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Joe shwarizmi
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Killian O'Driscoll
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Deniss Ozerskis
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Gerd Wichers
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6
Matthew peters
98
7
Joonas Majuri
97
8
Oskar Treffner
97
10
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97
12
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96
13
Joonas Majuri
96
14
MartiBe
96
15
pi mileto
95
16
Gilles Vanderveken
95
17
Leonid Didyk
94
18
Miguel Juncais
94
19
Arne Langwitzki
94
20
Hessischer Landbote
94
21
Mariacristina Gugliandolo
93
22
Tommy
93
23
Michał Bielicki
93
24
Pablo
93
25
Patryk Cichecki
93
26
Yitan Lou
92
27
JIM ÖHMAN
92
28
Liz Maassen
92
29
Timself
92
30
Simão Vargas
92
31
AleksaT
91
32
Lo Dro
91
33
⬆️Schmiddy⚽
91
34
Orhan Yigit Yazicilar
90
35
Frock
90
36
SeptemberDU3
89
37
Giovanni Passuello
88
38
Olle Rehnquist
87
39
Sacha Di Martino
86
40
shield
85
41
Andrea Dalmonte
85
42
杨成博
85
44
Marco
83
45
Alberto Pola
83
46
Mart
82
48
Ihor Riabchich
82
49
JoEp
82
50
Miljan Raykovich
82
51
Kapablanca
82
53
François Cmn
81
54
Vitor Gouveia
80
55
Daphne Muller
80
56
Maciej Jaworski
79
57
Mateus Camelo de Campos Vilar Flores
79
58
Alejandro Ito-Aramendia
79
59
Julia Hänström
79
60
Marcell Szilvási
79
61
sd lp
79
62
Jonathan
77
63
Delage David
77
64
chl
77
65
dene
77
67
Miklós Horváth
77
68
Andrew Antoniou
77
69
Radu
77
70
Dov138
77
71
SK Spades
76
72
⬆️Schlaeger 🍓
76
73
Sandro Lindenmann
76
74
Clement molyn
75
75
Alex
75
76
KashmiriMirch
75
77
Siobhan Tobin
74
78
ferran baraut
74
79
Pablo❤💙💜 Antimadridista Culé Pucelano
74
80
inferential distance'); DROP TABLE leaderboard;--
73
81
Gerardo rp
73
82
Baris
73
83
Smith
73
84
ZH Liu
73
85
The Krasich
73
86
Lucía Borrego
73
87
asdgasdg sdfasf
73
88
Ruslan M.
72
89
Jason C
72
90
Asdad Dsaad
72
91
Hugo Sakrouge
72
92
François Ardèche
72
93
James Froehlich
72
94
Piotr Ryłko
71
95
KacaKacos
71
97
Martin Dollerup Nielsen
71
98
Filip
71
99
Gustaf Nordin
70
100
AmauryM
70
101
UES
70
102
Michel Zou
70
103
Yannick Vels
70
104
Tom Scotney
70
106
Joshua Rohrer
70
107
Jonas Gustafsson
69
108
le prell
69
109
Pedro Paulo Rocha Kahale Raimundo
69
110
LiviuRebreanu
69
111
Alex Kep
69
112
Tom Gornik
69
113
Brahim A
69
114
Brendan O'Dwyer
68
115
bennny
68
116
UKINEWE
68
117
Francois Méré
68
118
AnthonyC
68
119
Alonso Bobes
68
120
Giovanni Casalegno
68
121
Thibaut Herens
68
122
Carl Erik Samuel Nygren
68
123
Sonya Evlanchik
67
124
Joonas Jõeleht
67
125
Lucas Bobes
67
126
Titus Pellegrom
67
127
Robin M
66
128
Christian Petralito
66
129
marc
66
130
João Alves
66
131
Fabian
66
132
Tobias Kaiser
66
133
Dragonfly
66
134
Arouf Gangsta
65
135
Alex Andra
65
136
Andreas Falk
65
137
Shana
65
138
Lucas Silva
64
139
Zorba the Giant
64
140
MG
64
141
Tristan Becker
64
142
Przegrywacz
63
143
Benjamin
63
144
Julien Fraboulet
63
145
MG
63
146
miklos mobile
63
147
Haris Osmanovic
63
148
zhujik mnbv
63
149
Elina Hurskainen - Salonen
63
150
Matteo Magnano
63
151
Meterzolf of Symbols
63
152
Sacha DM
63
153
Cüneyit Kiriş
62
154
Estitxu Larralde
62
155
Raquelilla✌😝💜⚽💜
62
156
THE ROGERS
62
157
Jamie Porter
62
158
Wouter Huisman
62
159
Ana
62
160
P Kouw
61
161
Francesca Poli
61
162
Francesco D
61
163
Francesco Perniciaro Spatrisano
61
164
Baptiste
61
165
Gonçalo Ganhão
61
166
Pawan . N
61
167
Jan Pay
61
168
Arthur Fortanier
60
169
Giorgio S
60
170
Aleksandr Kostrub
60
171
João Pedro Costa Neto
60
172
alfred hamberg
60
173
Adrian Debski
60
174
Siggi
60
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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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