Leaderboard
Poland
Poland
Worldwide
Rank
Level
1
Amalgam
Mazowieckie
87
2
Longinus torwaldzki
Mazowieckie
81
3
Iwona P
Mazowieckie
80
5
User
Lubelskie
64
6
TheNewSaga
Mazowieckie
61
8
Raohk
Mazowieckie
55
10
Aleksander Dróżdż
Śląskie
51
11
User
Mazowieckie
48
12
User
Mazowieckie
48
13
User
Mazowieckie
48
14
User
Śląskie
45
15
User
Mazowieckie
45
16
Bruno Banaszczyk
Śląskie
44
17
User
Małopolskie
44
18
User
Pomorskie
43
19
NJ
Pomorskie
42
20
Janusz I Grażyna Kowalscy
Podlaskie
42
21
User
Mazowieckie
40
22
Jan Kociniak
Mazowieckie
40
23
Seweryn Piotrowski
Świętokrzyskie
39
24
User
Pomorskie
39
25
Karol Wojtyła
Śląskie
37
26
User
Lubelskie
36
27
User
Małopolskie
35
29
Mariusz Siemanko
Lubelskie
34
30
User
Mazowieckie
34
31
User
Mazowieckie
34
32
User
Małopolskie
33
33
User
Śląskie
32
34
Kasia
Mazowieckie
32
35
User
Mazowieckie
31
36
User
Mazowieckie
31
37
User
Śląskie
31
38
User
Mazowieckie
31
39
Eugene Karastoyanov
Mazowieckie
30
41
im at
Małopolskie
30
42
User
Mazowieckie
30
43
User
Mazowieckie
30
44
User
Małopolskie
30
45
User
Małopolskie
30
46
User
Mazowieckie
29
47
User
Podkarpackie
29
49
User
Małopolskie
28
50
User
Mazowieckie
28
51
User
Mazowieckie
27
52
User
Mazowieckie
27
53
User
Mazowieckie
27
54
User
Mazowieckie
27
55
User
Lubuskie
27
57
User
Mazowieckie
26
58
User
Pomorskie
26
59
User
Podlaskie
26
60
User
Łódzkie
26
61
User
Małopolskie
26
62
User
Małopolskie
26
63
User
Małopolskie
26
64
User
Lubuskie
25
65
User
Mazowieckie
25
66
User
Małopolskie
25
67
User
Małopolskie
25
68
Minion Music
Mazowieckie
25
69
Asia
Mazowieckie
25
70
User
Śląskie
24
71
User
Małopolskie
24
72
Konrad Nowacki
Małopolskie
24
74
User
Mazowieckie
23
75
User
Mazowieckie
23
76
Marek
Śląskie
23
79
User
Małopolskie
23
80
User
Małopolskie
23
81
User
Mazowieckie
22
82
Kuba Lolkowski
Mazowieckie
22
83
Jacek Winter
Łódzkie
22
84
User
Małopolskie
22
85
User
Małopolskie
22
87
Niclas Lundquist
Małopolskie
21
89
User
Mazowieckie
21
90
User
Małopolskie
21
91
Keiii0 0
Małopolskie
21
92
User
Śląskie
20
93
WojciechN
Dolnośląskie
20
94
User
Małopolskie
20
96
User
Mazowieckie
20
98
Fred Rock
Śląskie
20
99
User
Mazowieckie
20
100
Robert
Małopolskie
19
101
Mirtha Fuerza
Małopolskie
19
102
User
Wielkopolskie
19
103
User
Mazowieckie
19
104
User
Mazowieckie
18
106
User
Łódzkie
18
107
User
Mazowieckie
17
108
User
Podlaskie
17
109
User
Podkarpackie
17
111
User
Małopolskie
17
112
Alberto
Pomorskie
16
113
User
Mazowieckie
16
117
User
Mazowieckie
16
118
User
Małopolskie
16
119
User
Lubelskie
16
120
User
Mazowieckie
15
121
Darek
Mazowieckie
15
122
User
Pomorskie
15
124
User
Lubelskie
15
125
User
Mazowieckie
14
126
User
Mazowieckie
14
127
Jakub Kowalski
Mazowieckie
14
128
User
Mazowieckie
14
129
User
Wielkopolskie
14
130
User
Małopolskie
14
131
User
Podlaskie
14
132
User
Lubuskie
14
134
User
Mazowieckie
14
135
User
Mazowieckie
13
136
User
Mazowieckie
13
137
User
Mazowieckie
13
138
User
Śląskie
13
141
User
Mazowieckie
12
142
User
Mazowieckie
12
146
User
Śląskie
12
147
