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Miklos
Vorarlberg
98
2
User
Wien
57
3
User
Wien
54
4
hi
Tirol
52
5
TheDecayedOne
Wien
49
6
User
Wien
49
7
Yuppi
Wien
42
8
User
Wien
40
10
User
Wien
38
11
User
Wien
38
12
User
Wien
37
13
User
Wien
37
14
Bernhard Winter
Wien
35
15
User
Wien
35
16
User
Steiermark
34
17
User
Wien
33
18
hannah alice
Steiermark
29
19
Edward Agboraw
Niederösterreich
29
20
User
Wien
27
21
User
Wien
26
22
User
Tirol
25
23
User
Wien
25
24
User
Wien
25
26
User
Wien
24
27
User
Wien
23
28
User
Wien
23
29
User
Wien
22
30
User
Wien
22
31
User
Wien
21
32
User
Wien
21
33
Philipp
Wien
21
34
User
Wien
20
35
User
Wien
20
36
User
Wien
19
37
Luna
Wien
19
38
User
Wien
19
39
User
Wien
19
40
User
Steiermark
18
41
User
Wien
18
42
User
Wien
18
44
User
Wien
18
45
User
Steiermark
17
46
User
Wien
17
47
User
Wien
17
48
User
Wien
17
51
User
Salzburg
16
52
User
Wien
16
53
User
Wien
16
54
User
Wien
15
55
User
Tirol
15
56
User
Steiermark
14
57
Seb H
Wien
14
58
User
Wien
14
59
User
Steiermark
14
60
User
Wien
14
61
User
Salzburg
13
62
Dino
Wien
13
63
User
Steiermark
13
64
User
Wien
12
65
User
Wien
12
66
User
Wien
12
67
Patrick Smuda
Oberösterreich
12
68
chl
Wien
12
69
User
Wien
12
70
empanadilla
Wien
12
71
Alan
Wien
11
72
User
Wien
11
73
User
Tirol
11
74
John
Salzburg
11
75
User
Tirol
11
76
User
Wien
11
77
User
Wien
11
78
User
Wien
11
79
User
Wien
11
80
User
Wien
11
81
Hannes Gasteiger
Tirol
11
82
User
Wien
11
83
User
Wien
11
85
User
Wien
11
86
User
Wien
10
87
Max
Vorarlberg
10
88
User
Wien
10
89
User
Kärnten
10
91
User
Wien
10
92
User
Wien
10
93
User
Wien
10
94
User
Wien
10
97
User
Wien
10
98
User
Wien
10
100
User
Wien
9
102
User
Tirol
9
103
User
Kärnten
9
104
User
Wien
9
105
User
Wien
9
106
User
Wien
9
108
User
Kärnten
9
109
User
Wien
9
110
User
Wien
9
111
User
Wien
9
112
User
Wien
9
113
User
Wien
8
115
User
Wien
8
116
User
Tirol
8
117
User
Tirol
8
118
User
Wien
8
119
User
Wien
8
120
User
Wien
8
121
User
Wien
8
122
Raffi Jonas
Wien
8
123
User
Wien
8
125
User
Wien
8
126
User
Wien
8
127
User
Steiermark
8
128
User
Wien
8
129
User
Steiermark
7
131
User
Wien
7
132
User
Wien
7
134
User
Wien
7
135
JackPast
Niederösterreich
7
136
User
Wien
7
137
User
Wien
7
139
User
Salzburg
7
140
Lukas Johann-Markus Stangl
Wien
7
141
User
Wien
7
142
User
Wien
7
143
User
Wien
7
144
User
Wien
7
145
User
Wien
7
146
Jack Past
Wien
7
148
User
Wien
7
149
User
Tirol
7
151
User
Wien
6
152
User
Wien
6
153
Chi Hammer
Wien
6
154
Milan Peric
Wien
6
155
User
Wien
6
156
Maximilian Plut
Wien
6
157
User
Wien
6
158
User
Wien
6
159
User
Wien
6
160
User
Wien
6
161
Anders Olesen
Wien
5
164
User
Region
5
165
User
Wien
5
166
User
Wien
5
167
User
Tirol
5
168
User
Wien
5
169
User
Wien
5
170
User
Wien
5
171
User
Steiermark
5
172
User
Wien
5
173
User
Wien
5
174
User
Wien
5
175
User
Wien
5
176
User
Wien
5
177
User
Wien
5
178
User
Tirol
5
179
User
Kärnten
4
180
User
Wien
4
181
Christian Langreiter
Tirol
4
182
User
Wien
4
183
User
Tirol
4
185
User
Steiermark
4
186
User
Wien
4
187
User
Burgenland
4
188
User
Tirol
4
189
User
Wien
4
190
User
Kärnten
4
191
User
Wien
4
192
User
Wien
4
193
User
Vorarlberg
4
194
User
Wien
4
195
User
Wien
4
196
User
Steiermark
4
197
User
Wien
3
198
User
Wien
3
199
User
Wien
3
200
User
Vorarlberg
3
201
User
Wien
3
202
User
Tirol
3
203
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Tirol
3
204
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Wien
3
205
User
Wien
3
207
User
Wien
3
208
User
Wien
3
209
User
Wien
3
211
User
Wien
3
212
breadnbutter
Wien
3
213
User
Kärnten
2
214
User
Wien
2
215
User
Wien
2
216
User
Wien
2
217
User
Wien
2
218
User
Wien
2
219
User
Wien
2
220
User
Burgenland
2
221
User
Wien
2
222
User
Wien
2
223
User
Steiermark
2
224
User
Wien
2
226
User
Wien
2
227
User
Steiermark
2
228
User
Wien
2
229
User
Wien
2
231
User
Steiermark
2
232
User
Wien
2
233
User
Steiermark
2
235
User
Wien
2
236
User
Wien
2
237
User
Wien
2
238
User
Kärnten
2
239
User
Wien
2
240
User
Wien
2
241
User
Wien
2
242
User
Wien
2
243
User
Tirol
1
244
User
Wien
1
245
User
Steiermark
1
246
User
Wien
1
247
User
Tirol
1
248
User
Wien
1
249
User
Salzburg
1
250
User
Vorarlberg
1
251
User
Wien
1
252
User
Tirol
1
253
User
Wien
1
254
User
Wien
1
255
User
Wien
1
256
User
Salzburg
1
257
User
Wien
1
258
User
Wien
1
259
User
Wien
1
260
User
Steiermark
1
261
User
Tirol
1
262
User
Salzburg
1
263
User
Wien
1
264
User
Wien
1
265
User
Wien
1
266
User
Wien
1
267
User
Wien
1
268
User
Wien
1
269
User
Wien
1
270
User
Wien
1
271
User
Wien
1
272
User
Wien
1
273
User
Wien
1
274
User
Wien
1
275
User
Wien
1
276
User
Wien
1
277
User
Wien
1
278
User
Burgenland
1
279
User
Wien
1
281
User
Wien
1
282
User
Steiermark
1
283
User
Wien
1
284
User
Wien
1
285
User
Wien
1
286
User
Wien
1
287
User
Wien
1
288
User
Wien
1
289
User
Vorarlberg
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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