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1
User
Auckland
82
2
Mandiv Sujan
Auckland
66
4
User
Auckland
55
5
User
Auckland
53
6
User
Auckland
53
7
User
Auckland
46
8
User
Auckland
45
9
User
Auckland
44
10
User
Wellington
43
11
User
Wellington
40
12
User
Auckland
38
13
User
Auckland
38
14
User
Wellington
37
15
User
Auckland
36
16
User
Wellington
36
17
User
Canterbury
35
19
User
Waikato
35
20
User
Auckland
34
21
Christine
Auckland
34
22
Shadman Jahin
Bay of Plenty
33
23
User
Auckland
33
24
Taylor Taylor Yi
Auckland
32
25
Dion
Auckland
32
26
User
Auckland
32
27
Winston Zhao
Auckland
32
29
wryao64
Auckland
31
30
User
Auckland
31
31
User
Auckland
31
32
User
Auckland
30
33
User
Auckland
29
34
User
Taranaki
29
35
User
Canterbury
29
36
User
Auckland
29
37
User
Auckland
29
38
User
Auckland
28
39
User
Auckland
28
40
Joseph Edwards
Wellington
28
41
User
Auckland
28
42
User
Auckland
27
43
User
Auckland
27
44
jahseh
Auckland
27
45
timothy m
Canterbury
26
46
User
Wellington
26
47
Condog
Auckland
26
48
User
Auckland
26
49
User
Otago
25
50
User
Auckland
25
51
User
Auckland
25
52
Oliver Wilkinson
Canterbury
25
53
User
Auckland
24
54
User
Auckland
24
55
User
Auckland
24
56
User
Auckland
23
57
User
Canterbury
23
58
User
Canterbury
23
59
User
Hawke\'s Bay
23
60
User
Auckland
23
61
User
Auckland
22
62
User
Wellington
22
63
User
Auckland
22
64
User
Nelson City
22
65
User
Wellington
22
66
User
Auckland
22
67
User
Auckland
22
68
User
Auckland
22
69
User
Otago
21
70
User
Auckland
21
71
User
Auckland
21
72
Amy Lauridsen
Wellington
21
73
Best Moonsan
Auckland
21
74
User
Canterbury
21
75
User
Auckland
21
76
User
Auckland
21
77
Adda Meow
Wellington
20
78
User
Otago
20
79
User
Auckland
20
80
User
Wellington
20
81
User
Wellington
20
82
User
Wellington
20
83
User
Auckland
20
84
Kay Paterson
Canterbury
20
85
User
Auckland
19
86
User
Auckland
19
87
User
Northland
19
88
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Auckland
19
89
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Wellington
19
90
User
Auckland
19
91
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Otago
19
92
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Auckland
18
93
User
Wellington
18
94
User
Northland
18
95
Jason van Schaeck Mathon
Wellington
18
96
User
Auckland
18
97
Andrew Sunde
Auckland
18
98
User
Wellington
18
99
User
Auckland
17
100
User
Waikato
17
101
User
Auckland
17
102
User
Canterbury
17
103
Matt Pottinger
Auckland
16
104
User
Auckland
16
105
User
Waikato
16
106
User
Auckland
16
107
User
Auckland
15
108
User
Wellington
15
109
User
Auckland
15
110
User
Auckland
15
111
User
Auckland
15
112
User
Auckland
15
113
User
Auckland
15
114
User
Auckland
15
115
User
Auckland
14
116
User
Auckland
14
117
User
Wellington
14
118
User
Auckland
14
119
User
Auckland
14
120
User
Bay of Plenty
14
121
User
Bay of Plenty
14
122
User
Wellington
14
123
User
Auckland
14
124
User
Auckland
14
125
User
Auckland
14
126
User
Bay of Plenty
14
127
User
Wellington
14
128
User
Wellington
14
129
User
Auckland
13
130
User
Auckland
13
131
User
Auckland
13
132
User
Auckland
13
133
User
Auckland
13
134
User
Wellington
13
135
User
Auckland
12
136
Kupa
Waikato
12
137
User
Wellington
12
138
User
Auckland
12
139
User
Auckland
12
140
User
Auckland
12
141
User
Auckland
12
142
User
Wellington
12
143
imissuhard lol
Auckland
12
144
User
Auckland
12
145
User
Auckland
12
146
User
Auckland
11
147
User
Northland
11
148
User
Auckland
11
149
User
Canterbury
11
150
User
Auckland
11
151
User
Wellington
11
152
User
Auckland
11
153
User
Wellington
11
154
User
Auckland
11
155
User
Auckland
11
156
User
Auckland
11
157
User
Bay of Plenty
11
158
User
Wellington
11
159
User
Wellington
11
160
User
Auckland
11
161
User
Auckland
10
162
User
Auckland
10
163
User
Auckland
10
164
User
Auckland
10
165
User
Auckland
10
166
User
Taranaki
10
168
User
Wellington
10
169
User
Auckland
10
170
User
Auckland
10
171
User
Auckland
10
172
Joy Heather
Auckland
9
173
User
Northland
9
174
User
Auckland
9
175
User
Auckland
9
176
User
Waikato
9
177
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Auckland
9
178
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Auckland
9
179
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Auckland
9
180
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Waikato
9
181
User
Wellington
9
182
User
Canterbury
9
183
User
Auckland
9
184
User
Auckland
8
185
User
Auckland
8
186
Ngaio
Auckland
8
187
Leila Tansley
Auckland
8
188
User
Otago
8
189
User
Auckland
8
190
User
Auckland
8
191
User
Wellington
8
192
User
Auckland
8
193
User
Auckland
8
194
User
Auckland
8
195
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Auckland
8
196
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Wellington
8
197
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Northland
8
198
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Wellington
8
199
User
Auckland
7
200
User
Auckland
7
201
User
Canterbury
7
202
Nik Voykovich
Auckland
7
204
User
Auckland
7
205
User
Auckland
7
206
User
Waikato
7
207
User
Auckland
7
208
User
Wellington
7
209
User
Auckland
7
210
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Wellington
7
211
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Wellington
7
212
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Auckland
7
214
User
Auckland
6
215
Maxwell Fysh
Auckland
6
216
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Auckland
6
217
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Auckland
6
218
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Auckland
6
219
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Canterbury
6
220
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Otago
6
221
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Auckland
6
222
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Auckland
6
223
User
Auckland
6
225
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Auckland
6
226
