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Rank
Level
1
Seb
Salt Lake City
87
2
User
Salt Lake City
80
3
User
Salt Lake City
75
4
User
Salt Lake City
72
5
User
Salt Lake City
71
6
User
Salt Lake City
71
7
User
Salt Lake City
68
8
User
Salt Lake City
67
9
User
Salt Lake City
67
10
User
Salt Lake City
65
11
User
Salt Lake City
61
12
User
Salt Lake City
57
13
User
Salt Lake City
54
14
JD Hawkins
West Jordan
54
15
User
Salt Lake City
53
16
Niel Christensen
Provo
51
17
Skyler Olds
Salt Lake City
48
18
User
Provo
45
19
Tyson Barney
Provo
43
20
User
Salt Lake City
42
21
User
Provo
42
22
deaner
Salt Lake City
42
23
User
Layton
40
24
User
Salt Lake City
39
25
User
Salt Lake City
38
26
User
Salt Lake City
38
27
Leon Tran
West Valley City
37
28
User
Salt Lake City
37
29
User
Salt Lake City
37
30
User
Salt Lake City
36
31
ilovemath
Murray
36
32
User
Salt Lake City
34
33
Clayton Angell
Lehi
34
34
User
Salt Lake City
32
35
User
Salt Lake City
32
36
Kathleen Dao Garlick
Provo
31
37
Tun minn
Murray
30
38
User
Salt Lake City
30
39
User
Sandy
30
40
User
Salt Lake City
29
41
User
Sandy
29
42
User
Provo
27
43
User
Salt Lake City
27
44
User
Salt Lake City
27
45
Owen Maxfield
Sandy
27
46
User
Provo
27
47
User
West Jordan
25
48
User
West Jordan
25
49
User
Salt Lake City
25
50
User
Provo
25
51
User
Provo
25
52
User
Midvale
24
53
User
Lindon
24
54
Ryan Caplin
Orem
24
55
User
Provo
23
56
User
Clearfield
22
57
Kyle McBride
Provo
21
58
User
Ivins
21
59
p par
Salt Lake City
20
60
User
Provo
20
61
Jesse Hawkley
Taylorsville
19
62
Alan Zhao
Midvale
19
63
User
Salem
19
64
User
Midvale
18
65
User
Provo
18
66
User
Salt Lake City
18
67
Skyler Kirby
Sandy
17
68
User
Salt Lake City
17
69
User
Salt Lake City
17
70
User
Holladay
17
71
User
Tropic
17
72
User
West Valley City
16
73
Hayley
Salt Lake City
16
74
User
Riverton
16
75
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Cottonwood Heights
15
76
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Salt Lake City
15
77
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Huntsville
15
78
User
Provo
15
79
User
Provo
15
80
paul willams
Layton
14
81
User
Salt Lake City
14
82
User
Salt Lake City
13
83
Legit Puzzles
Clearfield
13
84
User
Bountiful
13
85
Silas King
Layton
13
86
User
North Salt Lake
13
87
Mitzi Vite
Taylorsville
13
88
User
Springville
12
89
User
Salt Lake City
12
90
Ben
Salt Lake City
11
91
BraeLynne Jensen
Cedar City
11
92
User
Layton
11
93
Jennifer Mai
West Valley City
11
94
User
Ephraim
11
95
User
Salt Lake City
11
96
User
Layton
11
97
User
Salt Lake City
10
98
User
Bountiful
10
99
User
Cottonwood Heights
10
100
Jj Pachev
Provo
10
101
User
Salt Lake City
10
102
User
West Valley City
9
103
User
Logan
9
104
User
St. George
9
105
User
Layton
9
106
User
Lehi
8
107
User
West Valley City
8
108
User
Clearfield
8
109
User
Clearfield
8
110
User
Salt Lake City
8
111
User
Salt Lake City
8
112
User
Kaysville
8
113
User
Salt Lake City
8
114
User
Salt Lake City
8
115
Marcus
Clearfield
8
116
User
Salt Lake City
7
117
User
Park City
7
118
User
Salt Lake City
7
119
User
Salt Lake City
7
120
TIFFANY ROSS-JENSEN
Draper
7
121
Carrie E. Gold
Salt Lake City
7
122
User
Layton
7
123
User
Salt Lake City
7
124
User
Cottonwood Heights
6
125
User
West Valley City
6
126
User
Layton
6
127
User
Eagle Mountain
6
128
User
Millcreek
6
129
User
Salt Lake City
6
130
User
Moab
6
131
User
Layton
6
132
User
Murray
6
133
User
West Valley City
6
134
User
Sandy
6
135
User
Layton
6
136
User
Murray
5
137
User
Clinton
5
138
User
Erda
5
139
User
Salt Lake City
5
140
User
Vernal
5
141
User
West Jordan
5
142
User
Salt Lake City
5
143
User
Salt Lake City
5
144
User
West Valley City
5
145
User
Riverton
5
146
User
Ogden
5
147
User
Salt Lake City
5
148
User
Clinton
5
149
User
Provo
5
150
User
Layton
5
151
User
West Valley City
5
152
User
Provo
4
153
User
Eagle Mountain
4
154
User
West Valley City
4
155
User
Salt Lake City
4
156
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South Jordan
4
157
Dana Kerr
Farr West
4
158
User
Park City
4
159
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Provo
4
160
User
Salt Lake City
4
161
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Salt Lake City
4
162
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Enoch
4
163
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St. George
4
164
User
Layton
4
165
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St. George
4
166
User
Layton
3
167
Tanner Fennemore
Bountiful
3
168
User
Heber City
3
169
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Salt Lake City
3
170
Kadon Dabel
Layton
3
171
User
Clearfield
3
172
User
Heber City
3
173
User
Cottonwood Heights
3
174
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Provo
3
175
User
Provo
3
176
User
Layton
3
177
User
Salt Lake City
3
178
User
West Valley City
3
179
User
Sandy
3
180
User
Provo
3
181
User
Lehi
3
182
User
West Valley City
3
183
User
Layton
3
184
User
Lehi
3
185
User
Sandy
3
186
User
West Jordan
3
187
User
Layton
2
188
User
South Jordan
2
189
Abel Beland
Logan
2
190
User
Bountiful
2
191
User
Bountiful
2
192
User
Layton
2
193
User
Orem
2
194
User
Salt Lake City
2
195
User
Salt Lake City
2
196
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Vineyard
2
197
User
Midvale
2
198
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Lehi
2
199
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Clearfield
2
200
User
West Valley City
2
201
User
Salt Lake City
2
202
User
Salt Lake City
2
203
Kalina
Salt Lake City
2
204
Distracted Cloud
Payson
2
205
User
Salt Lake City
2
206
User
Layton
2
207
User
Bountiful
2
208
User
Salt Lake City
2
209
User
