Leaderboard
Arizona
Rank
Level
1
Justin
Mesa
79
2
Kris Patel
Kingman
72
3
Gabe Korer
Scottsdale
66
4
Kris Patel
Kingman
65
5
Gabe B
Avondale
57
6
User
Scottsdale
54
7
User
Mesa
51
8
User
Chandler
51
9
User
Chandler
49
10
User
Tempe
48
11
Michael Neal
Tempe
44
12
User
Phoenix
43
13
User
San Tan Valley
41
14
chad
Phoenix
40
15
User
Scottsdale
38
16
User
Florence
38
17
Julie F
Phoenix
38
18
User
Florence
37
19
User
San Tan Valley
37
20
User
Phoenix
35
21
User
Phoenix
34
22
User
Mesa
33
23
User
Phoenix
32
24
User
Phoenix
31
25
User
Phoenix
30
26
User
Phoenix
30
27
User
Phoenix
30
28
User
Chandler
30
29
User
Tempe
28
30
Sunil Devaraj
Mesa
27
31
User
Tempe
27
32
User
Phoenix
26
33
SBmath
Phoenix
26
34
User
Phoenix
25
35
User
Phoenix
25
36
User
Scottsdale
25
37
User
Phoenix
24
38
User
Lake Havasu City
24
39
User
Phoenix
22
40
User
Scottsdale
22
41
User
Phoenix
22
42
User
Chandler
22
43
User
Phoenix
22
44
Julian T.
Phoenix
22
45
User
Mesa
21
46
Kris Patel
Kingman
21
47
User
Phoenix
21
48
Yug Patel
Kingman
20
49
User
Phoenix
20
50
User
Catalina Foothills
20
51
User
San Tan Valley
20
52
User
Lake Havasu City
19
53
User
San Tan Valley
19
54
User
Tortolita
19
55
User
Phoenix
19
56
User
Catalina Foothills
19
57
ahmadnur muhammad-isa
Phoenix
18
58
User
Tucson
18
59
User
Scottsdale
18
60
User
Mesa
18
61
User
Phoenix
17
62
User
Phoenix
17
63
Clayton Garnier
Mesa
17
64
User
Tempe
17
65
User
Tempe
17
66
User
City
17
67
User
Phoenix
16
68
tlannister
Flagstaff
15
69
User
Mesa
15
70
User
San Tan Valley
14
71
User
Scottsdale
14
72
Bianca Supomo
Tucson
14
73
Amy Andrews
Glendale
14
74
User
City
14
75
User
Mesa
14
76
User
Phoenix
13
77
User
Glendale
13
78
User
Scottsdale
13
79
Jaydan Solorio
Glendale
13
80
Briant Trejo
Avondale
12
81
Danny Harvell
Phoenix
12
82
User
Sun City
12
83
User
Chandler
12
84
User
Mesa
12
85
User
Tucson
12
86
User
Tempe
12
87
User
Phoenix
12
88
User
Yuma
11
89
User
Fountain Hills
11
90
Emanuele Saladini
Phoenix
11
91
User
Phoenix
11
92
User
Tempe
11
93
Yug Patel
Kingman
11
94
User
San Tan Valley
11
95
User
Mesa
11
96
User
Marana
11
97
User
Phoenix
11
98
User
Phoenix
11
99
User
Phoenix
11
100
User
Tucson
10
101
User
Tempe
10
102
Tara Ruhland
Phoenix
10
103
jakob miller
Glendale
10
104
Naiya Martinez
Glendale
10
105
Sonia Devaraj
Mesa
10
106
User
Maricopa
10
107
User
Phoenix
10
108
Brayden Duran
Tucson
10
109
User
Tucson Estates
10
110
User
Phoenix
10
111
User
Tempe
10
112
User
Chandler
10
113
User
Scottsdale
10
114
User
Phoenix
10
115
User
Mesa
9
116
User
Bullhead City
9
117
Rafael Molina
Phoenix
9
118
Ahmed Sheekh-ahmed
Phoenix
9
119
User
Mesa
9
120
User
Phoenix
9
121
User
Phoenix
9
122
User
Phoenix
9
123
User
Glendale
9
124
User
Phoenix
9
125
User
Snowflake
9
126
User
Glendale
8
127
User
Phoenix
8
128
User
Phoenix
8
129
steven pace
Glendale
8
130
User
Tempe
8
131
User
Phoenix
8
132
User
Gilbert
8
133
User
Mesa
8
134
User
Phoenix
8
135
User
Glendale
8
136
User
