Leaderboard
Maryland
Rank
Level
1
Sawyer West
Saint Marys City
95
2
User
Saint Marys City
94
3
User
Baltimore
83
4
User
Saint Marys City
73
5
Sheikh Selim
Baltimore
64
6
Akash Marakath
Columbia
63
7
User
Greenbelt
62
8
User
Saint Marys City
61
9
User
City
58
10
Alexander Paskal
College Park
55
11
akansha sehgal
Baltimore
53
12
User
College Park
51
13
User
La Vale
50
14
User
Saint Marys City
50
15
User
College Park
49
16
Lane Martin
Monkton
47
17
User
Baltimore
47
18
Micheal Erb
Gaithersburg
45
19
User
Baltimore
45
20
User
Severn
44
21
User
Elkridge
43
22
Matthew Lee
Gaithersburg
43
23
User
Frederick
40
24
User
College Park
40
25
Nathan Mozden
Silver Spring
39
26
Ceca
Greenbelt
39
27
User
Annapolis
39
28
User
Baltimore
38
29
User
College Park
37
30
Raghavendra Murthi
Bethesda
37
31
YUNTK
College Park
35
32
User
Baltimore
35
33
User
Olney
34
34
Momma G
Cape Saint Claire
33
35
User
Columbia
33
36
User
Ellicott City
33
37
User
College Park
32
38
User
Fort Meade
32
39
User
Fort Washington
32
40
User
Gaithersburg
32
41
Jesus c
Severn
31
42
User
Ellicott City
31
43
User
Baltimore
31
44
User
Severn
31
45
User
Baltimore
31
46
User
Ellicott City
31
47
User
Ellicott City
30
48
User
Rockville
30
49
User
Baltimore
30
50
User
Rockville
29
51
User
Hyattsville
28
52
User
Baltimore
28
53
User
College Park
28
54
Kaitlyn Sharo
Severn
28
55
Cole Dwiggins
Glenwood
27
56
Frank Imoehl
Rockville
27
57
User
Gaithersburg
27
58
User
College Park
27
59
User
North Bethesda
26
60
User
Ocean Pines
26
61
User
Grantsville
26
62
User
Baltimore
26
63
User
Germantown
26
64
User
Baltimore
26
65
User
Baltimore
25
66
User
College Park
24
67
TheGr8TJ
Takoma Park
24
68
User
Baltimore
24
69
User
Bethesda
24
70
User
Catonsville
23
71
User
Elkton
23
72
User
Parole
23
73
User
Baltimore
23
74
User
College Park
23
75
User
Baltimore
23
76
User
Rockville
22
77
User
College Park
22
78
User
Silver Spring
22
79
User
Bethesda
22
80
User
Baltimore
22
81
Rebecca Huynh
Owings Mills
22
82
User
Beltsville
22
83
User
Baltimore
22
84
User
Baltimore
21
85
User
Crofton
21
86
User
Bethesda
21
87
User
Montgomery Village
21
88
User
Taneytown
21
89
User
College Park
21
90
User
Potomac
20
91
User
Ellicott City
20
92
User
Takoma Park
20
93
User
Silver Spring
20
94
Hunter Rice
Annapolis
19
95
User
Reisterstown
19
96
TheGr8TJ
Takoma Park
19
97
User
Baltimore
19
98
User
Sykesville
19
99
User
Baltimore
18
100
User
Columbia
18
101
User
Baltimore
18
102
Taurian Gibson-Gardner
Takoma Park
18
103
User
Bethesda
18
104
sassy
Silver Spring
18
105
User
Takoma Park
18
106
User
Takoma Park
18
107
User
Bethesda
18
108
User
Gaithersburg
18
109
James Blaser
Saint Marys City
18
110
Berkeley Poulsen
College Park
18
111
User
Hyattsville
18
112
User
Severna Park
18
113
User
Rockville
18
114
User
Ellicott City
18
115
Somto Nweke
Baltimore
17
116
User
Baltimore
17
117
User
Bethesda
17
118
Safwan Sheikh
Baltimore
17
119
User
Olney
17
120
User
Bethesda
17
121
User
Fairland
16
122
User
Owings Mills
16
123
User
Silver Spring
16
124
User
Urbana
16
125
User
College Park
16
126
User
Owings Mills
16
127
User
College Park
15
128
User
Rockville
15
129
User
Severn
15
130
User
College Park
15
131
User
Pikesville
15
132
Fernando Lopez Torres
Takoma Park
15
133
User
Takoma Park
