Leaderboard
Malaysia
Malaysia
Worldwide
Rank
Level
2
ongzz
Johor
77
5
User
Selangor
75
6
User
Selangor
75
8
Hayley
Selangor
73
10
User
Sarawak
72
11
User
Selangor
71
12
User
Selangor
70
13
User
Johor
67
15
User
Selangor
64
17
User
Terengganu
62
19
User
Kedah
58
22
kepler
Johor
57
23
Singapore Math Academy
Wilayah Persekutuan Kuala Lumpur
57
26
User
Selangor
56
27
Bryan Lean
Perak
56
28
User
Selangor
55
30
Bryan Gan
Selangor
54
32
User
Selangor
49
33
User
Kedah
48
34
hewhew
Johor
46
41
Muhammad Ammar
Selangor
43
42
User
Selangor
43
43
User
Pulau Pinang
42
48
User
Selangor
38
50
User
Selangor
37
53
User
Selangor
37
56
User
Selangor
36
59
User
Selangor
34
60
User
Sarawak
34
62
User
Pulau Pinang
33
63
Teik seam
Selangor
32
65
User
Pulau Pinang
31
66
User
Selangor
30
69
User
Selangor
30
70
User
Selangor
30
72
User
Selangor
29
73
User
Selangor
29
74
User
Selangor
29
75
User
Selangor
29
76
Kear Kyii Wong
Selangor
29
78
Kelly Chin KW
Selangor
28
79
User
Selangor
28
80
User
Selangor
27
81
User
Selangor
27
85
okay
Selangor
26
87
User
Selangor
26
88
Nikolas Adiprasetya
Selangor
26
89
User
Selangor
26
90
User
Pahang
26
92
User
Selangor
25
93
User
Kedah
24
96
User
Selangor
24
97
Sze Jia
Selangor
24
98
User
Selangor
23
99
JaclynY
Perak
23
100
User
Selangor
23
101
Mr. Wave
Pahang
23
102
User
Selangor
23
104
User
Selangor
22
106
User
Selangor
22
107
User
Selangor
22
108
erik sonny
Kelantan
22
109
User
Johor
22
112
User
Selangor
21
117
User
Selangor
21
118
User
Selangor
20
119
User
Johor
20
120
User
Selangor
20
122
User
Selangor
20
126
User
Johor
19
127
User
Selangor
19
129
User
Selangor
19
134
User
Selangor
18
135
User
Selangor
18
136
User
Perlis
18
137
User
Selangor
18
146
User
Sarawak
17
147
User
Johor
17
148
ELYN TAN
Selangor
17
149
User
Selangor
17
151
User
Selangor
16
152
User
Johor
16
154
Suyinn Lee
Selangor
16
156
User
Selangor
16
159
User
Johor
16
160
User
Sabah
16
161
Isaac Lim
Selangor
16
162
Rio Fukuda
Pulau Pinang
16
164
User
Selangor
16
168
User
Selangor
15
169
User
Selangor
15
170
User
Selangor
15
171
User
Selangor
15
172
User
Selangor
15
173
User
Selangor
15
174
NanoNanoNano
Selangor
15
175
Sindhu Rajendran@vejendran
Selangor
15
177
User
Selangor
14
178
Ng yinzhi
Selangor
14
179
User
Selangor
14
183
User
Selangor
14
185
User
Selangor
14
186
User
Selangor
14
187
User
Selangor
14
190
User
Johor
14
191
User
Selangor
14
192
Matthew Ong
Johor
14
194
User
Selangor
13
196
User
Selangor
13
197
User
Pahang
13
199
User
Selangor
13
201
User
Selangor
13
202
User
Selangor
13
204
User
Selangor
13
206
User
Selangor
13
211
User
Pahang
13
213
User
Selangor
13
214
User
Pahang
13
215
User
Pahang
12
216
User
Selangor
12
217
User
Selangor
12
218
User
Pahang
12
220
User
Selangor
12
222
User
Selangor
12
223
User
Selangor
12
226
User
Selangor
12
229
User
Selangor
12
230
User
Selangor
12
232
Nishita Deverapalli
Sabah
12
233
User
Selangor
12
234
User
Pahang
12
235
User
Pahang
12
236
User
Johor
11
