Leaderboard
Ireland
Ireland
Worldwide
Rank
Level
2
Thomas Joyce
Limerick
84
4
User
Louth
79
6
NestleSnipes
Baile Átha Cliath
64
7
Sophie O'Brien
Baile Átha Cliath
62
8
Kevin Cooke
Baile Átha Cliath
59
9
Jonathan Lester
Baile Átha Cliath
57
11
Louis Angelini
Corcaigh
54
16
User
Ciarraí
53
18
User
Gaillimh
52
20
Gordon Cowpar
Limerick
51
22
Lucy Gorey
Cill Dara
50
23
User
Louth
50
30
User
An Cabhán
44
33
User
An Cabhán
43
35
User
Gaillimh
43
36
Billy Lee
Corcaigh
41
37
User
An Cabhán
41
39
User
An Cabhán
40
40
User
Port Láirge
40
41
Steffen Bakken
Baile Átha Cliath
40
43
User
Corcaigh
39
47
User
Ciarraí
38
48
User
An Cabhán
37
50
User
An Cabhán
36
51
User
Port Láirge
36
54
User
Louth
35
55
User
Port Láirge
35
58
User
An Cabhán
34
59
User
Donegal
34
60
abi power
Port Láirge
32
61
User
Port Láirge
32
62
User
Laois
32
66
User
Ciarraí
31
68
James(^•ᴥ•^)
Baile Átha Cliath
30
69
User
An Cabhán
29
70
User
An Cabhán
29
71
User
Port Láirge
29
72
User
Cill Dara
29
73
User
Ros Comáin
29
75
Martina Nowotny
Port Láirge
28
77
User
Carlow
28
78
Bla Cotter
Baile Átha Cliath
28
79
User
Connacht
28
80
User
Corcaigh
27
82
Maria Rusu
Port Láirge
27
84
User
Port Láirge
27
85
User
Offaly
27
88
roisin kiersey
Port Láirge
26
89
User
Port Láirge
26
93
User
Gaillimh
26
94
User
Limerick
26
96
User
Connacht
26
98
User
Ciarraí
25
100
User
Corcaigh
25
101
User
Port Láirge
25
102
Emma Fitzpatrick
Port Láirge
25
103
User
Port Láirge
25
104
User
Port Láirge
25
105
User
Port Láirge
25
106
User
Laois
25
108
User
Corcaigh
25
110
User
An Cabhán
24
111
User
An Cabhán
24
112
User
Corcaigh
24
113
User
Gaillimh
24
115
Siri Nandipaty
Baile Átha Cliath
24
116
User
Port Láirge
23
117
User
Port Láirge
23
118
User
Cill Dara
23
120
User
An Cabhán
22
121
User
Port Láirge
22
123
User
Gaillimh
22
125
User
Port Láirge
22
126
User
Cill Dara
22
129
Sarah Tighe
Gaillimh
22
131
User
An Cabhán
21
132
User
Port Láirge
21
133
User
Port Láirge
21
134
User
Port Láirge
21
137
ruth kearney
Port Láirge
21
138
User
Port Láirge
21
139
User
Port Láirge
21
140
User
Port Láirge
21
141
User
Port Láirge
21
142
User
Port Láirge
21
143
User
Port Láirge
21
144
Lauren Douris
Port Láirge
21
145
User
Port Láirge
21
146
User
Port Láirge
21
149
User
An Cabhán
20
151
User
Port Láirge
20
152
User
Port Láirge
20
153
User
Port Láirge
20
154
User
Port Láirge
20
156
User
Port Láirge
20
158
User
Gaillimh
20
162
User
Port Láirge
19
163
User
Port Láirge
19
164
User
Port Láirge
19
165
User
Donegal
19
167
E Murphy
Louth
18
171
User
Port Láirge
18
172
User
Port Láirge
18
174
User
Port Láirge
18
175
User
Port Láirge
18
176
User
Port Láirge
18
177
User
Donegal
18
181
User
An Cabhán
17
182
User
An Cabhán
17
183
User
Port Láirge
17
184
User
Port Láirge
17
185
User
Port Láirge
17
186
User
Port Láirge
17
187
User
Port Láirge
17
188
User
Port Láirge
17
189
User
Port Láirge
17
190
User
Donegal
17
192
User
Cill Dara
16
193
User
An Cabhán
16
194
User
Louth
16
195
User
Port Láirge
16
197
User
Port Láirge
16
198
User
Port Láirge
16
199
User
An Clár
16
204
User
An Cabhán
15
205
User
An Cabhán
15
206
User
An Cabhán
15
208
User
Corcaigh
15
209
User
Maigh Eo
15
210
User
Port Láirge
15
211
User
Port Láirge
15
212
User
Port Láirge
15
213
User
Port Láirge
15
214
User
Gaillimh
15
215
User
An Clár
15
216
User
Loch Garman
15
221
User
Port Láirge
14
222
User
Port Láirge
14
224
User
Port Láirge
14
225
User
Port Láirge
14
228
Éilis Russell
Baile Átha Cliath
14
232
User
An Cabhán
13
233
User
An Cabhán
13
235
User
Port Láirge
13
236
User
Port Láirge
13
237
User
Port Láirge
13
238
User
Port Láirge
13
241
User
