Leaderboard
Pakistan
Pakistan
Worldwide
Rank
Level
1
Malik Muhammad Kashif Saeed
Panjāb
75
2
User
Sindh
52
3
User
Sindh
45
4
User
Sindh
43
5
User
Panjāb
42
7
User
Panjāb
40
8
User
Panjāb
39
9
User
Sindh
38
10
User
Sindh
38
11
User
Panjāb
37
12
Faraz
Islāmābād
37
13
User
Sindh
36
14
User
Sindh
36
15
User
Panjāb
35
16
User
Sindh
34
17
User
Panjāb
34
18
User
Panjāb
34
19
User
Islāmābād
33
20
User
Islāmābād
33
21
Ali Hanif
Sindh
31
22
User
Panjāb
30
23
User
Sindh
30
24
User
Panjāb
29
25
User
Sindh
29
26
User
Sindh
29
27
User
Sindh
28
28
User
Panjāb
28
29
User
Sindh
27
30
User
Islāmābād
27
31
User
Panjāb
26
32
User
Sindh
25
33
User
Panjāb
25
34
User
Islāmābād
24
35
User
Panjāb
23
36
User
Sindh
23
37
User
Panjāb
23
38
User
Panjāb
23
39
User
Panjāb
23
40
User
Sindh
23
41
User
Panjāb
22
42
User
Panjāb
22
43
User
Panjāb
22
44
User
Sindh
22
45
User
Sindh
21
46
User
Sindh
21
47
User
Panjāb
21
48
User
Panjāb
21
49
Tai moor
Region
21
50
User
Islāmābād
20
51
User
Sindh
20
52
User
Panjāb
20
53
User
Islāmābād
20
54
User
Panjāb
20
55
User
Sindh
20
56
User
Panjāb
20
57
User
Islāmābād
20
58
User
Sindh
19
59
User
Sindh
19
60
User
Panjāb
19
61
User
Islāmābād
19
62
User
Panjāb
19
63
User
Sindh
19
64
User
Sindh
18
65
User
Sindh
17
66
User
Panjāb
17
67
User
Panjāb
17
68
User
Sindh
17
69
User
Sindh
17
70
User
Islāmābād
17
71
User
Sindh
16
72
User
Panjāb
16
73
User
Panjāb
16
74
User
Sindh
16
75
User
Panjāb
15
76
Fahd
Islāmābād
15
77
User
Panjāb
15
78
User
Panjāb
15
79
User
Panjāb
15
80
User
Panjāb
15
81
User
Sindh
15
82
User
Sindh
14
83
User
Sindh
14
84
User
Panjāb
14
85
User
Sindh
14
86
User
Sindh
14
87
User
Panjāb
13
88
User
Panjāb
13
89
User
Panjāb
13
90
User
Sindh
13
91
User
Panjāb
13
92
User
Panjāb
13
93
User
Sindh
13
94
User
Panjāb
13
95
User
Sindh
13
96
User
Sindh
12
97
User
Sindh
12
98
User
Sindh
12
99
User
Panjāb
12
100
User
Panjāb
12
101
Farhaj Ahmed
Sindh
12
102
User
Islāmābād
12
103
User
Sindh
12
104
User
Panjāb
12
105
User
Panjāb
11
107
User
Panjāb
11
108
User
Sindh
11
109
User
Panjāb
11
110
User
Panjāb
11
111
User
Sindh
11
112
User
Islāmābād
11
113
Yousuf Khawaja
Panjāb
11
114
more what
Region
11
115
Zahra
Region
11
116
User
Panjāb
10
117
User
Sindh
10
118
User
Sindh
10
119
User
Sindh
10
120
User
Sindh
10
121
User
Sindh
10
122
User
Sindh
10
123
User
Panjāb
10
124
User
Panjāb
10
125
User
Sindh
10
126
User
Panjāb
9
128
User
Sindh
9
129
User
Sindh
9
130
User
Sindh
9
131
User
Islāmābād
9
132
User
Islāmābād
9
133
User
Sindh
9
134
User
Panjāb
9
135
User
Sindh
9
136
User
Sindh
8
137
User
Panjāb
8
140
User
Panjāb
8
141
User
Panjāb
8
142
User
Sindh
8
143
User
Sindh
8
144
User
Sindh
8
145
Hina Tahir
Sindh
8
146
User
Sindh
8
147
Sadia Mamji
Sindh
8
148
User
Islāmābād
8
149
User
Sindh
8
150
User
Islāmābād
8
151
User
Islāmābād
8
152
User
Sindh
7
153
User
Sindh
7
154
User
Panjāb
7
156
User
Sindh
7
157
User
Panjāb
7
158
User
Panjāb
7
159
User
Panjāb
7
160
User
Sindh
7
161
User
Panjāb
7
162
User
Sindh
7
163
User
Islāmābād
7
164
User
Sindh
7
165
User
Sindh
7
166
User
Sindh
7
167
User
Islāmābād
7
168
User
Panjāb
7
169
User
Panjāb
7
170
User
Sindh
7
171
User
Sindh
7
172
User
Panjāb
7
173
User
Panjāb
7
174
User
Islāmābād
6
175
User
Sindh
6
176
User
Sindh
6
177
User
Panjāb
6
178
User
Panjāb
6
179
Saad Akhtar
Sindh
6
180
User
Sindh
6
181
User
Sindh
6
182
User
Panjāb
6
183
User
Sindh
6
184
User
Islāmābād
6
185
User
Sindh
6
186
User
Panjāb
6
187
User
Sindh
6
188
User
Sindh
6
189
User
Sindh
6
190
User
Panjāb
6
191
User
Panjāb
6
192
User
Sindh
6
193
User
Sindh
6
194
User
Sindh
6
195