238
User
Selangor
11
241
User
Selangor
11
242
User
Sarawak
11
243
User
Sarawak
11
244
User
Johor
11
246
User
Selangor
11
247
Bryan SymTdm MC
Sabah
11
250
User
Perak
11
252
User
Selangor
11
254
User
Selangor
11
255
User
Sarawak
11
258
User
Melaka
10
261
User
Selangor
10
262
User
Selangor
10
265
User
Selangor
10
266
User
Selangor
10
271
User
Melaka
10
272
Shinu
Selangor
10
273
User
Selangor
10
275
User
Selangor
10
276
User
Selangor
10
278
User
Johor
10
279
User
Pahang
10
280
User
Johor
10
281
User
Selangor
10
282
User
Johor
10
283
User
Melaka
10
284
User
Sarawak
10
285
User
Selangor
9
287
User
Selangor
9
292
User
Pahang
9
293
User
Selangor
9
294
User
Selangor
9
295
User
Selangor
9
296
User
Selangor
9
297
User
Sarawak
9
298
User
Johor
9
300
User
Selangor
9
302
User
Selangor
9
303
User
Perak
9
305
User
Selangor
9
306
User
Selangor
9
308
User
Selangor
9
309
User
Selangor
9
310
User
Selangor
9
311
User
Selangor
9
312
User
Sarawak
9
314
User
Terengganu
9
315
User
Pahang
9
316
User
Sabah
9
319
User
Johor
9
320
User
Selangor
9
324
User
Selangor
9
325
User
Selangor
8
328
User
Selangor
8
329
Zhuan Yi
Johor
8
330
User
Johor
8
331
User
Johor
8
333
User
Sabah
8
334
User
Johor
8
335
User
Pulau Pinang
8
336
User
Selangor
8
338
User
Selangor
8
340
User
Pulau Pinang
8
342
Zen Yyi
Selangor
8
344
User
Sabah
8
345
User
Johor
8
346
Zhuan Yi
Johor
8
347
User
Johor
8
348
User
Johor
8
349
Bobsac
Johor
8
352
User
Johor
8
353
User
Johor
8
354
User
Selangor
8
355
Rion Connolly
Selangor
8
358
User
Kelantan
8
359
User
Selangor
8
360
User
Selangor
8
364
User
Johor
8
367
User
Kedah
8
370
User
Selangor
8
371
User
Sarawak
8
372
User
Selangor
8
373
User
Melaka
8
374
User
Selangor
8
375
User
Selangor
8
377
User
Johor
8
378
User
Johor
8
379
User
Johor
8
381
User
Kedah
8
383
Sethu Rajeswari
Negeri Sembilan
7
384
User
Selangor
7
389
User
Johor
7
390
User
Kedah
7
392
User
Selangor
7
394
User
Perak
7
396
User
Selangor
7
402
User
Johor
7
403
User
Johor
7
404
yejun
Johor
7
405
User
Johor
7
407
User
Selangor
7
410
User
Selangor
7
411
User
Selangor
7
412
User
Selangor
7
413
User
Selangor
6
414
User
Johor
6
415
User
Johor
6
417
User
Sabah
6
418
User
Johor
6
419
User
Johor
6
420
supermanlol
Johor
6
421
isabel
Johor
6
424
User
Perak
6
427
User
Selangor
6
428
User
Selangor
6
433
User
Perak
6
434
User
Selangor
6
436
User
Selangor
6
437
User
Selangor
6
438
Aaryan
Selangor
6
439
User
Selangor
6
441
User
Selangor
6
442
User
Selangor
6
444
User
Selangor
6
447
User
Selangor
6
449
User
Selangor
6
452
User
Selangor
6
455
User
Sarawak
6
457
User
Johor
6
458
User
Johor
6
460
User
Johor
6
461
User
Johor
6
462
User
Johor
6
464
User
Perak
6
467
User
Johor
6
469
User
Selangor
5
470
User
Selangor
5
471
User
Selangor
5
474
User
Selangor
5
475
User
Selangor
5
478
Akif Rabbani
Selangor
5
479
User
Terengganu
5
480
User
Selangor
5
481
User
Selangor
5
482
User
Selangor
5
485
User
Selangor
5
488
User
Selangor
5
490
User
Selangor
5
491
User
