Leaderboard
Indiana
Rank
Level
1
David Keen
Greenfield
91
2
Oleg Aprelikov
West Lafayette
85
3
Joseph Yu
West Lafayette
84
4
User
Indianapolis
77
5
User
Indianapolis
74
6
User
Whiting
64
7
User
West Lafayette
56
8
User
Carmel
52
9
User
Lebanon
52
10
User
Connersville
52
11
User
Brownsburg
52
12
User
Terre Haute
52
13
User
North Manchester
49
14
User
Winamac
46
15
Chloe McGuire
West Lafayette
45
16
User
North Manchester
45
17
User
North Manchester
45
18
User
Bloomington
44
19
User
North Manchester
42
20
User
Columbus
42
21
User
North Manchester
41
22
User
Bloomington
41
23
Buckeye fan
Carmel
40
24
User
Granger
39
25
User
Bloomington
39
26
User
West Lafayette
39
27
User
Carmel
38
28
User
West Lafayette
38
29
User
West Lafayette
37
30
User
Bloomington
37
31
User
West Lafayette
37
32
User
West Lafayette
36
33
User
Bloomington
36
34
User
West Lafayette
36
35
cherrsig
Indianapolis
35
36
User
Indianapolis
35
37
Kevin Lu
Bloomington
34
38
User
South Bend
33
39
User
West Lafayette
33
40
User
North Manchester
32
41
User
Bloomington
31
42
User
Notre Dame
31
43
Valerie Schultz
Fishers
30
44
User
West Lafayette
30
45
User
Indianapolis
30
46
User
Indianapolis
29
47
Will Hippe
Muncie
29
48
User
Bloomington
29
49
Allen Sayger
Bunker Hill
29
50
User
North Manchester
29
51
User
Terre Haute
28
52
User
Franklin
28
53
User
West Lafayette
28
54
Joshin Kumar
West Lafayette
27
55
User
Noblesville
27
56
User
Fort Wayne
27
57
B
Bloomington
27
58
User
Bloomington
27
59
User
Notre Dame
27
60
User
Avon
26
61
Barrett Schrock
Lebanon
26
62
User
Indianapolis
26
63
User
Indianapolis
26
64
User
Columbus
26
65
User
Indianapolis
26
66
User
Indianapolis
26
67
User
Valparaiso
25
68
User
Franklin
25
69
User
North Manchester
24
70
Maria
Munster
24
71
User
West Lafayette
23
72
User
Carmel
23
73
User
North Manchester
23
74
User
North Manchester
23
75
User
Carmel
23
76
User
West Lafayette
22
77
User
Indianapolis
22
78
User
Notre Dame
22
79
User
Fort Wayne
21
80
Nicholi
Westfield
21
81
User
Crown Point
21
82
User
La Porte
21
83
User
Indianapolis
21
84
User
North Manchester
21
85
User
Granger
21
86
User
Indianapolis
21
87
User
Notre Dame
21
88
Austin Bollinger
West Lafayette
21
89
User
Knightstown
21
90
Joe Wata
La Porte
20
91
User
Bloomington
20
92
User
Fishers
20
93
User
Plainfield
20
94
Calvin
Bloomington
19
95
User
Evansville
19
96
User
Bloomington
18
97
User
Goshen
18
98
User
Indianapolis
18
99
User
Mccordsville
18
100
User
Noblesville
17
101
User
Merrillville
17
102
User
Notre Dame
17
103
PPAL
Zionsville
17
104
User
North Manchester
17
105
User
Bloomington
17
106
User
North Manchester
17
107
User
Granger
17
108
User
Brazil
16
109
User
West Lafayette
16
110
User
West Lafayette
16
111
User
North Manchester
16
112
User
Schererville
16
113
User
Indianapolis
16
114
User
Carmel
15
115
User
North Manchester
15
116
User
Bloomington
15
117
User
Paoli
15
118
User
North Manchester
15
119
User
Granger
15
120
User
Bloomington
15
121
User
Indianapolis
14
122
Joshua Schrock
Lebanon
14
123
User
Culver
14
124
User
Fishers
14
125
User
Indianapolis
14
126
User
Union City
14
127
User
La Porte
13
128
User
Brownsburg
13
129
User
West Lafayette
13
130
User
Bloomington
13
131
User
Sheridan
13
132
User
Fishers
13
133
User
Bloomington
13
134
User
Bloomington
13
135
User
North Manchester
12
136
User
Franklin
12
137
User
North Manchester
12
138
User
North Manchester
12
139
User
Brazil
12
140
User
North Manchester
12
141
User
Indianapolis
12
142
User
Hammond
12
143
User
West Lafayette
12
144
User
Bloomington
12
145
User
Indianapolis
12
146
User
Fairland
11
147
User
Greenwood
11
148
User
Lebanon
11
149
User
North Manchester
11
150
User
North Manchester
11
151
User
Terre Haute
11
152
User
Indianapolis
11
153
User
Bloomington
11
154
Jaycie
Indianapolis
10
155
User
Franklin
10
156
User
Greenwood
10
157
User
Fort Wayne
10
158
User
Lebanon
10
159
User
Lawrence
10
160
Rayan Nasser
Bloomington
10
161
User
Terre Haute
10
162
User
North Manchester
10
163
User
North Manchester
10
164
User
North Manchester
10
165
User
Indianapolis
10
166
User
North Manchester
10
167
User
Bloomington
10
168
User
North Manchester
10
169
User
Bloomington
10
170
User