15
134
User
Takoma Park
15
135
User
Takoma Park
15
136
User
Takoma Park
15
137
User
Catonsville
15
138
User
Towson
15
139
User
Baltimore
15
140
User
Germantown
15
141
User
Bethesda
15
142
User
Upper Marlboro
14
143
User
Takoma Park
14
144
User
Takoma Park
14
145
User
Beltsville
14
146
User
Gaithersburg
14
147
User
Gaithersburg
14
148
User
Glen Burnie
14
149
User
Rockville
14
150
User
Ellicott City
14
151
User
Columbia
13
152
Adi Renduchintala
Baltimore
13
153
User
Glenelg
13
154
Mauricio Apolinar Alberto
Takoma Park
13
155
User
Takoma Park
13
156
Syco
Takoma Park
13
157
User
Gaithersburg
13
158
User
Ellicott City
13
159
User
Bowleys Quarters
13
160
User
Potomac
13
161
User
Rockville
13
162
User
Columbia
12
163
User
Columbia
12
164
JSB
Bethesda
12
165
User
Baltimore
12
166
User
Columbia
12
167
User
Germantown
12
168
User
Takoma Park
12
169
User
Pasadena
12
170
User
Parkville
12
171
User
Rockville
12
172
User
Olney
12
173
User
East Riverdale
12
174
User
Catonsville
12
175
User
Germantown
11
176
User
Fort Meade
11
177
User
Rockville
11
178
Benedict Wills
Annapolis
11
179
User
Takoma Park
11
180
Miriam Ortiz Gonzalez
Takoma Park
11
181
User
Catonsville
11
182
User
Wheaton-Glenmont
11
183
User
Columbia
11
184
User
Bethesda
11
185
User
College Park
11
186
User
Rockville
10
187
User
Takoma Park
10
188
User
Takoma Park
10
189
User
Takoma Park
10
190
User
Baltimore
10
191
User
Hyattsville
10
192
User
Montgomery Village
10
193
User
Baltimore
10
194
Matheus Mendes
Catonsville
10
195
User
Rockville
10
196
User
Bel Air
9
197
User
Edgewood
9
198
User
Silver Spring
9
199
User
Ashton-Sandy Spring
9
200
Dha
Owings Mills
9
201
User
Severn
9
202
User
Takoma Park
9
203
User
Baltimore
9
204
User
Takoma Park
9
205
User
Potomac
9
206
User
Bethesda
9
207
User
College Park
9
208
User
Gaithersburg
9
209
User
Lutherville-Timonium
9
210
User
Baltimore
9
211
User
Rockville
9
212
User
Fort Washington
8
213
User
Hollywood
8
214
User
College Park
8
215
User
Columbia
8
216
User
Rockville
8
217
User
Takoma Park
8
218
User
Gaithersburg
8
219
User
Takoma Park
8
220
User
Takoma Park
8
221
User
Edgewood
8
222
User
Bethesda
8
223
Katie
Baltimore
8
224
User
Bethesda
8
225
User
Fort Washington
7
226
User
Urbana
7
227
User
Rockville
7
228
User
Bethesda
7
229
User
Fort Washington
7
230
User
Gaithersburg
7
231
User
Takoma Park
7
232
User
Takoma Park
7
233
User
Takoma Park
7
234
User
Takoma Park
7
235
User
Takoma Park
7
236
User
Takoma Park
7
237
User
Takoma Park
7
238
User
Gaithersburg
7
239
User
Parkton
7
240
User
North Bethesda
7
241
User
Towson
7
242
User
Owings Mills
7
243
User
Ellicott City
7
244
User
Towson
7
245
User
Reisterstown
7
246
User
College Park
7
247
User
Germantown
7
248
User
Columbia
7
249
User
Bowie
6
250
User
Rockville
6
251
User
Carney
6
252
User
Rockville
6
253
User
Baltimore
6
254
Sierra Reid
Towson
6
255
User
Catonsville
6
256
User
Potomac
6
257
User
Arnold
6
258
User
Baltimore
6
259
User
Takoma Park
6
260
User
Takoma Park
6
261
User
Takoma Park
6
262
User
Takoma Park
6
263
User
Takoma Park
6
264
User
Takoma Park
6
265
User
Takoma Park
6
266
User
Bethesda
6
267
User
Baltimore
6
268
User
Gaithersburg
6
269
User
Rockville
6
270
User
Baltimore
6
271
User
Ellicott City
6
272
User
Bethesda