User
Wellington
6
227
User
Auckland
6
228
User
Wellington
6
229
User
Auckland
6
230
bobknight42
Wellington
6
231
User
Auckland
6
232
User
Auckland
5
233
User
Auckland
5
234
User
Auckland
5
235
Jane
Canterbury
5
236
User
Auckland
5
237
josie
Auckland
5
238
User
Auckland
5
239
Tom Bell
Wellington
5
240
User
Auckland
5
241
User
Auckland
5
242
User
Auckland
5
243
User
Canterbury
5
244
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Auckland
5
245
Alyssa Leddie
Auckland
5
246
Vicki Crozier
Hawke\'s Bay
5
247
User
Auckland
5
248
User
Wellington
5
249
User
Auckland
5
250
User
Auckland
5
252
User
Auckland
5
253
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Auckland
5
254
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Auckland
5
255
User
Waikato
5
256
Hayden Rabel
Canterbury
5
257
User
Auckland
5
258
User
Hawke\'s Bay
4
259
Lybeck
Canterbury
4
260
tupu
Auckland
4
261
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Auckland
4
262
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Auckland
4
263
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Auckland
4
264
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Auckland
4
265
luca
Auckland
4
266
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Auckland
4
267
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Auckland
4
268
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Canterbury
4
269
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Auckland
4
270
Tommy
Waikato
4
271
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Waikato
4
272
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Waikato
4
273
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Auckland
4
274
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Auckland
4
275
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Auckland
4
278
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Auckland
4
279
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Auckland
4
280
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Auckland
4
281
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Auckland
4
282
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Wellington
4
283
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Auckland
4
284
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Auckland
4
285
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Wellington
4
286
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Auckland
4
287
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Auckland
4
288
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Auckland
4
289
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Auckland
4
290
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Canterbury
4
291
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Waikato
4
293
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Canterbury
4
294
User
Auckland
3
295
Max
Auckland
3
296
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Auckland
3
298
NOAH
Auckland
3
299
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Wellington
3
300
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Auckland
3
301
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Auckland
3
302
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Otago
3
303
gmoney
Auckland
3
304
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Auckland
3
305
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Auckland
3
306
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Auckland
3
307
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Auckland
3
308
Mafi-Haapai Valentine Manufekai
Auckland
3
309
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Auckland
3
310
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Auckland
3
311
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Auckland
3
312
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Auckland
3
313
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Auckland
3
314
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Auckland
3
315
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Auckland
3
316
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Waikato
3
317
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Auckland
3
318
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Auckland
3
319
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Wellington
3
320
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Auckland
3
321
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Wellington
3
322
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Wellington
3
323
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Auckland
3
324
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Auckland
3
325
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Canterbury
3
326
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Waikato
3
327
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Auckland
3
328
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Auckland
3
329
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Otago
3
330
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Auckland
3
331
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Canterbury
3
332
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Wellington
3
333
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Auckland
3
334
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Auckland
3
335
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Auckland
3
336
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Auckland
3
337
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Southland
2
338
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Canterbury
2
339
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Auckland
2
340
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Auckland
2
341
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Canterbury
2
342
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Auckland