Selangor
5
496
User
Selangor
5
497
User
Perak
5
500
User
Pulau Pinang
5
502
User
Perak
5
506
User
Selangor
5
507
User
Selangor
5
509
User
Johor
5
510
Zhuan Yi
Johor
5
511
User
Johor
5
512
User
Johor
5
513
User
Selangor
5
516
User
Johor
5
520
User
Selangor
5
523
User
Kedah
5
525
Felice Wong
Selangor
5
527
User
Sarawak
4
528
Anna Wood
Selangor
4
530
User
Johor
4
531
User
Terengganu
4
532
User
Pulau Pinang
4
534
User
Pulau Pinang
4
536
User
Johor
4
537
User
Sarawak
4
540
vapidf
Selangor
4
541
User
Selangor
4
543
User
Selangor
4
544
User
Sabah
4
545
User
Pulau Pinang
4
548
User
Johor
4
549
User
Selangor
4
550
User
Selangor
4
552
User
Selangor
4
553
User
Selangor
4
555
User
Johor
4
556
User
Johor
4
557
User
Selangor
4
559
User
Johor
4
560
User
Johor
4
561
User
Johor
4
562
User
Selangor
4
563
User
Selangor
4
564
User
Johor
4
566
User
Selangor
4
567
User
Selangor
4
568
User
Selangor
4
569
User
Selangor
4
572
Yizhea
Johor
4
574
User
Selangor
4
575
User
Selangor
4
576
User
Selangor
4
577
User
Selangor
4
578
User
Selangor
4
579
User
Selangor
4
580
User
Selangor
4
581
User
Selangor
4
582
User
Selangor
4
584
User
Selangor
3
586
User
Selangor
3
587
User
Perak
3
588
User
Johor
3
591
User
Selangor
3
592
User
Selangor
3
595
User
Johor
3
596
User
Johor
3
597
User
Johor
3
601
User
Selangor
3
602
User
Selangor
3
603
User
Selangor
3
604
User
Selangor
3
606
User
Johor
3
607
User
Johor
3
608
eva the poopy pants
Johor
3
609
User
Selangor
3
610
User
Pulau Pinang
3
611
User
Johor
3
612
User
Johor
3
613
User
Johor
3
614
Yizhe
Johor
3
615
User
Melaka
3
616
Kanagasegaran Supramaniam
Pulau Pinang
3
617
User
Johor
3
618
User
Johor
3
619
User
Johor
3
620
User
Johor
3
621
User
Selangor
3
623
User
Selangor
3
625
User
Selangor
3
629
User
Selangor
3
630
User
Selangor
3
631
User
Selangor
3
634
User
Selangor
3
635
Mikael Adrian Adrin Shafil
Selangor
3
636
User
Selangor
3
637
User
Selangor
3
640
User
Selangor
3
641
User
Selangor
3
642
User
Perak
3
644
User
Selangor
3
647
User
Selangor
3
648
User
Sabah
3
649
User
Kedah
3
650
User
Pulau Pinang
3
651
User
Selangor
3
654
User
Sarawak
2
655
User
Sarawak
2
660
arshan
Johor
2
661
methw
Johor
2
662
User
Johor
2
663
User
Johor
2
664
User
Selangor
2
667
User
Selangor
2
668
User
Sarawak
2
670
User
Melaka
2
671
User
Johor
2
672
User
Johor
2
673
User
Johor
2
674
User
Selangor
2
675
anmol sahu
Johor
2
677
User
Johor
2
678
User
Johor
2
679
User
Johor
2
680
User
Johor
2
681
User
Johor
2
682
User
Johor
2
683
User
Johor
2
684
User
Johor
2
685
User
Perak
2
686
User
Johor
2
687
Eva chong
Johor
2
688
User
Johor
2
689
User
Johor
2
690
ye jun
Johor
2
691
User
Johor
2
692
User
Johor
2
695
User
Selangor
2
698
User
Sabah
2
699
User
Kedah
2
700
User
Selangor
2
703
User
Perak
2
705
User
Selangor
2
710
User
Selangor
2
711
User
Melaka
2
712
User
Selangor
2
713
User
Selangor
2
714
projek peribadi
Perak
2
715
User
Selangor
2
720
User
Melaka
2
722
User
Pulau Pinang
2
724
User
Johor
2
725
User