Chandler
8
137
User
Mesa
8
138
User
Tempe
8
139
Scott Campbell
Phoenix
8
140
Matt
Phoenix
8
141
User
Phoenix
8
142
Nellie Garcia
Tucson
8
143
User
Phoenix
7
144
User
Mesa
7
145
User
Queen Creek
7
146
User
Sahuarita
7
147
User
Phoenix
7
148
User
Phoenix
7
149
User
Phoenix
7
150
User
Chandler
7
151
User
Phoenix
7
152
User
Glendale
7
153
Gordon He
Mesa
7
154
User
Phoenix
7
155
User
Phoenix
7
156
User
Scottsdale
6
157
User
Phoenix
6
158
User
Chandler
6
159
User
Avondale
6
160
User
Tempe
6
161
User
Casas Adobes
6
162
Allie Williams
Tempe
6
163
Brett Gustafson
Flowing Wells
6
164
User
Tucson
6
165
User
Scottsdale
6
166
User
Phoenix
6
167
User
Queen Creek
6
168
User
Phoenix
6
169
User
Chandler
6
170
User
San Luis
6
171
User
Gilbert
6
172
User
Glendale
6
173
User
Phoenix
6
174
User
Scottsdale
6
175
User
Tempe
5
176
User
Peoria
5
177
User
Phoenix
5
178
User
Tempe
5
179
User
Phoenix
5
180
User
Oro Valley
5
181
User
Tucson
5
182
User
Phoenix
5
183
User
Tempe
5
184
User
Phoenix
5
185
User
Gilbert
5
186
User
Phoenix
5
187
User
Gilbert
5
188
User
Phoenix
5
189
User
Tucson
5
190
User
Tucson
5
191
User
Kingman
5
192
User
Goodyear
5
193
Efren Ponce
Glendale
5
194
User
Phoenix
5
195
User
Phoenix
5
196
User
Phoenix
5
197
User
Phoenix
5
198
User
Maricopa
4
199
User
Glendale
4
200
User
Bisbee
4
201
User
Chandler
4
202
User
Glendale
4
203
User
Tucson
4
204
User
Chandler
4
205
User
Phoenix
4
206
User
Oro Valley
4
207
User
Surprise
4
208
User
Nogales
4
209
User
Glendale
4
210
User
Phoenix
4
211
User
Mesa
4
212
User
Goodyear
4
213
User
Phoenix
4
214
User
Phoenix
4
215
User
Phoenix
4
216
User
Chandler
4
217
User
Phoenix
4
218
User
Phoenix
4
219
julian pippins
Glendale
4
220
User
Tucson
4
221
User
Tempe
4
222
User
Phoenix
4
223
User
Mesa
4
224
User
Catalina Foothills
3
225
User
Phoenix
3
226
User
Glendale
3
227
User
Glendale
3
228
Andy Guerra
Glendale
3
229
User
Gilbert
3
230
User
Kingman
3
231
Tammy
Phoenix
3
232
User
Tempe
3
233
User
Phoenix
3
234
User
Phoenix
3
235
User
Phoenix
3
236
User
Phoenix
3
237
User
Phoenix
3
238
User
Phoenix
3
239
User
Phoenix
3
240
User
Phoenix
3
241
User
Scottsdale
3
242
User
Phoenix
3
243
User
Tucson
3
244
User
Prescott Valley
3
245
User
Casas Adobes
3
246
User
Phoenix
3
247
User
Glendale
3
248
User
Litchfield Park
3
249
User
Phoenix
3
250
User
Glendale
3
251
User
Tucson
3
252
User
Phoenix
3
253
User
Phoenix
3
254
User
Prescott
3
255
User
Glendale
3
256
User
Tucson
3
257
User
Kingman
3
258
User
Scottsdale
3
259
User
Scottsdale
3
260
User
Phoenix
3
261
User
Oro Valley
3
262
User
Maricopa
2
263
User
Phoenix
2
264
User
Phoenix
2
265
User
Mesa
2
266
User
Phoenix
2
267
User
Phoenix
2
268
User
Globe
2
269
User
Glendale
2
270
User
Phoenix
2
271
User
Phoenix
2
272
User
Phoenix
2
273
User
Glendale
2
274
User
Tucson
2
275
User
Glendale
2
276
User
Phoenix
2
277
User
Mesa
2
278
User
Phoenix
2
279
User
Gilbert
2
280
User
Scottsdale
2
281
User
Phoenix
2
282
User
Phoenix
2
283