2
343
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Hawke\'s Bay
2
344
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Auckland
2
345
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Auckland
2
346
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Otago
2
347
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Auckland
2
348
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Auckland
2
349
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Auckland
2
350
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Auckland
2
351
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Auckland
2
352
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Auckland
2
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Auckland
2
354
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Canterbury
2
355
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Waikato
2
356
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Auckland
2
357
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Auckland
2
358
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Hawke\'s Bay
2
359
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Auckland
2
360
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Auckland
2
361
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Auckland
2
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Auckland
2
363
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Auckland
2
364
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Auckland
2
365
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Auckland
2
366
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Auckland
2
367
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Wellington
2
368
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Auckland
2
369
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Auckland
2
370
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Auckland
2
371
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Wellington
2
372
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Canterbury
2
373
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Auckland
2
374
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Taranaki
2
375
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Auckland
2
376
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Canterbury
2
377
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Auckland
2
378
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Wellington
2
379
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Wellington
2
380
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Wellington
2
381
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Auckland
2
382
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Auckland
2
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Auckland
2
384
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Wellington
2
385
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Auckland
2
386
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Auckland
2
387
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Auckland
2
388
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2
389
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Auckland
2
390
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Auckland
2
391
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Auckland
2
392
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Auckland
2
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Auckland
2
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Canterbury
2
395
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Auckland
2
396
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Auckland
2
397
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Auckland
2
398
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Auckland
2
400
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Auckland
2
401
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Auckland
2
402
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Canterbury
2
403
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Canterbury
2
404
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Auckland
2
405
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Wellington
2
406
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Auckland
2
407
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Auckland
1
408
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Wellington
1
409
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Waikato
1
410
Kimberlyn Vaka
Auckland
1
411
Sophie Munro
Auckland
1
412
NOAH
Auckland
1
413
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Wellington
1
414
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Auckland
1
415
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Auckland
1
416
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Waikato
1
417
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Waikato
1
418
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Otago
1
419
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Northland
1
420
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Northland
1
421
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Auckland
1
423
pirate
Northland
1
424
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Wellington
1
425
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Auckland
1
426
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Auckland
1
427
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Auckland
1
428
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Canterbury
1
429
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Auckland
1
430
JEFF JERK
Auckland
1
431
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Northland
1
432
User
Hawke\'s Bay
1
433
Pede Fikkemand
Canterbury
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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