Johor
2
727
User
Sarawak
2
733
User
Johor
2
734
User
Johor
2
735
User
Johor
2
736
User
Selangor
2
737
User
Johor
2
738
User
Johor
2
739
richmond
Johor
2
740
anmol sahu
Johor
2
741
ETHAN
Johor
2
742
User
Johor
2
743
User
Johor
2
744
User
Johor
2
745
User
Johor
2
746
User
Johor
2
747
User
Johor
2
749
User
Johor
2
750
User
Johor
2
751
User
Johor
2
752
ET
Johor
2
753
User
Johor
2
754
User
Johor
2
755
yizhea
Johor
2
756
User
Johor
1
757
User
Johor
1
758
User
Johor
1
759
Lily The Savage
Johor
1
761
User
Johor
1
762
User
Johor
1
763
User
Johor
1
764
User
Johor
1
765
User
Johor
1
766
User
Johor
1
767
User
Johor
1
768
User
Johor
1
769
anmol sahu
Johor
1
770
User
Selangor
1
774
User
Sarawak
1
776
User
Pulau Pinang
1
778
User
Selangor
1
781
User
Johor
1
782
User
Selangor
1
783
Luji yufgp
Selangor
1
784
User
Selangor
1
788
User
Selangor
1
792
User
Pulau Pinang
1
797
User
Selangor
1
798
emily lee yi hsuen
Selangor
1
799
Lai Yu Xuan
Selangor
1
800
User
Selangor
1
801
User
Sarawak
1
804
User
Selangor
1
806
User
Selangor
1
808
User
Selangor
1
809
User
Selangor
1
810
User
Selangor
1
812
User
Selangor
1
813
User
Selangor
1
818
User
Selangor
1
819
User
Sarawak
1
822
User
Selangor
1
824
User
Sarawak
1
826
User
Melaka
1
827
User
Selangor
1
828
User
Selangor
1
830
User
Selangor
1
832
User
Sabah
1
835
User
Pulau Pinang
1
837
User
Selangor
1
839
User
Sarawak
1
844
User
Sarawak
1
846
User
Johor
1
857
User
Johor
1
858
User
Selangor
1
859
User
Selangor
1
860
User
Pulau Pinang
1
861
User
Selangor
1
866
User
Selangor
1
869
User
Perak
1
871
User
Johor
1
872
User
Selangor
1
873
User
Perak
1
874
User
Johor
1
875
Bernie Constantino
Kedah
1
876
Cameron
Johor
1
877
isabel
Johor
1
878
User
Johor
1
880
User
Johor
1
882
User
Johor
1
883
User
Johor
1
885
User
Kelantan
1
886
User
Johor
1
887
User
Johor
1
888
User
Johor
1
889
Bob
Johor
1
890
User
Johor
1
891
User
Johor
1
892
User
Johor
1
893
User
Johor
1
894
User
Selangor
1
895
Adam LaJoy
Johor
1
898
User
Selangor
1
900
User
Sabah
1
901
User
Johor
1
902
User
Pulau Pinang
1
903
User
Selangor
1
904
User
Sarawak
1
907
User
Selangor
1
908
User
Johor
1
909
User
Selangor
1
910
User
Selangor
1
912
User
Pulau Pinang
1
916
User
Johor
1
917
User
Selangor
1
918
yolo duuddudude
Selangor
1
919
User
Selangor
1
920
User
Selangor
1
921
User
Selangor
1
924
User
Selangor
1
925
User
Sarawak
1
926
User
Selangor
1
929
User
Selangor
1
931
User
Johor
1
932
User
Johor
1
933
User
Pulau Pinang
1
934
User
Sarawak
1
935
User
Sabah
1
937
User
Perak
1
938
User
Sabah
1
939
User
Selangor
1
942
User
Selangor
1
944
User
Selangor
1
946
User
Selangor
1
947
Nicki Coombs
Selangor
1

Free

Free basic access

Login Optional

Progress saved automatically

Students

Works great in classrooms

25,000,000
Questions answered
100,000
Users
100
Difficulty levels

Cross-Platform

Use any operating system with Chrome, Safari, or Firefox

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.


Privacy Policy