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Austria
Worldwide
Rank
Level
1
User
Wien
88
2
User
Wien
70
3
User
Wien
62
4
User
Wien
61
5
Boris Szelcsanyi
Wien
60
6
User
Tirol
52
7
User
Wien
51
8
User
Wien
49
9
User
Wien
48
10
User
Wien
47
11
User
Wien
47
12
Philipp
Wien
46
13
User
Wien
45
14
User
Wien
45
15
User
Wien
44
16
saladin selo
Wien
43
17
User
Wien
43
18
User
Wien
42
19
User
Wien
42
20
User
Wien
42
21
User
Wien
41
22
User
Wien
41
23
User
Wien
40
24
User
Wien
40
25
User
Wien
39
27
Christian Langreiter
Wien
37
28
User
Wien
37
29
Bernhard Winter
Wien
36
30
User
Tirol
35
31
User
Steiermark
35
32
User
Wien
34
33
User
Wien
34
34
User
Wien
34
35
empanadilla
Wien
34
36
User
Wien
33
37
User
Tirol
33
38
User
Wien
32
39
Hannes Gasteiger
Tirol
32
40
Max
Vorarlberg
32
41
Seb H
Wien
31
42
Patrick Smuda
Oberösterreich
31
43
User
Wien
31
44
User
Wien
30
47
John
Salzburg
29
48
User
Salzburg
28
49
User
Wien
28
50
User
Wien
28
51
User
Wien
27
52
User
Wien
27
53
User
Wien
26
54
User
Wien
26
55
User
Wien
26
56
User
Tirol
25
57
User
Wien
24
58
User
Salzburg
24
59
User
Wien
24
60
Lukas Johann-Markus Stangl
Wien
24
61
User
Wien
23
62
User
Wien
23
63
User
Wien
23
64
JackPast
Niederösterreich
23
66
User
Wien
22
67
User
Tirol
22
68
User
Wien
22
69
User
Wien
22
70
User
Wien
22
71
User
Wien
21
72
User
Wien
21
75
User
Wien
21
76
User
Wien
21
77
Jack Past
Wien
21
80
Lukas Ruckensteiner
Wien
20
82
User
Wien
19
83
User
Tirol
19
84
User
Wien
18
85
User
Wien
18
86
User
Wien
18
87
User
Wien
17
90
User
Wien
17
91
User
Wien
17
92
User
Wien
16
94
User
Wien
16
95
User
Wien
16
97
User
Tirol
15
98
User
Wien
15
99
User
Wien
15
100
User
Wien
15
101
User
Wien
15
102
User
Wien
14
103
User
Wien
14
104
User
Wien
14
105
User
Wien
14
106
User
Wien
14
107
User
Wien
14
108
User
Wien
14
109
User
Wien
14
110
User
Wien
14
111
User
Wien
14
112
User
Wien
13
113
User
Wien
13
114
User
Wien
13
115
User
Wien
13
116
User
Wien
13
117
User
Wien
13
118
User
Wien
13
119
Maximilian Plut
Wien
13
120
User
Wien
13
121
User
Steiermark
12
122
Alan
Wien
11
123
User
Kärnten
11
124
Raffi Jonas
Wien
11
125
User
Steiermark
11
127
User
Salzburg
11
128
User
Wien
11
129
Milan Peric
Wien
11
131
User
Wien
11
132
User
Wien
10
134
User
Wien
10
136
User
Tirol
10
137
User
Wien
10
138
User
Wien
10
139
User
Wien
10
140
User
Wien
10
141
User
Kärnten
10
142
User
Wien
9
143
User
Wien
9
144
User
Wien
9
145
User
Wien
9
146
User
Wien
8
147
User
Wien
8
149
User
Steiermark
8
150
User
Wien
7
151
User
Wien
7
152
Anders Olesen
Wien
7
153
User
Region
7
154
Christian Langreiter
Tirol
7
155
User
Wien
7
156
User
Wien
7
157
User
Vorarlberg
7
158
User
Wien
6
159
User
Wien
6
160
User
Tirol
6
162
User
Wien
6
163
User
Wien
6
164
User
Wien
6
165
User
Wien
6
166
User
Wien
6
168
User
Wien
6
169
User
Wien
6
170
User
Wien
6
171
User
Wien
5
172
User
Steiermark
5
173
User
Burgenland
5
174
User
Wien
5
175
User
Kärnten
5
176
User
Vorarlberg
5
177
User
Wien
5
178
User
Tirol
5
179
User
Tirol
5
180
breadnbutter
Wien
5
181
User
Wien
5
183
User
Burgenland
5
184
User
Steiermark
5
185
User
Wien
4
186
User
Wien
4
187
User
Wien
4
188
User
Wien
4
189
User
Wien
4
190
User
Wien
4
191
User
Wien
4
192
User
Steiermark
4
193
User
Wien
4
194
User
Wien
4
195
User
Steiermark
4
196
User
Tirol
4
197
User
Wien
4
198
User
Salzburg
4
199
User
Wien
3
200
User
Wien
3
201
User
Wien
3
203
User
Wien
3
206
User
Wien
3
207
User
Wien
3
208
User
Salzburg
3
209
User
Vorarlberg
3
210
User
Wien
3
211
User
Wien
3
212
User
Steiermark
3
213
User
Wien
3
214
User
Wien
2
215
User
Tirol
2
216
User
Wien
2
217
User
Tirol
2
218
User
Wien
2
219
User
Wien
2
220
User
Wien
2
221
User
Salzburg
2
222
User
Wien
2
223
User
Wien
2
224
User
Wien
2
225
User
Wien
2
226
User
Wien
2
227
User
Wien
2
228
User
Wien
2
229
User
Wien
2
230
User
Wien
2
231
User
Burgenland
2
233
User
Wien
2
234
User
Vorarlberg
2
236
User
Wien
1
237
User
Wien
1
238
User
Wien
1
239
User
Wien
1
240
User
Wien
1
241
User
Steiermark
1
242
User
Wien
1
243
User
Wien
1
244
User
Wien
1
245
User
Wien
1
246
User
Wien
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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