Leaderboard
Mexico
Mexico
Worldwide
Rank
Level
3
Danaé Villanueva
Ciudad de México
68
4
User
Jalisco
61
8
Saul Villa
Ciudad de México
55
9
Eduardo Escamilla
Nuevo León
54
10
User
Nuevo León
54
11
Raul Aldana
Sinaloa
46
13
Luis Vazquez
Jalisco
43
14
Jesús José Tronco Valencia
Nuevo León
42
15
User
Nuevo León
42
16
Paulina Diaz De La Paz
Baja California
41
17
Herman Santos
Ciudad de México
41
18
User
Jalisco
38
20
User
México
37
21
User
Nuevo León
37
24
Hach
Querétaro
35
25
User
Jalisco
35
27
Xavier B
Nuevo León
35
28
Alvaro
Nuevo León
34
29
User
México
34
30
Leonardo Rodriguez Gutierrez
Chihuahua
33
32
User
Nuevo León
30
33
User
Nuevo León
29
34
User
Yucatán
29
35
Jose Pijamas
Oaxaca
28
36
User
Oaxaca
28
37
User
Nuevo León
28
38
Riley Hollis
Baja California Sur
27
41
User
Nuevo León
27
42
Hannah Jeong
Nuevo León
27
43
User
Jalisco
27
44
User
México
27
45
Garcia
México
27
46
User
Nuevo León
26
48
User
Jalisco
26
49
User
Puebla
26
50
User
Nuevo León
25
51
User
Chihuahua
25
52
User
México
25
53
User
México
24
54
User
Nuevo León
24
55
User
Chihuahua
23
56
Woo Jin Kang
Nuevo León
23
57
User
Nuevo León
23
58
User
Jalisco
23
59
NEHEMIASQUISPE
Nuevo León
23
60
User
Nuevo León
23
61
Eduardo Valencia
Nuevo León
22
63
User
México
22
64
User
Nuevo León
22
65
User
Nuevo León
22
66
User
Nuevo León
22
69
Matt Smelser
Jalisco
21
70
User
México
21
73
User
Sinaloa
21
74
User
Guanajuato
21
75
User
México
20
76
User
México
20
77
User
Nuevo León
20
78
User
México
20
79
User
México
20
80
User
México
20
81
User
Nuevo León
19
83
Ivan Charles
Nuevo León
19
84
User
Nuevo León
19
85
User
Nuevo León
19
86
User
Nuevo León
19
87
marioplus
Puebla
19
88
User
México
19
89
User
Nuevo León
19
90
User
Puebla
19
91
User
Tabasco
18
92
User
Nayarit
18
93
Sarah Namorado
México
18
94
User
México
18
95
User
México
18
96
User
México
18
97
User
México
18
100
User
Jalisco
17
101
User
México
17
102
User
Nuevo León
17
103
User
Nuevo León
17
104
User
Nuevo León
16
105
User
Querétaro
16
106
User
Guanajuato
16
107
User
Nuevo León
15
108
User
México
15
110
User
México
15
112
User
México
15
113
veronica amaya
Puebla
14
115
User
Nuevo León
14
116
User
Nuevo León
14
117
User
Jalisco
14
119
Sandra Carolina Peréz Castillo
Nuevo León
14
120
User
Nuevo León
14
121
User
Nuevo León
14
122
User
Nuevo León
13
123
User
Chihuahua
13
124
User
México
13
125
Quasimodo y Moly
Baja California
13
126
User
Tamaulipas
13
127
User
México
13
128
User
Chihuahua
13
129
Tacos
Guanajuato
12
130
User
México
12
131
DAVID PRUNEDA
Coahuila de Zaragoza
12
132
User
Nuevo León
12
133
User
Nuevo León
12
134
Ivan Viveros
Nuevo León
12
135
User
Nuevo León
12
136
User
Jalisco
12
137
Favio Villaseñor
Jalisco
11
140
User
México
11
141
User
México
11
142
Lucia Martinez Gonzalez
Nuevo León
11
143
User
Nuevo León
11
144
User
México
11
145
User
México
11
146
User
México
11
147
User
Nuevo León
11
149
User
México
11
150
User
Jalisco
10
151
User
México
10
152
User
Guanajuato
10
153
User
Guanajuato
10
154
User
Nuevo León
10
155
Victoria Fernández
Nuevo León
10
156
User
Jalisco
9
158
User
México
9
160
User
Nuevo León
9
161
Cemhta C
Nuevo León
9
162
User
México
9
163
Juan Felipe Cantu Garza
Nuevo León
9
164
User
Jalisco
9
165
User
Nuevo León
9
166
User
Nuevo León
9
167
Bibi
Hidalgo
9
168
User
Nuevo León
9
169
User
Nuevo León
8
170
Yohanan Salmerón Chaparro
Guerrero
8
171
Armando Villarino
Baja California
8
172
User
Guanajuato
8
174
User
Quintana Roo
8
175
User
Sinaloa
8
176
User
Nuevo León
8
177
User
Sonora
8
178
John Santa Maria
Puebla
8
179
User
Puebla
8
180
Karen Fonseca
Baja California
8
182
User
Nuevo León
8
184
User
México
7
185
User
Nuevo León
