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Alex Dumitrascu
Bucureşti
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InSane Samp
Neamţ
84
3
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Bucureşti
81
4
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Cluj
81
5
User
Iaşi
79
6
User
Timiş
77
7
Zoltán Király
Timiş
77
8
User
Bucureşti
74
9
Dan Damian
Ilfov
67
10
Alexandru Stefan
Iaşi
66
11
User
Neamţ
64
12
User
Mureş
60
13
User
Argeş
58
14
hagea
Bucureşti
55
15
Ion Prodan
Bucureşti
53
16
User
Bucureşti
52
17
Andreea
Cluj
51
18
User
Bucureşti
51
19
Akos
Region
50
20
User
Cluj
49
21
User
Bucureşti
48
22
ChaSeR
Bucureşti
48
23
Tibor Toro
Bucureşti
48
24
User
Hunedoara
48
25
User
Bucureşti
48
26
User
Neamţ
47
27
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Suceava
47
28
User
Bucureşti
47
29
User
Bucureşti
46
30
User
Mureş
45
31
User
Bucureşti
45
32
Horea Stefan
Mureş
45
33
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Iaşi
45
34
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43
35
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42
36
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42
37
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42
38
Tina
Arad
41
39
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40
40
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40
41
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40
42
User
Prahova
40
43
Vanilla
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39
44
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Bucureşti
39
45
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Neamţ
39
46
User
Cluj
39
47
Raz3Romania
Suceava
38
48
MrAlexozo
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37
49
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Bucureşti
35
50
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35
51
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35
52
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34
53
Luca Fanut
Prahova
34
54
User
Cluj
34
55
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Botoşani
34
56
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Bucureşti
33
57
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33
58
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33
59
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Timiş
32
60
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32
61
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Arad
32
62
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Bucureşti
32
63
User
Bucureşti
32
64
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31
65
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Bucureşti
31
66
User
Cluj
31
67
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31
68
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Arad
30
69
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Suceava
30
70
User
Cluj
30
71
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30
72
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Cluj
30
73
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29
74
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Bucureşti
29
75
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29
76
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Hunedoara
28
77
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Bucureşti
28
78
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28
79
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28
80
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28
81
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28
82
User
Cluj
27
83
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27
84
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Bucureşti
27
85
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Cluj
27
86
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Cluj
27
87
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Suceava
27
88
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Neamţ
26
89
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Bucureşti
26
90
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Suceava
26
91
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Arad
26
92
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Bucureşti
26
93
Sara
Arad
25
94
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Arad
25
95
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Timiş
25
96
Zacky LPYi
Sibiu
25
97
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Bacău
25
98
User
Iaşi
24
99
User
Bucureşti
23
100
User
Cluj
23
101
User
Cluj
23
102
User
Cluj
23
103
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23
104
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Constanţa
23
105
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Braşov
23
106
Tudor Oprescu
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23
107
User
Ilfov
23
108
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Bucureşti
23
109
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22
110
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22
111
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Bucureşti
22
112
User
Cluj
22
113
LyonSsS L
Bucureşti
22
114
User
Bucureşti
22
115
User
Neamţ
21
116
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Bucureşti
21
117
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Bucureşti
21
118
User
Arad
21
119
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21
120
User
Harghita
21
121
User
Cluj
21
122
User
Iaşi
21
123
Negură Eugen-Andrei
Suceava
21
124
C Alex
Timiş
21
125
User
Neamţ
20
126
User
Neamţ
20
127
User
Timiş
20
128
User
Bucureşti
20
129
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20
130
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Neamţ
20
131
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Bucureşti
20
132
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Cluj
19
133
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19
134
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19
135
Zsolt Tasnadi
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19
136
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Braşov
19
137
mihai Gameplays
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19
138
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18
139
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18
140
odv
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18
141
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18
142
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18
143
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17
144
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17
145
User
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17
146
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17
147
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17
148
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16
149
User
Cluj
16
150
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Bucureşti
16
151
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Cluj
16
152
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16
153
Daniel Georgescu
Sibiu
16
154
Enes Production Gaming
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16
155
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16
156
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16
157
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16
158
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16
159
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15
160
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Arad
15
161
User
Cluj
15
162
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Timiş
15
163
User
Botoşani
15
164
User
Prahova
15
165
User
Prahova
15
166
User
Cluj
14
167
User
Bucureşti
14
168
User
Bucureşti
13
169
User
Timiş
13
170
George Cristian Pruteanu
Bucureşti
13
171
User
Cluj
13
172
User
Bihor
13
173
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Prahova
13
174
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Bucureşti
13
175
User
Neamţ
12
176
User
Cluj
12
177
User
Bacău
12
178
User
Sălaj
12
179
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12
180
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Arad
12
181
User
Braşov
12
182
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Bucureşti
12
183
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12
184
User
Iaşi
12
185
Samantha Swan
Dolj
11
186
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Constanţa
11
187
User
Dolj
11
188
User
Bihor
11
189
User
Bucureşti
11
190
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Dolj
11
191
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11
192
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11
193
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11
194
User
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10
195
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10
196
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Bucureşti
10
197
Andrei Muntean
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10
198
User
Cluj
10
199
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Arad
10
200
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Arad
10
201