User
Islāmābād
6
196
User
Panjāb
6
197
User
Panjāb
6
198
User
Sindh
6
199
User
Sindh
6
200
User
Islāmābād
6
201
User
Sindh
6
202
User
Sindh
6
203
User
Panjāb
5
204
User
Sindh
5
206
User
Islāmābād
5
207
User
Sindh
5
208
User
Sindh
5
209
User
Panjāb
5
210
User
Islāmābād
5
211
User
Panjāb
5
212
User
Sindh
5
213
User
Panjāb
5
214
User
Sindh
5
215
User
Sindh
5
216
User
Panjāb
5
217
User
Panjāb
5
218
User
Sindh
5
219
User
Islāmābād
5
220
User
Sindh
5
221
User
Sindh
5
222
User
Sindh
5
223
User
Panjāb
5
224
User
Panjāb
5
225
User
Sindh
5
226
User
Panjāb
4
228
User
Sindh
4
229
User
Sindh
4
230
User
Sindh
4
231
User
Panjāb
4
232
hi
Sindh
4
233
User
Sindh
4
234
User
Panjāb
4
235
User
Sindh
4
236
User
Sindh
4
237
User
Sindh
4
238
User
Sindh
4
239
User
Islāmābād
4
240
User
Balochistan
4
241
User
Sindh
4
242
Muhammad Jafri
Sindh
4
243
User
Sindh
4
244
User
Sindh
4
245
User
Sindh
4
246
User
Sindh
4
247
User
Islāmābād
4
248
User
Sindh
4
249
User
Sindh
4
250
User
Sindh
4
251
User
Sindh
4
252
User
Islāmābād
3
253
User
Sindh
3
254
User
Panjāb
3
255
User
Panjāb
3
257
User
Panjāb
3
258
User
Panjāb
3
259
User
Sindh
3
260
User
Panjāb
3
261
User
Sindh
3
264
User
Sindh
3
265
User
Sindh
3
266
User
Sindh
3
267
User
Islāmābād
3
268
User
Panjāb
3
269
Lovely
Sindh
3
270
User
Sindh
3
271
User
Sindh
3
272
User
Sindh
3
273
User
Sindh
3
274
User
Sindh
3
275
User
Sindh
3
276
User
Sindh
3
277
User
Sindh
3
278
User
Panjāb
3
279
User
Panjāb
3
280
User
Panjāb
3
281
User
Panjāb
3
282
User
Sindh
3
283
User
Sindh
3
284
User
Sindh
3
285
User
Sindh
3
286
User
Panjāb
3
287
User
Islāmābād
3
288
User
Sindh
3
289
User
Panjāb
3
290
User
Panjāb
3
291
User
Panjāb
3
292
User
Panjāb
3
293
User
Islāmābād
3
294
User
Sindh
3
295
User
Sindh
3
296
User
Sindh
3
297
User
Panjāb
3
298
User
Islāmābād
3
299
Ayesha Anwar
Region
3
300
User
Islāmābād
2
301
User
Sindh
2
302
User
Islāmābād
2
303
User
Sindh
2
304
User
Sindh
2
305
User
Sindh
2
306
User
Sindh
2
307
User
Islāmābād
2
308
User
Panjāb
2
309
User
Panjāb
2
310
User
Panjāb
2
311
User
Sindh
2
313
User
Panjāb
2
314
User
Panjāb
2
315
User
Islāmābād
2
316
User
Sindh
2
317
User
Sindh
2
318
User
Sindh
2
319
User
Sindh
2
320
User
Sindh
2
321
User
Sindh
2
322
User
Sindh
2
323
User
Sindh
2
324
User
Sindh
2
325
User
Sindh
2
326
User
Panjāb
2
327
User
Sindh
2
328
User
Sindh
2
329
User
Panjāb
2
330
User
Sindh
2
331
User
Sindh
2
333
User
Panjāb
2
334
User
Panjāb
2
335
User
Panjāb
2
336
User
Panjāb
2
337
User
Panjāb
2
338
User
Islāmābād
2
339
User
Panjāb
2
340
User
Sindh
2
341
User
Sindh
2
342
User
Sindh
2
343
User
Sindh
2
345
User
Panjāb
2
346
User
Sindh
2
347
User
Panjāb
2
348
User
Panjāb
2
349
User
Sindh
2
350
User
Sindh
2
351
User
Sindh
2
352
User
Panjāb
2
353
User
Sindh
2
354
User
Sindh
2
355
User
Islāmābād
2
356
User
Sindh
2
357
User
Balochistan
2
358
User
Sindh
2
359
User
Sindh
2
360
User
Sindh
2
361
User
Islāmābād
2
362
User
Sindh
2
363
User
Sindh
2
364
User
Sindh
2
365
User
Sindh
2
366
User
Sindh
2
367
User
Sindh
1
368
User
Islāmābād
1
369
User
Panjāb
1
370
User
Sindh
1
371
User
Sindh
1
372
User
Sindh
1
374
User
Sindh
1
375
User
Panjāb
1
376
User
Sindh
1
377
User
Sindh
1
378
User
Panjāb
1
379
User
Sindh
1
380
User
Sindh
1
381
User
Sindh
1
382
User
Sindh
1
383
User
Sindh
1
384
User
Islāmābād
1
385
User
Sindh
1
386
User
Panjāb
1
387
User
Panjāb
1
388
User
Sindh
1
389
User
Sindh
1
390
User
Sindh
1
391
Ali Shan
Sindh
1
392
User
Sindh
1
393
ajea zahid
Region
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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