Leaderboard
District of Columbia
District of Columbia
United States
Worldwide
Rank
Level
1
User
Washington
78
2
Andrew Wu
Washington
75
3
Bob Basmaji
Washington
67
4
User
Washington
62
5
User
Washington
53
6
User
Washington
53
7
User
Washington
49
8
User
Washington
43
9
User
Washington
42
10
User
Washington
41
11
User
Washington
40
12
User
Washington
40
13
User
Washington
39
14
User
Washington
39
15
User
Washington
35
16
User
Washington
35
17
User
Washington
35
18
User
Washington
34
19
User
Washington
34
20
User
Washington
34
21
User
Washington
33
22
User
Washington
33
23
Nikiforos Meletiadis
Washington
32
24
User
Washington
32
25
User
Washington
32
26
User
Washington
32
27
User
Washington
32
28
User
Washington
31
29
User
Washington
31
30
Phi Le
Washington
30
31
User
Washington
30
32
User
Washington
30
33
User
Washington
29
34
Elizabeth Sexton
Washington
29
35
User
Washington
29
36
Erica
Washington
29
37
User
Washington
29
38
User
Washington
28
39
User
Washington
28
40
Damini Satija
Washington
28
41
User
Washington
27
42
Robbie Skinner
Washington
27
43
User
Washington
27
44
User
Washington
26
45
User
Washington
26
46
User
Washington
26
47
User
Washington
26
48
User
Washington
26
49
Sogyel Lhungay
Washington
25
50
User
Washington
25
51
User
Washington
25
52
User
Washington
24
53
User
Washington
24
54
User
Washington
24
55
User
Washington
24
56
User
Washington
24
57
User
Washington
23
58
User
Washington
23
59
User
Washington
23
60
User
Washington
23
61
User
Washington
23
62
User
Washington
22
63
User
Washington
21
64
Jiles Alexander
Washington
21
65
User
Washington
21
66
User
Washington
21
67
User
Washington
21
68
User
City
20
69
User
Washington
20
70
User
Washington
20
71
User
Washington
20
72
User
City
19
73
User
Washington
19
74
User
Washington
19
75
Joshua Smith
Washington
19
76
User
Washington
19
77
User
Washington
19
78
User
Washington
18
79
User
Washington
18
80
User
Washington
18
81
User
Washington
18
82
User
Washington
18
83
User
Washington
18
84
User
Washington
17
85
User
Washington
17
86
User
Washington
16
87
User
Washington
16
88
User
Washington
16
89
User
Washington
16
90
User
Washington
16
91
User
Washington
16
92
User
Washington
16
93
Braydan Chmiel
Washington
16
94
User
Washington
15
95
User
Washington
15
96
User
Washington
15
97
User
Washington
15
98
User
City
15
99
User
Washington
15
100
User
Washington
15
101
User
Washington
15
102
User
Washington
15
103
User
Washington
15
104
User
Washington
14
105
User
Washington
14
106
User
Washington
14
107
User
Washington
14
108
User
Washington
14
109
User
Washington
14
110
User
Washington
14
111
User
Washington
14
112
User
Washington
13
113
User
Washington
13
114
Kaydin Jerome
Washington
13
115
User
Washington
13
116
User
Washington
13
117
User
Washington
13
118
User
Washington
13
119
User
Washington
12
120
User
Washington
12
121
User
Washington
12
122
User
Washington
12
123
User
Washington
12
124
Mick Bernstein
Washington
11
125
User
Washington
11
126
User
Washington
11
127
User
Washington
11
128
User
Washington
11
129
User
Washington
11
130
User
Washington
11
131
User
Washington
11
132
User
Washington
11
133
User
Washington
11
134
User
Washington
10
135
User
Washington
10
136
User
City
10
137
User
Washington
10
138
User
Washington
10
139
User
Washington
10
140
User
Washington
9
141
User
Washington
9
142
User
Washington
9
143
null
Washington
9
144
User
Washington
9
145
User
Washington
9
146
User
Washington
9
147
User
Washington
9
148
User
Washington
9
149
Josh Perez
Washington
9
150
User
Washington
9
151
User
Washington
9
152
User
Washington
9
153
User
Washington
9
154
User
Washington
9
155
