Leaderboard
Utah
Rank
Level
1
Tyson Barney
Provo
92
2
User
Provo
76
3
User
Midvale
74
4
User
Provo
59
5
User
Holladay
57
6
User
West Jordan
55
7
User
Provo
53
8
User
Midvale
53
9
Clayton Angell
Lehi
52
10
User
Clearfield
47
11
User
Provo
46
12
Tun minn
Murray
45
13
Ryan Caplin
Orem
45
14
Ben
Salt Lake City
40
15
Alan Zhao
Midvale
37
16
User
North Salt Lake
37
17
User
Provo
36
18
Kyle McBride
Provo
34
19
User
Huntsville
34
20
User
Bountiful
34
21
User
Ogden
34
22
User
Salt Lake City
33
23
User
Tropic
31
24
Legit Puzzles
Clearfield
29
25
User
Clearfield
26
26
paul willams
Layton
25
27
Silas King
Layton
25
28
User
Layton
24
29
Derek Schetselaar
Provo
24
30
User
Orem
24
31
Matt Wattendorf
Salt Lake City
24
32
User
Provo
23
33
User
Layton
22
34
User
Salt Lake City
21
35
User
Layton
21
36
User
Salt Lake City
21
37
User
West Valley City
21
38
User
Ephraim
20
39
User
Bountiful
20
40
User
Salt Lake City
20
41
BraeLynne Jensen
Cedar City
19
42
User
Provo
19
43
Jj Pachev
Provo
18
44
User
West Valley City
18
45
User
Kaysville
18
46
JD Hawkins
Salt Lake City
17
47
User
Layton
17
48
User
Lehi
17
49
User
Clearfield
17
50
User
Salt Lake City
17
51
User
West Valley City
17
52
User
Salt Lake City
17
53
User
Layton
17
54
User
Salt Lake City
17
55
User
Erda
16
56
User
Riverton
16
57
User
Logan
15
58
Marcus
Clearfield
15
59
User
Cottonwood Heights
15
60
User
Salt Lake City
15
61
User
Salt Lake City
15
62
User
Clearfield
14
63
User
Salt Lake City
14
64
User
Layton
14
65
User
Bountiful
14
66
User
Park City
13
67
User
Salt Lake City
13
68
Carrie E. Gold
Salt Lake City
13
69
User
Eagle Mountain
13
70
User
Layton
13
71
User
Providence
13
72
User
West Valley City
12
73
User
Layton
11
74
User
Sandy
11
75
User
Vernal
11
76
User
Spanish Fork
11
77
User
Salt Lake City
10
78
User
Millcreek
10
79
User
Layton
10
80
User
Murray
10
81
User
West Valley City
10
82
User
Kamas
10
83
User
Layton
9
84
User
Murray
9
85
User
West Valley City
9
86
User
Enoch
9
87
User
Sandy
9
88
User
Layton
8
89
User
Saratoga Springs
8
90
User
Salt Lake City
8
91
User
Provo
8
92
User
West Jordan
8
93
User
West Jordan
7
94
User
Salt Lake City
7
95
User
West Valley City
7
96
User
Ogden
7
97
User
South Jordan
7
98
Dana Kerr
Farr West
7
99
User
Salt Lake City
7
100
User
Cottonwood Heights
7
101
User
Provo
7
102
User
Riverton
7
103
User
Park City
6
104
User
Provo
6
105
User
Salt Lake City
6
106
User
Layton
6
107
User
Layton
6
108
Tanner Fennemore
Bountiful
6
109
User
Heber City
6
110
User
Salt Lake City
6
111
User
West Valley City
6
112
User
Sandy
6
113
User
Lehi
6
114
User
West Valley City
6
115
User
Lehi
6
116
User
Sandy
6
117
User
West Jordan
6
118
User
St. George
5
119
Kadon Dabel
Layton
5
120
User
Clearfield
5
121
User
Heber City
5
122
User
Provo
5
123
User
Layton
5
124
Abel Beland
Logan
5
125
User
Vineyard
5
126
User
Lehi
5
127
User
Layton
4
128
User
Bountiful
4
129
User
Orem
4
130
User
Midvale
4
131
User
West Valley City
4
132
User
Lehi
4
133
User
Lehi
4
134
User
Highland
4
135
User
Provo
4
136
User
Salt Lake City
4
137
User
Salt Lake City
3
138
Kalina
Salt Lake City
3
139
Jimmy Kudo
Murray
3
140
User
Provo
3
141
User
Pleasant Grove
3
142
User
West Valley City
3
143
User
West Valley City
3
144
User
West Valley City
3
145
User
Salt Lake City
3
146
User
West Valley City
3
147
User
East Millcreek
3
148
User
Lehi
3
149
User
Lehi
3
150
User
Lehi
3
151
User
Lehi
3
152
User
Lehi
3
153
User
Lehi
3
154
User
Lehi
3
155
User
Lehi
3
156
User
Provo
3
157
User
Enoch
3
158
User
South Jordan
3
159
User
Salt Lake City
2
160
User
Salt Lake City
2
161
User
Clearfield
2
162
User
Layton
2
163
User
Layton
2
164
User
Layton
2
165
User
Taylorsville
2
166
User
Clearfield
2
167
User
Clearfield
2
168
User
Clearfield
2
169
User
Taylorsville
2
170
User
Taylorsville
2
171
User
West Valley City
2
172
User
West Valley City
2
173
User
West Valley City
2
174
User
West Valley City
2
175
User
West Valley City
2
176
User
Salt Lake City
2
177
User
West Valley City
2
178
User
West Valley City
2
179
User
West Valley City
2
180
User
Lehi
2
181
User
Lehi
2
182
User
Lehi
2
183
User
Lehi
2
184
User
Lehi
2
185
User
Lehi
2
186
User
Lehi
2
187
User
Lehi
2
188
User
Lehi
2
189
User
Lehi
2
190
User
Lehi
2
191
User
Lehi
2
192
User
Lehi
2
193
User
Lehi
2
194
User
Lehi
2
195
User
Lehi
2
196
User
Lehi
2
197
User
Lehi
2
198
User
Lehi
2
199
User
Lehi
2
200
User
Lehi
2
201
User
Lehi
2
202
User
Lehi
2
203
User
Lehi
2
204
User
Lehi
2
205
User
Lehi
2
206
User
South Jordan
2
207
User
Salt Lake City
2
208
User
Manti
2
209
User
Salt Lake City
2
210
User
Sandy
2
211
User
Kanab
2
212
User
South Jordan
2
213
User
Salt Lake City
2
214
User
Layton
1
215
User
Salt Lake City
1
216
User
Layton
1
217
User
West Valley City
1
218
User
Draper
1
219
User
Salt Lake City
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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