6
273
User
Westminster
5
274
User
Baltimore
5
275
LifeKnight
Bowie
5
276
User
Fairland
5
277
User
Severna Park
5
278
User
Saint Marys City
5
279
User
Takoma Park
5
280
David Cerna Martir
Takoma Park
5
281
User
Annapolis
5
282
User
Takoma Park
5
283
Eleshady Gebreyohannes
Takoma Park
5
284
User
Takoma Park
5
285
User
Takoma Park
5
286
User
Takoma Park
5
287
User
Takoma Park
5
288
User
Takoma Park
5
289
User
Takoma Park
5
290
User
Takoma Park
5
291
User
Takoma Park
5
292
Ariel Dickison
Takoma Park
5
293
User
Rockville
5
294
User
Takoma Park
5
295
User
Takoma Park
5
296
User
Takoma Park
5
297
User
Owings Mills
5
298
Cristina Tous
College Park
5
299
User
Catonsville
5
300
User
Travilah
4
301
User
Montgomery Village
4
302
User
College Park
4
303
User
Bethesda
4
304
User
Perry Hall
4
305
User
Catonsville
4
306
User
Baltimore
4
307
User
South Laurel
4
308
User
Hagerstown
4
309
User
Baltimore
4
310
User
Severna Park
4
311
User
Glenelg
4
312
User
Annapolis
4
313
User
Takoma Park
4
314
User
Takoma Park
4
315
User
Takoma Park
4
316
User
Takoma Park
4
317
User
Takoma Park
4
318
User
Takoma Park
4
319
User
Takoma Park
4
320
User
Takoma Park
4
321
User
Takoma Park
4
322
User
Takoma Park
4
323
User
Takoma Park
4
324
User
Fort Washington
4
325
User
Reisterstown
4
326
User
Bethesda
4
327
User
Middle River
4
328
User
Edgewood
4
329
User
Bel Air North
4
330
User
Potomac
4
331
User
Bethesda
4
332
User
Frederick
4
333
User
Rockville
4
334
User
Baltimore
4
335
User
Ellicott City
3
336
User
Dundalk
3
337
User
Lutherville-Timonium
3
338
User
Laurel
3
339
User
Parkville
3
340
User
Baltimore
3
341
User
College Park
3
342
User
Cumberland
3
343
User
Hanover
3
344
User
Owings Mills
3
345
User
Baltimore
3
346
User
Upper Marlboro
3
347
User
Takoma Park
3
348
User
Takoma Park
3
349
User
Takoma Park
3
350
User
Takoma Park
3
351
User
Reisterstown
3
352
User
Saint Marys City
3
353
User
Baltimore
3
354
User
Takoma Park
3
355
User
Takoma Park
3
356
Amate Ayivi Koutodjo
Takoma Park
3
357
User
Takoma Park
3
358
User
Takoma Park
3
359
Ozy Silverstone
Takoma Park
3
360
User
Takoma Park
3
361
User
Takoma Park
3
362
User
Takoma Park
3
363
User
Takoma Park
3
364
Ranashia
Takoma Park
3
365
User
Takoma Park
3
366
User
Takoma Park
3
367
User
Takoma Park
3
368
User
Takoma Park
3
369
User
Takoma Park
3
370
User
Takoma Park
3
371
User
Takoma Park
3
372
User
Baltimore
3
373
User
Edgewood
3
374
User
Bowie
3
375
User
Rockville
3
376
User
Columbia
3
377
User
Glen Arm
3
378
User
Crofton
3
379
User
Montgomery Village
3
380
User
Prince GeorgeS County
3
381
User
Rockville
3
382
User
Beltsville
3
383
User
Potomac
3
384
User
Rockville
3
385
User
Olney
3
386
User
Gaithersburg
3
387
User
Ballenger Creek
2
388
User
Bel Air
2
389
User
Largo
2
390
User
Severna Park
2
391
User
Glenwood
2
392
User
Rockville
2
393
User
Rockville
2
394
User
Bethesda
2
395
User
Catonsville
2
396
User
Rockville
2
397
User
Sparks Glencoe
2
398
Matthew Lee
Gaithersburg
2
399
User
Stevensville
2
400
User
Clarksville
2
401
Toddy Ison
Gaithersburg
2
402
User
Baltimore
2
403
User
Bethesda
2
404
User
Baltimore
2
405
Lane Martin
Lutherville-Timonium
2
406
User
Takoma Park
2
407
User
North Laurel
2
408
User
North Bethesda
2
409
Elijah Peaks
Takoma Park
2
410
User