Millcreek
2
210
User
Provo
1
211
User
Kaysville
1
212
User
Heber City
1
213
Jimmy Kudo
Murray
1
214
User
Clinton
1
215
User
Provo
1
216
User
Salt Lake City
1
217
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Smithfield
1
218
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Pleasant Grove
1
219
User
West Valley City
1
220
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Lehi
1
221
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Ogden
1
222
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Provo
1
223
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Lehi
1
224
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Highland
1
225
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West Valley City
1
226
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Provo
1
227
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West Valley City
1
228
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Salt Lake City
1
229
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West Valley City
1
230
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Salt Lake City
1
231
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Salt Lake City
1
232
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East Millcreek
1
233
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Layton
1
234
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Layton
1
235
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Clearfield
1
236
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Layton
1
237
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Lehi
1
238
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Lehi
1
239
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Lehi
1
240
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Lehi
1
241
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Lehi
1
242
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Lehi
1
243
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Lehi
1
244
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Lehi
1
245
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Provo
1
246
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Taylorsville
1
247
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Clearfield
1
248
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Clearfield
1
249
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Clearfield
1
250
User
St. George
1
251
User
Enoch
1
252
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Salt Lake City
1
253
User
South Jordan
1
254
User
Taylorsville
1
255
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Taylorsville
1
256
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Riverton
1
257
User
Logan
1
258
User
West Valley City
1
259
User
Lehi
1
260
User
West Valley City
1
261
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West Valley City
1
262
User
West Valley City
1
263
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Lehi
1
264
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Salt Lake City
1
265
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West Valley City
1
266
User
Kaysville
1
267
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Salt Lake City
1
268
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West Valley City
1
269
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Ogden
1
270
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Salt Lake City
1
271
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West Valley City
1
272
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Salt Lake City
1
273
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Tooele
1
274
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Salt Lake City
1
275
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West Valley City
1
276
Deepak Reddy Sama
Lehi
1
277
User
Salt Lake City
1
278
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Lehi
1
279
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Lehi
1
280
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Lehi
1
281
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Lehi
1
282
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Lehi
1
283
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Lehi
1
284
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Lehi
1
285
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Lehi
1
286
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Lehi
1
287
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Lehi
1
288
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Lehi
1
289
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Lehi
1
290
User
Lehi
1
291
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Lehi
1
292
User
Lehi
1
293
User
Lehi
1
294
User
Lehi
1
295
User
Lehi
1
296
User
Lehi
1
297
User
Lehi
1
298
User
Lehi
1
299
User
Lehi
1
300
User
Lehi
1
301
User
Lehi
1
302
User
Lehi
1
303
User
Lehi
1
304
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Saratoga Springs
1
305
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South Jordan
1
306
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Salt Lake City
1
307
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Manti
1
308
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Layton
1
309
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Salt Lake City
1
310
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Layton
1
311
User
West Valley City
1
312
User
Draper
1
313
User
Salt Lake City
1
314
User
Sandy
1
315
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 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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