Louth
13
243
User
Connacht
13
244
User
Corcaigh
12
248
User
An Mhí
12
250
josephine
An Clár
12
251
User
Port Láirge
12
252
sarah tighe
Gaillimh
12
253
User
Port Láirge
12
254
User
Port Láirge
12
255
User
Port Láirge
12
256
User
Port Láirge
12
257
User
Port Láirge
12
258
User
Cill Dara
12
261
User
An Mhí
12
262
User
Loch Garman
12
263
User
Gaillimh
12
271
User
Port Láirge
11
272
User
Port Láirge
11
273
User
Port Láirge
11
274
User
Port Láirge
11
275
User
Port Láirge
11
276
User
Port Láirge
11
277
User
Port Láirge
11
278
Fel_iix
Baile Átha Cliath
11
279
User
Port Láirge
11
280
User
Port Láirge
11
281
User
Limerick
11
286
Tom Walsh
Baile Átha Cliath
11
289
User
Donegal
11
298
User
Carlow
10
299
User
Port Láirge
10
300
Black Uchiha
Baile Átha Cliath
10
301
User
Donegal
10
302
User
Port Láirge
10
303
User
Maigh Eo
10
305
User
Gaillimh
10
313
User
Port Láirge
9
316
User
Port Láirge
9
317
User
Port Láirge
9
318
User
Port Láirge
9
319
User
Port Láirge
9
320
User
Port Láirge
9
321
User
Port Láirge
9
323
User
An Clár
9
327
Domhnall O'Suibhne
Baile Átha Cliath
9
331
User
An Mhí
8
335
User
Port Láirge
8
336
Ciara Lenane
Port Láirge
8
337
User
Port Láirge
8
341
User
Port Láirge
8
342
User
Port Láirge
8
343
User
Loch Garman
8
344
User
Port Láirge
8
345
User
Port Láirge
8
346
User
Port Láirge
8
347
User
Port Láirge
8
349
User
Corcaigh
8
352
User
Leitrim
8
353
User
Offaly
8
357
User
Limerick
7
359
User
Port Láirge
7
360
User
Port Láirge
7
361
User
Port Láirge
7
362
User
Port Láirge
7
363
User
Port Láirge
7
366
User
Port Láirge
7
367
User
Port Láirge
7
368
User
Port Láirge
7
369
User
Port Láirge
7
370
User
Port Láirge
7
373
User
Donegal
7
374
User
Laois
7
376
User
Carlow
7
379
User
An Mhí
7
389
User
Corcaigh
6
392
User
Port Láirge
6
393
User
Port Láirge
6
394
User
Port Láirge
6
395
Lilianna Broderick
Port Láirge
6
396
User
Port Láirge
6
398
User
Port Láirge
6
399
Andrea
Port Láirge
6
400
User
Port Láirge
6
403
User
Port Láirge
6
405
User
Gaillimh
6
407
User
Maigh Eo
5
410
User
An Cabhán
5
415
User
Port Láirge
5
416
User
Port Láirge
5
417
User
Port Láirge
5
418
User
Port Láirge
5
421
User
Port Láirge
5
423
User
Port Láirge
5
424
User
Port Láirge
5
426
User
Corcaigh
5
429
User
Louth
5
430
User
Donegal
5
432
User
An Clár
5
438
User
An Cabhán
4
442
User
Loch Garman
4
443
User
Port Láirge
4
444
User
Port Láirge
4
445
User
Port Láirge
4
446
User
Port Láirge
4
447
User
Port Láirge
4
448
User
Port Láirge
4
449
User
Port Láirge
4
450
User
Port Láirge
4
451
User
Gaillimh
4
452
User
An Clár
4
453
User
Port Láirge
4
454
User
Port Láirge
4
455
User
Port Láirge
4
459
User
An Mhí
4
460
User
Donegal
4
461
User
Louth
4
464
User
Corcaigh
3
470
User
Port Láirge
3
471
User
Port Láirge
3
472
User
Gaillimh
3
473
User
Gaillimh
3
475
User
Gaillimh
3
476
User
Port Láirge
3
477
User
Port Láirge
3
478
User
Port Láirge
3
479
User
Port Láirge
3
480
User
Donegal
3
482
User
Limerick
3
489
User
Connacht
3
494
User
Ciarraí
2
495
User
Donegal
2
497
User
Corcaigh
2
499
User
Corcaigh
2
500
User
Port Láirge
2
501
User
Port Láirge
2
503
User
Gaillimh
2
504
User
Port Láirge
2
507
User
Corcaigh
2
509
User
Port Láirge
2
516
User
Limerick
2
518
User
Ciarraí
2
522
User
An Mhí
2
523
User
An Mhí
2
526
User
Limerick
2
531
User
Louth
2
532
User
Corcaigh
1
537
User
Maigh Eo
1
539
User
Louth
1
546
User
An Longfort
1
548
User
Louth
1
550
User
Gaillimh
1
551
User
Ciarraí
1
554
User
Port Láirge
1
557
Martu N
Port Láirge
1
559
Graham James Keane
Connacht
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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