7
186
User
Nuevo León
7
187
User
Sinaloa
7
190
User
Morelos
7
191
User
Nuevo León
7
192
User
Jalisco
7
193
User
Guanajuato
7
194
User
México
7
195
User
México
7
196
User
Nuevo León
7
197
User
Nuevo León
7
201
User
Nuevo León
6
202
User
México
6
203
User
Jalisco
6
204
User
Puebla
6
205
User
México
6
207
User
Guanajuato
6
208
User
Tamaulipas
6
210
User
Guanajuato
6
211
User
México
6
212
User
Nuevo León
6
213
User
Chihuahua
6
216
User
México
5
217
User
Nuevo León
5
220
User
Jalisco
5
221
User
Querétaro
5
222
User
Querétaro
5
223
User
Morelos
5
224
User
Sonora
5
225
User
México
5
226
User
México
5
227
User
Nuevo León
5
228
User
Nuevo León
5
229
User
Puebla
5
230
User
Puebla
5
231
User
Nuevo León
5
232
User
Nuevo León
4
233
User
Yucatán
4
237
User
Nuevo León
4
239
User
Nuevo León
4
240
User
Nuevo León
4
241
User
Puebla
4
243
User
Guanajuato
4
244
User
Sonora
4
246
User
Nuevo León
4
247
User
Jalisco
4
248
User
Nuevo León
4
249
User
Nuevo León
4
250
User
Nuevo León
4
251
User
Nuevo León
4
252
User
México
4
253
Marcella Judith Figueroa-Pelayo
Baja California
3
254
User
Nuevo León
3
255
User
Nuevo León
3
256
User
Quintana Roo
3
257
User
Nuevo León
3
258
User
Nuevo León
3
260
User
México
3
261
User
Durango
3
263
User
Jalisco
3
264
User
Querétaro
3
265
User
Quintana Roo
3
266
User
Guanajuato
3
267
Cynthia Lisbeth Alonso Plancarte
Nuevo León
3
268
User
México
3
269
User
Puebla
3
270
User
Querétaro
3
271
User
México
3
272
User
México
3
273
User
Puebla
3
274
User
Nuevo León
3
275
User
Nuevo León
3
276
Humberto Mtz.
Nuevo León
3
277
User
Jalisco
3
278
User
Nuevo León
3
279
User
Nuevo León
3
280
User
Nuevo León
3
281
User
Quintana Roo
3
282
User
México
3
283
User
Nuevo León
3
284
User
Jalisco
3
286
User
Nuevo León
2
287
User
Nuevo León
2
288
User
Nuevo León
2
289
User
Nuevo León
2
290
User
Hidalgo
2
293
User
Durango
2
295
User
Puebla
2
296
User
Jalisco
2
298
User
Querétaro
2
299
User
Querétaro
2
300
User
Nuevo León
2
301
User
Nuevo León
2
302
User
México
2
303
User
Nuevo León
2
304
User
Nuevo León
2
305
Mariana Ramirez Cisneros
Nuevo León
2
306
Arantza Luis Garcia
Nuevo León
2
307
User
Nuevo León
2
308
Maria Luisa Fernandez Maltos
Nuevo León
2
309
User
Nuevo León
2
310
User
México
2
311
User
Guanajuato
2
312
User
Nuevo León
2
313
User
Guanajuato
2
314
User
Jalisco
2
315
User
Guanajuato
2
316
User
Guerrero
2
317
User
Querétaro
2
318
User
Puebla
2
319
User
Nuevo León
2
320
User
Nuevo León
2
321
User
Nuevo León
2
322
User
Puebla
2
324
User
Puebla
2
325
User
Nuevo León
2
326
User
Nuevo León
2
327
User
México
2
328
User
Yucatán
2
329
User
México
2
330
User
Puebla
2
331
User
México
2
332
User
Nuevo León
2
333
User
Nuevo León
2
334
User
Nuevo León
2
335
User
Nuevo León
2
336
User
Nuevo León
2
337
User
Nuevo León
2
338
User
Nuevo León
2
339
User
Nuevo León
2
340
User
Nuevo León
2
341
User
Nuevo León
2
342
User
Nuevo León
2
343
User
Nuevo León
2
344
User
Nuevo León
2
345
User
Nuevo León
2
348
User
Zacatecas
2
349
User
México
2
350
User
Jalisco
2
351
User
Jalisco
2
352
User
Puebla
2
355
User
Puebla
1
356
User
Nuevo León
1
358
User
Tamaulipas
1
359
Nicolás Mancera De Olloqui
Aguascalientes
1
360
Nico Mancera
Aguascalientes
1
361
User
México
1
362
User
Nuevo León
1
363
User
México
1
365
User
México
1
366
User
Jalisco
1
367
User
Nuevo León
1
368
User
Nuevo León
1
369
User
Nuevo León
1
370
User
Nuevo León
1
372
User
México
1
374
User
México
1
377
User
México
1
378
Veronica Amaya
Puebla
1
379
Fatima Lucia Cadena Martin
Nuevo León
1
380
Miryam Jeanneth Briseño Melicoff
Sonora
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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