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Rank
Level
1
User
Osaka
86
2
CM
Tôkyô
85
3
pupo
Aichi
83
4
KSUKan
Fukuoka
82
5
Jackie
Ehime
81
6
minh thuận trần
Shizuoka
70
7
David Calalang
Kanagawa
65
8
Divyansh Gupta
Tôkyô
59
9
User
Fukuoka
58
10
User
Tôkyô
57
11
User
Fukuoka
56
12
User
Osaka
55
13
User
Osaka
53
14
josh kai
Osaka
50
15
User
Fukuoka
47
16
User
Osaka
47
17
User
Tôkyô
45
18
User
Osaka
45
19
Bunga Putik S
Saitama
45
20
User
Tôkyô
44
21
User
Osaka
42
22
Watty
Kyoto
42
23
User
Osaka
41
24
User
Tôkyô
40
25
dd
Tôkyô
40
26
User
Tôkyô
39
27
User
Tôkyô
39
28
User
Osaka
38
29
User
Fukuoka
36
30
でぃ~も
Ehime
36
31
Richard Thornton
Niigata
35
32
User
Fukuoka
33
33
User
Chiba
33
34
User
Tôkyô
33
35
User
Hyogo
32
36
User
Tôkyô
32
37
User
Tôkyô
32
38
User
Kanagawa
30
39
User
Hyogo
30
40
User
Tôkyô
30
41
User
Aichi
29
42
User
Tôkyô
27
43
User
Kanagawa
26
44
auesthesthicc
Kyoto
26
45
desmond
Tôkyô
26
46
Mana
Tôkyô
25
47
User
Tôkyô
25
48
User
Osaka
24
49
User
Shizuoka
23
50
User
Kanagawa
23
51
Punnawit Metheenopanant
Osaka
23
52
User
Tôkyô
21
53
Genki Nishimura
Chiba
21
54
ssry
Region
20
55
User
Tôkyô
20
56
User
Saitama
20
57
User
Tôkyô
20
58
User
Hokkaido
19
59
oshotaro
Hyogo
19
60
User
Tôkyô
19
61
User
Tôkyô
18
62
User
Tôkyô
18
63
rav ayag
Tôkyô
18
64
User
Okinawa
18
65
Brayan Peña
Hyogo
18
66
User
Tôkyô
18
67
User
Tôkyô
18
68
User
Tôkyô
17
69
User
Tôkyô
17
70
User
Nagasaki
17
71
User
Kanagawa
16
72
User
Yamaguchi
16
73
User
Tôkyô
15
74
User
Nagasaki
15
75
User
Saitama
14
76
User
Tôkyô
14
77
User
Tôkyô
14
78
User
Tôkyô
13
79
User
Osaka
13
80
User
Ehime
13
81
User
Tôkyô
13
82
User
Tôkyô
13
83
User
Okinawa
12
84
User
Tôkyô
12
85
User
Aichi
12
86
Rattana Suesat
Tôkyô
12
87
Mario Peterson
Tôkyô
12
88
User
Kanagawa
12
89
User
Osaka
12
90
User
Osaka
12
91
User
Tôkyô
11
92
User
Tôkyô
11
93
User
Hyogo
11
94
User
Osaka
11
95
User
Chiba
10
96
Mayu Ono
Tôkyô
10
97
Henry Minamisawa
Tôkyô
10
98
Kaiwen Hu
Kanagawa
10
99
User
Ehime
10
100
User
Osaka
10
101
Lena Morita
Tôkyô
10
102
User
Shizuoka
10
103
User
Tôkyô
10
104
User
Tôkyô
10
105
User
Tôkyô
10
106
User
Tochigi
9
107
User
Tôkyô
9
108
User
Tôkyô
9
109
User
Tôkyô
8
110
User
Hyogo
8
111
Julia
Yamaguchi
8
112
User
Osaka
8
113
User
Wakayama
8
114
User
Kanagawa
8
115
User
Tôkyô
7
116
User
Aichi
7
117
User
Tôkyô
7
118
User
Tôkyô
7
119
User
Tôkyô
7
120
User
Hyogo
7
121
User
Tôkyô
7
122
User
Tôkyô
7
123
User
Hyogo
7
124
User
Ishikawa
7
125
User
Kanagawa
7
126
User
Tôkyô
7
127
User
Tôkyô
7
128
User
Chiba
7
129
Tom Kitazawa
Tôkyô
7
130
Ichiro Suzuki
Fukuoka
7
131
User
Okinawa
7
132
User
Kyoto
6
133
User
Tôkyô
6
134
User
Kanagawa
6
135
User
Osaka
6
136
User
Tôkyô
6
137
User
Tôkyô
6
138
User
Fukuoka
6
139
User
Tôkyô