West Lafayette
10
171
User
Granger
10
172
User
Bloomington
9
173
User
Muncie
9
174
User
Notre Dame
9
175
Dan Gustafson
Indianapolis
9
176
User
Lebanon
9
177
User
North Manchester
9
178
User
Bloomington
9
179
User
Bloomington
9
180
User
North Manchester
9
181
User
North Manchester
9
182
User
Carmel
8
183
User
Indianapolis
8
184
User
North Manchester
8
185
User
Shelbyville
8
186
User
South Bend
8
187
User
Indianapolis
8
188
User
Sellersburg
8
189
User
North Manchester
8
190
User
South Bend
8
191
User
Indianapolis
8
192
User
Carmel
7
193
User
Marion
7
194
User
Middlebury
7
195
User
Valparaiso
7
196
User
Lebanon
7
197
User
Indianapolis
7
198
User
Indianapolis
7
199
User
Indianapolis
7
200
User
New Albany
7
201
User
North Manchester
7
202
User
South Bend
7
203
User
North Manchester
7
204
User
North Manchester
7
205
User
North Manchester
7
206
User
North Manchester
7
207
User
North Manchester
7
208
User
North Manchester
7
209
User
Ferdinand
7
210
User
Indianapolis
7
211
User
Lawrenceburg
7
212
Adeboye
Indianapolis
7
213
User
Bristol
6
214
User
West Lafayette
6
215
User
Fort Wayne
6
216
User
Greenwood
6
217
User
Advance
6
218
User
Indianapolis
6
219
User
Shelbyville
6
220
User
Carmel
6
221
User
West Lafayette
6
222
User
North Manchester
6
223
User
North Manchester
6
224
User
Crown Point
6
225
User
Notre Dame
6
226
User
Chandler
6
227
User
Bloomington
6
228
User
Shelbyville
6
229
User
North Manchester
6
230
User
North Manchester
6
231
User
North Manchester
6
232
User
North Manchester
6
233
User
Lakes Of The Four Seasons
6
234
User
Goshen
6
235
User
Indianapolis
6
236
User
North Manchester
6
237
User
North Manchester
6
238
User
North Manchester
6
239
User
Elkhart
6
240
User
Indianapolis
6
241
User
West Lafayette
5
242
User
South Bend
5
243
User
Bloomington
5
244
Anna Schrock
Lebanon
5
245
User
Warsaw
5
246
User
West Lafayette
5
247
User
North Manchester
5
248
User
West Lafayette
5
249
User
North Manchester
5
250
User
Crown Point
5
251
Nunya Buisness
Newburgh
5
252
User
North Manchester
5
253
User
North Manchester
5
254
User
Goshen
5
255
User
North Manchester
5
256
User
North Manchester
5
257
User
North Manchester
5
258
User
North Manchester
5
259
User
North Manchester
5
260
User
North Manchester
5
261
User
Poseyville
5
262
User
Shelbyville
4
263
User
Plymouth
4
264
User
Notre Dame
4
265
User
Hebron
4
266
User
Columbus
4
267
User
South Bend
4
268
User
North Manchester
4
269
Alec Burtner-Abt
Indianapolis
4
270
User
North Manchester
4
271
User
North Manchester
4
272
User
Indianapolis
4
273
User
Indianapolis
4
274
User
Indianapolis
4
275
User
Bloomington
4
276
User
Mishawaka
4
277
User
North Manchester
4
278
User
North Manchester
4
279
User
North Manchester
4
280
User
North Manchester
4
281
User
Zionsville
4
282
User
North Manchester
4
283
User
North Manchester
4
284
User
Carmel
4
285
User
West Lafayette
4
286
User
North Manchester
4
287
User
North Manchester
4
288
User
North Manchester
4
289
User
Columbus
4
290
User
North Manchester
4
291
User
North Manchester
4
292
User
Indianapolis
4
293
User
North Manchester
4
294
User
North Manchester
4
295
User
North Manchester
4
296
User
North Manchester
4
297
User
North Manchester
4
298
User
North Manchester
4
299
User
North Manchester
4
300
User
North Manchester
4
301
User
Elkhart
4
302
User
Plymouth
3
303
User
Highland
3
304
User
West Lafayette
3
305
User
Lebanon
3
306
User
North Manchester
3
307
User
West Lafayette
3
308
User
North Manchester
3
309
User
Carmel
3
310
User
North Manchester
3
311
User
North Manchester
3
312
User
North Manchester
3
313
User
North Manchester
3
314
User
North Manchester
3
315
User
North Manchester
3
316
Yasmin Owens
North Manchester
3
317
User
North Manchester
3
318
User
Washington
3
319
User
West Lafayette
3
320
User
Westfield
3
321
User
West Lafayette
3
322
User
Lafayette
3
323
User
Fort Wayne
3
324
User
Bloomington
3
325
User
Fishers
3
326
User
West Lafayette
3
327
User
Indianapolis
3
328
User
North Manchester
3
329
User
North Manchester
3
330
User
North Manchester
3
331
User
North Manchester
3
332
User
Munster
3
333
User
North Manchester
3
334
User
Hammond
3
335
User
North Manchester
3
336
Audra
Franklin
3
337
User
