Leaderboard
Japan
Japan
Worldwide
Rank
Level
1
Zen SH
Kanagawa
96
2
User
Fukuoka
82
3
User
Fukuoka
81
4
User
Osaka
81
5
pupo
Aichi
80
6
User
Osaka
76
7
User
Tôkyô
74
8
Watty
Kyoto
73
9
User
Osaka
72
10
josh kai
Osaka
71
11
User
Osaka
70
12
User
Fukuoka
69
13
Bunga Putik S
Saitama
67
14
User
Osaka
67
15
User
Aichi
66
16
User
Osaka
65
17
User
Osaka
61
18
User
Fukuoka
60
19
User
Tôkyô
59
20
User
Hyogo
57
21
User
Tôkyô
56
22
User
Fukuoka
56
23
Genki Nishimura
Chiba
55
24
User
Tôkyô
55
25
User
Tôkyô
54
26
でぃ~も
Ehime
54
27
dd
Tôkyô
53
28
User
Tôkyô
51
29
auesthesthicc
Kyoto
51
30
User
Tôkyô
50
31
User
Kanagawa
50
32
User
Hyogo
50
33
User
Chiba
49
34
User
Okinawa
48
35
User
Tôkyô
48
36
desmond
Tôkyô
45
37
rsmiggle
Tôkyô
45
38
User
Shizuoka
43
39
ssry
Region
43
40
User
Tôkyô
43
41
User
Kanagawa
42
42
User
Tôkyô
42
43
User
Kanagawa
41
44
User
Osaka
40
45
User
Tôkyô
39
46
User
Tôkyô
39
47
Richard Thornton
Niigata
38
48
User
Tôkyô
38
49
User
Ehime
38
50
User
Tôkyô
37
51
User
Kanagawa
37
52
User
Osaka
37
53
User
Tôkyô
37
54
User
Osaka
37
55
oshotaro
Hyogo
34
56
Rattana Suesat
Tôkyô
34
57
Punnawit Metheenopanant
Osaka
33
58
User
Kanagawa
33
59
Mana
Tôkyô
32
60
User
Tôkyô
29
61
User
Hokkaido
28
62
User
Tôkyô
28
63
User
Hyogo
27
64
User
Saitama
26
65
User
Tôkyô
26
66
User
Tôkyô
26
67
Tayy SN
Tochigi
26
68
User
Kanagawa
26
69
User
Tôkyô
25
70
User
Tôkyô
25
71
User
Ehime
24
72
User
Hyogo
24
73
rav ayag
Tôkyô
23
74
User
Chiba
23
75
User
Tôkyô
23
76
User
Osaka
23
77
User
Kanagawa
23
78
User
Tôkyô
22
79
User
Chiba
22
80
User
Tôkyô
21
81
User
Tôkyô
21
82
User
Tôkyô
21
83
User
Tôkyô
20
84
User
Tôkyô
20
85
User
Osaka
19
86
User
Tôkyô
19
87
Tom Kitazawa
Tôkyô
19
88
User
Osaka
18
89
User
Osaka
18
90
User
Tôkyô
18
91
User
Tochigi
17
92
User
Hyogo
17
93
User
Tôkyô
17
94
User
Kyoto
17
95
User
Tôkyô
17
96
User
Tôkyô
17
97
User
Kanagawa
16
98
Mayu Ono
Tôkyô
16
99
User
Kanagawa
16
100
User
Tôkyô
16
101
User
Tôkyô
15
102
User
Tôkyô
15
103
User
Osaka
14
104
User
Tôkyô
14
105
User
Hyogo
14
106
User
Tôkyô
14
107
User
Tôkyô
14
108
User
Tôkyô
13
109
User
Hyogo
13
110
User
Tôkyô
12
111
User
Tôkyô
12
112
User
Osaka
12
113
User
Kanagawa
12
114
User
Aichi
11
115
User
Tôkyô
11
116
User
Kanagawa
11
117
User
Tôkyô
11
118
User
Hokkaido
11
119
User
Hyogo
10
120
Zaighum Rajput