Takoma Park
2
411
User
Takoma Park
2
412
User
Takoma Park
2
413
User
Takoma Park
2
414
User
Takoma Park
2
415
User
Takoma Park
2
416
User
Takoma Park
2
417
User
Takoma Park
2
418
User
Takoma Park
2
419
User
Takoma Park
2
420
User
Takoma Park
2
421
User
Takoma Park
2
422
User
Takoma Park
2
423
User
Takoma Park
2
424
User
Takoma Park
2
425
User
Takoma Park
2
426
User
Silver Spring
2
427
User
Fairland
2
428
User
Takoma Park
2
429
User
Takoma Park
2
430
User
Takoma Park
2
431
User
Takoma Park
2
432
User
Takoma Park
2
433
User
Takoma Park
2
434
User
Takoma Park
2
435
User
Takoma Park
2
436
User
Takoma Park
2
437
User
Takoma Park
2
438
User
Takoma Park
2
439
User
Takoma Park
2
440
User
Takoma Park
2
441
User
Takoma Park
2
442
User
Towson
2
443
User
Takoma Park
2
444
User
Takoma Park
2
445
Gary Einhorn
Takoma Park
2
446
User
Aspen Hill
2
447
User
Aberdeen
2
448
User
Edgewood
2
449
User
Gaithersburg
2
450
User
Gaithersburg
2
451
User
Columbia
2
452
User
Damascus
2
453
User
Elkridge
2
454
User
North Bethesda
2
455
User
Bowie
2
456
User
Oxon Hill-Glassmanor
2
457
User
Germantown
2
458
User
Hyattsville
2
459
User
Wheaton-Glenmont
2
460
User
Savage
2
461
User
Fort Washington
2
462
Jessica Stouffer
Rockville
2
463
User
Beltsville
2
464
User
Silver Spring
2
465
User
Columbia
2
466
User
Cockeysville
2
467
User
South Laurel
2
468
User
Baltimore
2
469
User
Linthicum Heights
2
470
User
Columbia
2
471
User
Bethesda
2
472
User
Columbia
2
473
User
College Park
2
474
User
Hyattsville
2
475
User
Rockville
2
476
User
Rockville
1
477
User
Rockville
1
478
User
Rockville
1
479
User
Rockville
1
480
User
Rockville
1
481
User
Rockville
1
482
User
Potomac
1
483
User
Rockville
1
484
User
Rockville
1
485
User
Rockville
1
486
User
Rockville
1
487
User
Aspen Hill
1
488
User
Rockville
1
489
User
Rockville
1
490
User
Baltimore
1
491
User
Rockville
1
492
User
Rockville
1
493
User
Rockville
1
494
User
Rockville
1
495
User
Rockville
1
496
User
Rockville
1
497
User
Rockville
1
498
User
Rockville
1
499
User
Rockville
1
500
User
Rockville
1
501
User
Potomac
1
502
User
Rockville
1
503
User
Rockville
1
504
User
Owings Mills
1
505
User
Rockville
1
506
User
Rockville
1
507
User
Rockville
1
508
User
Rockville
1
509
User
Rockville
1
510
User
Rockville
1
511
User
Rockville
1
512
User
Baltimore
1
513
User
Leonardtown
1
514
User
Upper Marlboro
1
515
User
Bowie
1
516
User
Baltimore
1
517
User
Chevy Chase
1
518
User
Baltimore
1
519
User
Pikesville
1
520
User
Baltimore
1
521
User
Baltimore
1
522
User
Green Valley
1
523
User
Greenbelt
1
524
User
Clarksburg
1
525
User
Stevensville
1
526
User
Baltimore
1
527
User
Greenbelt
1
528
User
Seabrook
1
529
User
Bethesda
1
530
User
Gaithersburg
1
531
User
Linganore-Bartonsville
1
532
User
Essex
1
533
User
Germantown
1
534
User
Silver Spring
1
535
Hayden Cookson
Takoma Park
1
536
Pamela Silva
Takoma Park
1
537
Carlos Winston
Owings Mills
1

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A Web App for Mathematics Training

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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
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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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