User
Washington
8
156
User
Washington
8
157
User
Washington
8
158
User
Washington
8
159
User
Washington
8
160
User
Washington
8
161
User
Washington
8
162
User
Washington
8
163
User
Washington
8
164
User
Washington
8
165
User
Washington
8
166
User
Washington
8
167
User
Washington
8
168
Rhea Handa
Washington
8
169
User
Washington
8
170
Sebby
Washington
7
171
Di
Washington
7
172
User
Washington
7
173
User
Washington
7
174
User
Washington
7
175
User
Washington
7
176
User
Washington
7
177
User
Washington
7
178
User
Washington
7
179
User
Washington
7
180
User
Washington
7
181
User
Washington
6
182
User
Washington
6
183
User
Washington
6
184
User
Washington
6
185
User
Washington
6
186
User
Washington
6
187
User
Washington
6
188
User
Washington
6
189
User
Washington
6
190
User
Washington
6
191
User
Washington
6
192
User
Washington
6
193
User
Washington
6
194
User
Washington
6
195
User
Washington
6
196
User
Washington
6
197
User
Washington
5
198
User
Washington
5
199
User
Washington
5
200
User
Washington
5
201
User
Washington
5
202
Naomi
Washington
5
203
User
Washington
5
204
User
Washington
5
205
User
Washington
5
206
User
Washington
5
207
User
Washington
5
208
User
Washington
5
209
User
Washington
5
210
User
Washington
5
211
User
Washington
5
212
Molly Skipper
Washington
5
213
User
Washington
5
214
User
Washington
5
215
User
Washington
4
216
User
Washington
4
217
User
Washington
4
218
User
Washington
4
219
User
Washington
4
220
User
Washington
4
221
User
Washington
4
222
User
Washington
4
223
User
Washington
4
224
User
Washington
4
225
User
Washington
4
226
User
Washington
4
227
User
Washington
4
228
User
Washington
4
229
User
Washington
4
230
User
Washington
3
231
User
Washington
3
232
User
Washington
3
233
User
Washington
3
234
User
Washington
3
235
User
Washington
3
236
User
Washington
3
237
User
Washington
3
238
User
Washington
3
239
User
Washington
3
240
User
Washington
3
241
User
Washington
3
242
User
Washington
3
243
Gabriel Yates
City
3
244
User
Washington
3
245
User
Washington
3
246
User
Washington
3
247
User
Washington
3
248
User
Washington
3
249
User
Washington
3
250
User
Washington
3
251
User
Washington
3
252
User
Washington
2
253
User
Washington
2
254
User
Washington
2
255
User
Washington
2
256
User
Washington
2
257
User
Washington
2
258
User
Washington
2
259
User
Washington
2
260
User
Washington
2
261
User
Washington
2
262
User
Washington
2
263
User
Washington
2
264
User
City
2
265
User
Washington
2
266
User
Washington
2
267
User
Washington
2
268
User
Washington
2
269
User
Washington
2
270
User
Washington
2
271
User
Washington
2
272
User
Washington
2
273
User
Washington
2
274
User
Washington
2
275
User
Washington
2
276
User
Washington
2
277
User
Washington
2
278
User
Washington
2
279
User
Washington
2
280
User
Washington
2
281
User
Washington
2
282
User
Washington
2
283
User
Washington
2
284
User
Washington
2
285
User
Washington
2
286
User
Washington
2
287
User
Washington
2
288
User
Washington
1
289
User
Washington
1
290
User
Washington
1
291
User
Washington
1
292
User
Washington
1
293
User
Washington
1
294
User
Washington
1
295
User
Washington
1
296
User
Washington
1
297
User
Washington
1
298
User
Washington
1
299
Kaydin Gage
Washington
1
300
User
Washington
1
301
User
Washington
1
302
User
Washington
1
303
User
Washington
1
304
User
Washington
1
305
User
Washington
1
306
User
Washington
1
307
User
Washington
1
308
User
Washington
1
309
User
Washington
1
310
User
Washington
1
311
User
Washington
1
312
User
Washington
1
313
Null
Washington
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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