justin bainey
Phoenix
2
284
Danny Lisker
Phoenix
2
285
User
Casa Grande
2
286
User
Phoenix
2
287
Nyla Blattner
Glendale
2
288
User
Phoenix
2
289
User
Scottsdale
2
290
User
Glendale
2
291
User
Tucson
2
292
User
Apache Junction
2
293
User
Glendale
2
294
User
Tucson
2
295
User
Scottsdale
2
296
User
Phoenix
2
297
User
Phoenix
2
298
User
Glendale
2
299
User
Tempe
2
300
User
Tucson
2
301
User
Phoenix
2
302
User
Kingman
2
303
User
Phoenix
2
304
User
Kingman
2
305
User
Casas Adobes
1
306
User
Marana
1
307
User
Tucson
1
308
User
Chandler
1
309
User
Gilbert
1
310
User
Kingman
1
311
User
San Luis
1
312
User
Phoenix
1
313
User
Phoenix
1
314
User
Tempe
1
315
User
Tucson
1
316
User
Kingman
1
317
User
Phoenix
1
318
User
Phoenix
1
319
User
Mesa
1
320
User
Phoenix
1
321
User
Kingman
1
322
User
Phoenix
1
323
User
Phoenix
1
324
User
Phoenix
1
325
User
Sahuarita
1
326
User
Maricopa
1
327
User
Glendale
1
328
User
Phoenix
1
329
User
Chandler
1
330
User
Casas Adobes
1
331
User
Tempe
1
332
User
Phoenix
1
333
User
Phoenix
1
334
User
Phoenix
1
335
User
Tucson
1
336
User
Phoenix
1
337
User
Glendale
1
338
User
Phoenix
1
339
User
Glendale
1
340
User
Phoenix
1
341
User
Surprise
1
342
User
Glendale
1
343
User
Phoenix
1
344
User
Mesa
1
345
Colette Blattner
Glendale
1
346
User
Glendale
1
347
User
Oro Valley
1
348
User
Glendale
1
349
User
Phoenix
1
350
User
Phoenix
1
351
User
Glendale
1
352
User
Glendale
1
353
User
Glendale
1
354
User
Glendale
1
355
User
Glendale
1
356
Pedro Hernandez Sanchez
Glendale
1
357
User
Sedona
1
358
User
Phoenix
1
359
User
Peoria
1
360
ahxmadnur
Phoenix
1
361
Kris Patel
Kingman
1
362
User
Mesa
1
363
User
Kingman
1
364
User
Phoenix
1
365
User
Tucson
1
366
User
Phoenix
1
367
User
Phoenix
1
368
User
Tempe
1
369
User
Mesa
1
370
Maitri Bhakta
Mesa
1
371
Nic Guererro
Mesa
1
372
User
Phoenix
1
373
User
Sun City
1
374
User
Phoenix
1
375
User
Phoenix
1
376
User
Chandler
1
377
User
Kingman
1
378
User
Peoria
1
379
User
Phoenix
1
380
User
Gilbert
1
381
User
Gilbert
1
382
User
Peoria
1
383
User
Glendale
1
384
User
Surprise
1
385
User
Phoenix
1
386
User
Tucson
1
387
User
Gilbert
1
388
User
Mesa
1
389
User
Arizona City
1
390
User
Arizona City
1
391
User
Bullhead City
1
392
User
Phoenix
1
393
User
Phoenix
1
394
User
Gilbert
1
395
User
Phoenix
1
396
User
Tucson
1
397
User
Phoenix
1
398
User
Tempe
1
399
User
Phoenix
1
400
User
Buckeye
1
401
User
Mesa
1
402
User
Phoenix
1
403
User
Tucson
1
404
User
Flagstaff
1
405
User
Gilbert
1
406
User
Phoenix
1
407
User
Goodyear
1
408
User
Tucson
1
409
User
Tucson Estates
1
410
User
Tucson
1
411
User
Tempe
1
412
User
Sahuarita
1
413
Justin Rainey
Phoenix
1
414
Dual Shotero
Phoenix
1

Free

Free basic access

Login Optional

Progress saved automatically

Students

Works great in classrooms

25,000,000
Questions answered
100,000
Users
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 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.


Privacy Policy