6
140
User
Hyogo
6
141
User
Kyoto
6
142
User
Tôkyô
6
143
User
Tôkyô
6
144
User
Kyoto
6
145
User
Tôkyô
5
146
User
Tôkyô
5
147
User
Tôkyô
5
148
User
Iwate
5
149
User
Kanagawa
5
150
User
Osaka
5
151
User
Tôkyô
5
152
User
Tôkyô
5
153
User
Hyogo
5
154
User
Tôkyô
5
155
User
Tôkyô
5
156
Suraj Pattar
Tôkyô
5
157
User
Tottori
5
158
User
Tôkyô
5
159
User
Hokkaido
4
160
User
Kanagawa
4
161
User
Saitama
4
162
User
Tôkyô
4
163
User
Kyoto
4
164
User
Tôkyô
4
165
User
Aichi
4
166
User
Kanagawa
4
167
User
Aichi
4
168
User
Tôkyô
4
169
User
Hyogo
4
170
User
Tôkyô
4
171
User
Osaka
4
172
User
Kanagawa
4
173
User
Kanagawa
4
174
User
Akita
4
175
User
Tôkyô
4
176
User
Kyoto
3
177
User
Kanagawa
3
178
User
Tôkyô
3
179
User
Nara
3
180
User
Tôkyô
3
181
User
Osaka
3
182
User
Tôkyô
3
183
User
Nagano
3
184
User
Kanagawa
3
185
User
Tôkyô
3
186
User
Osaka
3
187
User
Kyoto
3
188
User
Tôkyô
3
189
User
Hokkaido
3
190
User
Kyoto
3
191
User
Tôkyô
3
192
User
Tôkyô
3
193
User
Tôkyô
3
194
User
Miyagi
3
195
User
Tôkyô
2
196
User
Miyagi
2
197
User
Tôkyô
2
198
User
Tôkyô
2
199
User
Okinawa
2
200
User
Tôkyô
2
201
User
Tôkyô
2
202
User
Tôkyô
2
203
User
Hyogo
2
204
User
Chiba
2
205
User
Okinawa
2
206
User
Kagoshima
2
207
User
Hiroshima
2
208
User
Tôkyô
2
209
User
Osaka
2
210
User
Tôkyô
2
211
User
Tôkyô
2
212
User
Miyagi
2
213
User
Tôkyô
2
214
User
Tôkyô
2
215
User
Tôkyô
2
216
User
Aichi
2
217
User
Osaka
2
218
User
Chiba
2
219
User
Okinawa
2
220
User
Tôkyô
2
221
User
Osaka
2
222
User
Tôkyô
1
223
User
Mie
1
224
User
Tôkyô
1
225
User
Tôkyô
1
226
User
Tôkyô
1
227
User
Aichi
1
228
User
Tôkyô
1
229
User
Osaka
1
230
User
Tôkyô
1
231
User
Tôkyô
1
232
User
Tôkyô
1
233
User
Tôkyô
1
234
User
Tôkyô
1
235
User
Miyagi
1
236
User
Kanagawa
1
237
User
Aichi
1
238
User
Fukuoka
1
239
User
Hyogo
1
240
User
Tôkyô
1
241
User
Tôkyô
1
242
User
Saitama
1
243
User
Region
1
244
User
Saitama
1
245
User
Gifu
1
246
User
Kanagawa
1
247
User
Aichi
1
248
User
Tôkyô
1
249
User
Osaka
1
250
User
Tôkyô
1
251
User
Tôkyô
1
252
User
Aichi
1
253
User
Kanagawa
1
254
User
Tôkyô
1
255
User
Tôkyô
1
256
User
Tôkyô
1
257
User
Tôkyô
1
258
User
Kyoto
1
259
User
Tôkyô
1
260
User
Ibaraki
1
261
User
Tôkyô
1
262
User
Hyogo
1
263
User
Kyoto
1
264
User
Tôkyô
1
265
User
Tôkyô
1
266
User
Saitama
1
267
User
Tôkyô
1
268
User
Tôkyô
1
269
User
Osaka
1
270
User
Tôkyô
1
271
User
Tôkyô
1
272
User
Tôkyô
1
273
User
Tôkyô
1
274
User
Tôkyô
1
275
User
Tôkyô
1
276
User
Tôkyô
1
277
User
Tôkyô
1
278
User
Kanagawa
1
279
User
Tôkyô
1
280
User
Tôkyô
1
281
User
Gifu
1
282
User
Tôkyô
1
283
User
Tôkyô
1
284
User
Tôkyô
1
285
User
Tôkyô
1
286
User
Tôkyô
1
287
User
Tôkyô
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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