Leaderboard
Colombia
Colombia
Worldwide
Rank
Level
10
User
Santander
53
12
User
Santander
50
13
Santiago Palacino
Distrito Capital de Bogotá
49
16
User
Santander
43
20
User
Santander
41
21
User
Santander
41
22
User
Cundinamarca
40
23
User
Santander
39
24
Alejandro Piñeros
Distrito Capital de Bogotá
38
25
Laura Bermudez
Distrito Capital de Bogotá
37
27
User
Santander
35
28
User
Santander
33
29
Arsene1412
Norte de Santander
33
30
User
Santander
32
32
Jorge Tarazona
Distrito Capital de Bogotá
31
34
ANDREA DOMINGUEZ
Cundinamarca
30
35
User
Santander
30
37
User
Santander
29
38
User
Santander
28
39
User
Cundinamarca
28
40
User
Cundinamarca
28
41
User
Santander
28
42
Matias Anaya
Atlántico
27
43
User
Cundinamarca
26
44
User
Santander
25
45
User
Santander
25
46
User
Santander
25
47
User
Santander
25
49
User
Santander
25
52
User
Antioquia
23
54
User
Santander
23
57
User
Santander
22
60
Simon Venslauskas
Antioquia
22
61
User
Santander
21
63
User
Atlántico
20
66
User
Santander
19
69
Maria camila Garces
Distrito Capital de Bogotá
18
70
User
Santander
18
72
User
Antioquia
17
73
User
Santander
17
78
User
Cundinamarca
16
82
User
Santander
15
84
User
Santander
15
89
User
Santander
14
90
User
Magdalena
14
92
User
Santander
14
95
User
Santander
14
99
alejandra prada
Distrito Capital de Bogotá
13
100
User
Santander
13
101
User
Santander
13
104
User
Cundinamarca
13
105
User
Santander
13
106
User
Santander
13
107
User
Santander
13
108
User
Bolívar
12
109
Laura Martinez
Distrito Capital de Bogotá
12
110
User
Antioquia
12
114
User
Antioquia
12
117
User
Atlántico
12
120
User
Antioquia
11
123
User
Santander
11
125
User
Santander
11
127
User
Santander
11
128
User
Tolima
10
129
User
Santander
10
134
User
Antioquia
10
138
User
Santander
10
141
User
Santander
10
142
User
Antioquia
10
144
User
Santander
10
145
Nicolas Beltran
Quindío
9
148
User
Antioquia
9
149
User
Santander
9
150
User
Santander
9
151
User
Atlántico
9
156
User
Santander
9
159
User
Antioquia
9
160
User
Santander
9
161
User
Santander
9
162
sofia Pedraza Ciro
Distrito Capital de Bogotá
9
163
User
Cauca
9
169
User
Santander
9
170
User
Santander
9
173
User
Santander
8
174
Franklin Yulian
Distrito Capital de Bogotá
8
177
valentina Fonseca
Norte de Santander
8
178
User
Santander
8
179
User
Santander
8
180
User
Bolívar
8
183
User
Santander
8
184
User
Santander
8
188
User
Santander
7
191
User
Antioquia
7
192
User
Huila
7
195
User
Cundinamarca
7
196
User
Santander
7
198
User
Santander
7
199
User
Antioquia
7
200
Alejandro M.
Santander
7
201
User
Santander
7
207
User
Antioquia
6
209
User
Santander
6
210
eddyg
Córdoba
6
212
User
Santander
6
213
User
Santander
6
216
User
Bolívar
6
218
User
Santander
6
220
User
Antioquia
6
222
Héctor Arredondo
Antioquia
6
223
User
Santander
6
224
Ciro Rivera
Santander
6
225
User
Santander
5
226
User
Santander
5
227
User
Bolívar
5
228
User
Santander
5
229
User
Santander
5
230
User
Santander
5
231
User
Santander
5
232
User
Santander
5
233
User
Santander
5
236
User
Boyacá
5
241
User
Santander
5
245
User
Antioquia
5
247
User
Cundinamarca
5
248
User
Cundinamarca
5
249
User
Atlántico
5
250
User
Santander
5
251
User
Antioquia
4
252
User
Tolima
4
254
User
Santander
4
255
User
Santander
4
257
jose
Antioquia
4
261
User
Antioquia
4
262
User
Santander
4
263
User
Santander
4
264
User
Santander
4
267
User
Antioquia
4
268
User
Antioquia
4
269
User
Santander
4
272
User
Antioquia
4
274
User
Antioquia
4
275
Nicolás Tarazona Loaysa
Distrito Capital de Bogotá
4
277
User
Atlántico
4
279
User
Santander
4
280
User
Santander
4
287
User
Cundinamarca
3
288
Maria Antonia Hoyos
Distrito Capital de Bogotá
3
291
User
Atlántico
3
292
User
Cundinamarca
3
293
User
Antioquia
3
296
User
Antioquia
3
298
User
Risaralda
3
299
User
Santander
3
300
User
Santander
3
301
User
Antioquia
3
303
User
San Andrés
3
305
User
Cundinamarca
3
306
User
Antioquia
3
307
User
Santander
3
308
User
Santander
3
309
User
Santander
3
310
User
Santander
3
312
User
Santander
2
314
User
Santander
2
315
User
Santander
2
316
User
Santander
2
317
User
Santander
2
318
User
Antioquia
2
319
User
Antioquia
2
322
User
Atlántico
2
325
User
Atlántico
2
329
User
Antioquia
2
331
User
Atlántico
2
333
User
Atlántico
2
334
User
Santander
2
336
User
Atlántico
2
342
User
Atlántico
2
344
User
Antioquia
1
345
Mariantonia Rojas Cabal
Distrito Capital de Bogotá
1
346
User
Santander
1
347
User
Antioquia
1
348
User
Antioquia
1
349
User
Antioquia
1
353
User
Atlántico
1
355
User
Antioquia
1
356
User
Antioquia
1
361
User
Santander
1
362
User
Santander
1
363
User
Santander
1
364
User
Santander
1
365
User
Santander
1
366
User
Santander
1
369
User
Antioquia
1
370
User
Antioquia
1
375
User
Antioquia
1
376
User
Santander
1
377
User
Santander
1
379
Lina Marcela Gómez Quintero
Antioquia
1
381
rafael
Santander
1
385
User
Risaralda
1
387
User
Atlántico
1
391
User
Atlántico
1
393
User
Atlántico
1
394
User
Risaralda
1
395
User
Huila
1
396
User
Santander
1
401
User
Cundinamarca
1
402
User
Meta
1
403
User
Antioquia
1
404
User
Atlántico
1
405
User
Antioquia
1
406
User
Antioquia
1
407
User
Antioquia
1
408
User
Antioquia
1
409
User
Antioquia
1
410
User
Antioquia
1
412
maolomo
Santander
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 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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