia
8
146
User
Tolima
8
147
User
Santander
8
154
Laura Martinez
Distrito Capital de Bogotá
8
155
User
Santander
8
157
User
Antioquia
8
158
User
Tolima
8
160
User
Antioquia
7
162
User
Santander
7
163
User
Antioquia
7
164
User
Santander
7
165
User
Santander
7
166
User
Santander
7
167
User
Santander
7
170
User
Santander
7
175
User
Atlántico
7
177
User
Santander
7
179
User
Santander
7
181
User
Antioquia
7
184
User
Atlántico
7
185
User
Santander
7
186
User
Santander
7
191
GheTi
Antioquia
7
192
Nicolas Beltran
Quindío
6
196
User
Santander
6
199
User
Santander
6
201
User
Santander
6
202
User
Cauca
6
205
Franklin Yulian
Distrito Capital de Bogotá
6
206
User
Antioquia
6
208
User
Santander
6
210
User
Cundinamarca
5
215
User
Antioquia
5
216
User
Santander
5
217
User
Huila
5
218
User
Santander
5
219
User
Bolívar
5
226
sofia Pedraza Ciro
Distrito Capital de Bogotá
5
228
User
Santander
5
232
Tomas Clavijo Walter
Valle del Cauca
5
235
User
Santander
5
236
User
Santander
5
238
eddyg
Córdoba
5
239
User
Antioquia
5
241
Alejandro M.
Santander
5
243
User
Santander
5
245
User
Santander
5
246
valentina Fonseca
Norte de Santander
4
247
User
Santander
4
248
User
Santander
4
250
Ciro Rivera
Santander
4
251
User
Bolívar
4
252
Héctor Arredondo
Antioquia
4
253
User
Santander
4
254
User
Santander
4
255
User
Santander
4
256
User
Santander
4
257
User
Santander
4
258
User
Santander
4
259
User
Bolívar
4
260
User
Santander
4
264
User
Antioquia
4
266
User
Santander
4
268
User
Antioquia
4
275
User
Santander
4
281
User
Antioquia
3
286
User
Santander
3
287
User
Santander
3
291
User
Cundinamarca
3
292
User
Tolima
3
293
User
Boyacá
3
294
jose
Antioquia
3
295
User
Cundinamarca
3
296
User
Santander
3
297
User
Santander
3
298
User
Santander
3
299
User
Atlántico
3
301
User
Antioquia
3
303
User
Santander
3
305
User
Santander
3
307
User
Santander
3
312
User
Antioquia
3
317
User
Santander
3
318
User
Santander
3
325
User
Antioquia
3
326
User
Antioquia
3
329
User
Antioquia
3
330
User
Antioquia
3
331
User
Antioquia
3
332
User
Antioquia
2
334
User
Antioquia
2
335
User
Cundinamarca
2
342
Sofia Perez
Antioquia
2
344
User
Atlántico
2
345
User
Santander
2
346
User
Atlántico
2
347
User
Santander
2
350
User
Antioquia
2
351
User
Cundinamarca
2
355
User
Santander
2
356
User
Santander
2
357
User
Santander
2
359
User
Atlántico
2
360
Maria Antonia Hoyos
Distrito Capital de Bogotá
2
361
User
Santander
2
365
User
Santander
2
366
User
Santander
2
367
User
Santander
2
368
User
Santander
2
369
User
Antioquia
2
371
User
Cundinamarca
2
372
User
Risaralda
2
373
User
Antioquia
2
377
User
Antioquia
2
378
User
Antioquia
2
381
User
San Andrés
1
383
User
Santander
1
385
User
Atlántico
1
387
User
Atlántico
1
388
User
Atlántico
1
393
User
Santander
1
395
User
Atlántico
1
397
User
Antioquia
1
405
User
Atlántico
1
408
User
Antioquia
1
409
User
Atlántico
1
410
User
Antioquia
1
411
Mariantonia Rojas Cabal
Distrito Capital de Bogotá
1
412
User
Santander
1
413
User
Santander
1
414
User
Santander
1
415
User
Santander
1
416
User
Santander
1
417
User
Antioquia
1
418
User
Santander
1
420
User
Antioquia
1
421
User
Antioquia
1
423
User
Santander
1
429
User
Risaralda
1
433
User
Atlántico
1
435
User
Antioquia
1
436
User
Antioquia
1
437
User
Antioquia
1
438
User
Antioquia
1
445
User
Santander
1
446
User
Antioquia
1
447
User
Antioquia
1
448
User
Antioquia
1
450
rafael
Santander
1
455
User
Atlántico
1
458
User
Atlántico
1
460
User
Atlántico
1

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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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