User
Małopolskie
12
148
User
Pomorskie
12
149
User
Wielkopolskie
12
150
Stëfänië Vids
Mazowieckie
11
151
User
Mazowieckie
11
152
User
Wielkopolskie
11
153
User
Lubelskie
11
154
User
Małopolskie
11
155
User
Wielkopolskie
11
156
User
Pomorskie
11
157
User
Małopolskie
11
158
User
Mazowieckie
10
159
User
Mazowieckie
10
160
User
Mazowieckie
10
161
Pyjter Hazok
Śląskie
10
162
User
Mazowieckie
10
163
User
Małopolskie
10
164
Marcin Ogorzałek
Mazowieckie
10
165
User
Mazowieckie
10
166
Aleksander Goli
Śląskie
10
167
User
Mazowieckie
9
168
User
Mazowieckie
9
169
User
Małopolskie
9
170
User
Mazowieckie
9
173
User
Małopolskie
9
174
User
Mazowieckie
9
175
User
Małopolskie
9
176
User
Lubelskie
9
177
User
Mazowieckie
9
178
User
Małopolskie
8
179
User
Mazowieckie
8
180
User
Śląskie
8
181
User
Śląskie
8
182
User
Małopolskie
8
183
User
Mazowieckie
8
185
User
Podkarpackie
8
186
Vexie
Małopolskie
8
187
User
Lubelskie
7
188
User
Mazowieckie
7
189
User
Łódzkie
7
191
User
Mazowieckie
7
192
User
Mazowieckie
7
193
User
Małopolskie
7
194
User
Pomorskie
7
195
User
Mazowieckie
7
196
User
Mazowieckie
7
198
User
Pomorskie
6
201
User
Podlaskie
6
202
User
Mazowieckie
6
204
User
Mazowieckie
6
205
User
Mazowieckie
6
207
User
Lubelskie
5
208
Bartlomiej
Małopolskie
5
209
User
Mazowieckie
5
210
User
Mazowieckie
5
211
User
Podkarpackie
5
212
User
Mazowieckie
5
213
User
Mazowieckie
5
215
User
Małopolskie
5
216
User
Małopolskie
5
217
User
Śląskie
5
218
Malgorzata
Mazowieckie
4
219
User
Mazowieckie
4
220
User
Podlaskie
4
221
User
Małopolskie
4
223
User
Małopolskie
4
224
User
Mazowieckie
4
226
User
Mazowieckie
4
227
User
Łódzkie
4
228
User
Łódzkie
4
229
User
Podlaskie
4
230
User
Mazowieckie
4
231
User
Mazowieckie
4
232
User
Mazowieckie
4
233
User
Lubuskie
4
235
Michel
Mazowieckie
4
236
User
Mazowieckie
3
237
User
Mazowieckie
3
239
User
Łódzkie
3
241
User
Mazowieckie
3
242
User
Śląskie
3
244
User
Mazowieckie
3
245
User
Mazowieckie
3
247
User
Mazowieckie
3
248
User
Małopolskie
3
249
User
Podlaskie
3
250
User
Mazowieckie
3
253
John Liliputa
Małopolskie
3
256
User
Pomorskie
3
257
User
Podkarpackie
3
259
User
Mazowieckie
3
260
User
Lubuskie
3
261
User
Mazowieckie
2
262
User
Lubelskie
2
263
User
Małopolskie
2
264
User
Śląskie
2
265
User
Śląskie
2
266
User
Śląskie
2
267
User
Małopolskie
2
268
User
Mazowieckie
2
269
User
Mazowieckie
2
270
User
Małopolskie
2
271
User
Pomorskie
2
272
User
Małopolskie
2
273
User
Małopolskie
2
274
User
Mazowieckie
2
275
User
Podkarpackie
2
276
User
Mazowieckie
2
277
User
Małopolskie
2
278
User
Mazowieckie
2
279
User
Małopolskie
2
281
User
Mazowieckie
2
282
User
Mazowieckie
2
283
User
Mazowieckie
2
285
User
Mazowieckie
2
286
User
Lubelskie
2
287
User
Śląskie
2
288
User
Podlaskie
2
289
User
Lubelskie
2
290
User
Lubelskie
1
291
User
Małopolskie
1
292
User
Śląskie
1
293
User
Mazowieckie
1
294
User
Pomorskie
1
295
Nel Bauer
Małopolskie
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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