Tôkyô
10
121
User
Okinawa
10
122
User
Tôkyô
10
123
User
Hyogo
10
124
User
Kyoto
10
125
User
Tôkyô
10
126
User
Osaka
10
127
User
Tôkyô
10
128
User
Fukuoka
9
129
User
Iwate
9
130
User
Tôkyô
9
131
User
Kanagawa
9
132
User
Kanagawa
8
133
User
Kyoto
8
134
User
Tôkyô
8
135
User
Tôkyô
8
136
Suraj Pattar
Tôkyô
8
137
User
Kanagawa
8
138
User
Tôkyô
7
139
User
Tôkyô
7
140
User
Tôkyô
7
141
User
Tôkyô
7
142
User
Osaka
7
143
User
Akita
7
144
User
Kyoto
7
145
User
Tôkyô
7
146
User
Tôkyô
6
147
User
Saitama
6
148
User
Kanagawa
6
149
User
Aichi
6
150
User
Tôkyô
6
151
User
Nara
6
152
User
Tôkyô
6
153
User
Nagano
6
154
User
Miyagi
6
155
User
Miyagi
6
156
User
Kyoto
5
157
User
Tôkyô
5
158
User
Kyoto
5
159
User
Kanagawa
5
160
User
Tôkyô
5
161
User
Tôkyô
5
162
User
Okinawa
5
163
User
Kagoshima
5
164
User
Tôkyô
4
165
User
Osaka
4
166
User
Kyoto
4
167
User
Tôkyô
4
168
User
Tôkyô
4
169
User
Chiba
4
170
User
Tôkyô
4
171
User
Tôkyô
4
172
User
Tôkyô
4
173
User
Osaka
4
174
User
Tôkyô
4
175
User
Tôkyô
4
176
User
Fukuoka
4
177
User
Tôkyô
3
178
User
Okinawa
3
179
User
Tôkyô
3
180
User
Osaka
3
181
User
Tôkyô
3
182
User
Chiba
3
183
User
Okinawa
3
184
User
Tôkyô
3
185
User
Osaka
3
186
User
Tôkyô
3
187
User
Tôkyô
3
188
User
Aichi
3
189
User
Osaka
3
190
User
Tôkyô
3
191
User
Hyogo
3
192
User
Kanagawa
3
193
User
Tôkyô
3
194
User
Tôkyô
3
195
User
Tôkyô
3
196
User
Chiba
3
197
User
Kanagawa
3
198
User
Mie
2
199
User
Tôkyô
2
200
User
Tôkyô
2
201
User
Tôkyô
2
202
User
Hiroshima
2
203
User
Tôkyô
2
204
User
Miyagi
2
205
User
Kanagawa
2
206
User
Saitama
2
207
User
Saitama
2
208
User
Gifu
2
209
User
Kanagawa
2
210
User
Tôkyô
2
211
User
Aichi
2
212
User
Tôkyô
2
213
User
Kyoto
2
214
User
Tôkyô
2
215
User
Tôkyô
2
216
User
Kyoto
2
217
User
Tôkyô
2
218
User
Tôkyô
2
219
User
Tôkyô
2
220
User
Tôkyô
2
221
User
Tôkyô
2
222
User
Tôkyô
2
223
User
Tôkyô
2
224
User
Tôkyô
2
225
User
Tôkyô
2
226
User
Tôkyô
2
227
User
Tôkyô
2
228
User
Tôkyô
2
229
User
Tôkyô
1
230
User
Osaka
1
231
User
Tôkyô
1
232
User
Tôkyô
1
233
User
Tôkyô
1
234
User
Tôkyô
1
235
User
Kanagawa
1
236
User
Gifu
1
237
User
Tôkyô
1
238
User
Tôkyô
1
239
User
Tôkyô
1
240
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 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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