North Manchester
3
338
User
North Manchester
3
339
User
North Manchester
3
340
User
North Manchester
3
341
User
North Manchester
3
342
User
North Manchester
3
343
User
North Manchester
3
344
User
Portage
3
345
User
Warsaw
3
346
User
Hammond
3
347
User
Owensburg
2
348
User
Lebanon
2
349
User
Brownsburg
2
350
User
West Lafayette
2
351
User
Brownsburg
2
352
User
Muncie
2
353
Stephanie Garcia
Schererville
2
354
User
Notre Dame
2
355
User
Lebanon
2
356
User
Bloomington
2
357
User
North Manchester
2
358
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North Manchester
2
359
User
North Manchester
2
360
User
Charlestown
2
361
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North Manchester
2
362
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North Manchester
2
363
User
East Chicago
2
364
User
Fort Wayne
2
365
User
Bloomington
2
366
User
North Manchester
2
367
User
Fairbanks
2
368
User
Fort Wayne
2
369
User
Crawfordsville
2
370
User
North Manchester
2
371
User
North Manchester
2
372
User
Fishers
2
373
User
Noblesville
2
374
User
Fishers
2
375
User
North Manchester
2
376
User
North Manchester
2
377
User
North Manchester
2
378
User
North Manchester
2
379
User
North Manchester
2
380
User
North Manchester
2
381
User
North Manchester
2
382
User
Indianapolis
2
383
User
Indianapolis
2
384
User
North Manchester
2
385
User
North Manchester
2
386
User
North Manchester
2
387
User
Greenfield
2
388
User
North Manchester
2
389
User
North Manchester
2
390
User
North Manchester
2
391
User
North Manchester
2
392
User
North Manchester
2
393
User
North Manchester
2
394
User
North Manchester
2
395
User
North Manchester
2
396
User
North Manchester
2
397
User
North Manchester
2
398
User
North Manchester
2
399
User
North Manchester
2
400
User
North Manchester
2
401
User
Hammond
2
402
User
North Manchester
2
403
User
North Manchester
2
404
User
North Manchester
2
405
User
North Manchester
2
406
User
North Manchester
2
407
User
North Manchester
2
408
User
North Manchester
2
409
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North Manchester
2
410
User
North Manchester
2
411
User
North Manchester
2
412
User
North Manchester
2
413
User
North Manchester
2
414
User
North Manchester
2
415
User
North Manchester
2
416
User
North Manchester
2
417
User
North Manchester
2
418
User
West Lafayette
2
419
User
North Manchester
2
420
User
North Manchester
2
421
User
North Manchester
2
422
User
North Manchester
2
423
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North Manchester
2
424
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North Manchester
2
425
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North Manchester
2
426
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North Manchester
2
427
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North Manchester
2
428
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North Manchester
2
429
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North Manchester
2
430
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North Manchester
2
431
User
North Manchester
2
432
User
North Manchester
2
433
User
North Manchester
2
434
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North Manchester
2
435
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North Manchester
2
436
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North Manchester
2
437
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Indianapolis
2
438
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North Manchester
2
439
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Indianapolis
2
440
User
Indianapolis
1
441
User
Richmond
1
442
User
Indianapolis
1
443
User
Indianapolis
1
444
User
Plymouth
1
445
User
Kokomo
1
446
User
Crown Point
1
447
User
Lebanon
1
448
User
North Manchester
1
449
User
East Chicago
1
450
Alyssa Dunn
Indianapolis
1
451
User
Greenwood
1
452
User
Carmel
1
453
User
Indianapolis
1
454
User
Columbus
1
455
User
Moores Hill
1
456
User
Notre Dame
1
457
User
Bloomington
1
458
User
Crown Point
1
459
User
Indianapolis
1
460
User
Saint John
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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