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Arad
10
202
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10
203
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10
204
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10
205
User
Bucureşti
10
206
User
Bucureşti
9
207
User
Bucureşti
9
208
User
Bacău
9
209
User
Bucureşti
9
210
User
Iaşi
9
211
Nagy Imola
Cluj
9
212
User
Bucureşti
9
213
User
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9
214
User
Arad
9
215
User
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9
216
User
Iaşi
9
217
User
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9
218
User
Bucureşti
8
219
User
Botoşani
8
220
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8
221
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8
222
Andrea Molnar
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8
223
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8
224
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8
225
User
Arad
8
226
User
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8
227
User
Mureş
8
228
raptorus1984
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8
229
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8
230
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8
231
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8
232
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7
233
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7
234
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7
235
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7
236
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7
237
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7
238
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7
239
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7
240
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Iaşi
7
241
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7
242
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7
243
User
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7
244
User
Prahova
7
245
User
Timiş
7
246
User
Iaşi
7
247
Zselyku
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7
248
User
Prahova
7
249
User
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6
250
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6
251
User
Alba
6
252
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Bihor
6
253
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6
254
Eduard Zepciuc
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6
255
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6
256
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6
257
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6
258
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6
259
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6
260
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6
261
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6
262
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6
263
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6
264
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6
265
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6
266
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6
267
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5
268
OliNonstopGamer
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5
269
Frisan
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5
270
User
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5
271
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5
272
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5
273
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5
274
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5
275
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5
276
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5
277
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5
278
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5
279
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5
280
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5
281
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5
282
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4
283
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4
284
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4
285
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4
286
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4
287
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4
288
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4
289
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4
290
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4
291
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4
292
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4
293
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4
294
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4
295
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4
296
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4
297
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4
298
Frisan
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4
299
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4
300
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4
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4
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4
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4
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4
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4
309
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4
310
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4
311
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3
312
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3
313
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3
314
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3
315
Alexa Mateias
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3
316
User
Alba
3
317
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3
318
User
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3
319
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3
320
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3
321
User
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3
322
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3
323
User
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3
324
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3
325
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3
326
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3
327
User
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3
328
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3
329
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3
330
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3
331
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3
332
User
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3
333
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2
334
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2
335
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2
336
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2
337
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2
338
Covaciu Claudia
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2
339
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2
340
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2
341
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2
342
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2
343
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2
344
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2
345
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2
346
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2
347
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2
348
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2
349
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2
350
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2
351
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2
352
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2
353
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2
354
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2
355
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2
356
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2
357
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2
358
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2
359
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1
360
User
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1
361
User
Ilfov
1
362
User
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1
363
User
Constanţa
1
364
User
Prahova
1
365
User
Dolj
1
366
User
Arad
1
367
User
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1
368
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1
369
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1
370
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1
371
Dimitrie
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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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