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Alex Dumitrascu
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Palfi Csaba Sandor
Cluj
81
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Zoltán Király
Timiş
77
4
User
Bucureşti
74
5
Dan Damian
Ilfov
67
6
User
Bucureşti
65
7
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Mureş
60
8
User
Bucureşti
52
9
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Cluj
51
10
User
Bucureşti
51
11
Akos
Region
50
12
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Cluj
49
13
ChaSeR
Bucureşti
48
14
Tibor Toro
Bucureşti
48
15
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Hunedoara
48
16
User
Bucureşti
48
17
User
Bucureşti
47
18
User
Bucureşti
45
19
Horea Stefan
Mureş
45
20
User
Iaşi
45
21
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Bucureşti
43
22
User
Arad
42
23
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Bucureşti
42
24
Tina
Arad
41
25
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Maramureş
40
26
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Arad
40
27
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Iaşi
40
28
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Prahova
40
29
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Cluj
39
30
MrAlexozo
Bucureşti
37
31
Raz3Romania
Suceava
36
32
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Bucureşti
35
33
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Bucureşti
35
34
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Bucureşti
35
35
Luca Fanut
Prahova
34
36
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Cluj
34
37
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34
38
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Bucureşti
33
39
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33
40
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Arad
32
41
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Bucureşti
32
42
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32
43
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31
44
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31
45
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Cluj
31
46
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Bucureşti
31
47
User
Arad
30
48
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30
49
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Cluj
30
50
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Bucureşti
30
51
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30
52
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Cluj
30
53
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29
54
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29
55
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29
56
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28
57
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28
58
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59
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Cluj
27
60
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Cluj
27
61
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27
62
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Cluj
27
63
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Cluj
27
64
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Suceava
27
65
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Arad
26
66
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Bucureşti
26
67
Sara
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25
68
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Arad
25
69
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Timiş
25
70
Zacky LPYi
Sibiu
25
71
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Bacău
25
72
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Iaşi
24
73
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Cluj
23
74
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Cluj
23
75
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Cluj
23
76
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Bucureşti
23
77
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23
78
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Braşov
23
79
Tudor Oprescu
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23
80
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Ilfov
23
81
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Bucureşti
23
82
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22
83
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Bucureşti
22
84
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22
85
LyonSsS L
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22
86
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Bucureşti
22
87
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21
88
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Arad
21
89
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Bucureşti
21
90
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Harghita
21
91
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Cluj
21
92
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Iaşi
21
93
Negură Eugen-Andrei
Suceava
21
94
C Alex
Timiş
21
95
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Timiş
20
96
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Bucureşti
20
97
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Cluj
20
98
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20
99
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Bucureşti
20
100
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20
101
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19
102
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19
103
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19
104
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19
105
mihai Gameplays
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19
106
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Bucureşti
18
107
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18
108
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Sibiu
18
109
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Bacău
18
110
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18
111
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Bucureşti
18
112
User
Hunedoara
17
113
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Bucureşti
17
114
User
Cluj
17
115
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Cluj
17
116
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Bucureşti
17
117
User
Cluj
16
118
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Bucureşti
16
119
User
Cluj
16
120
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Bucureşti
16
121
Daniel Georgescu
Sibiu
16
122
Enes Production Gaming
Constanţa
16
123
User
Ilfov
16
124
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Bucureşti
16
125
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16
126
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16
127
User
Arad
15
128
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Cluj
15
129
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Timiş
15
130
User
Botoşani
15
131
User
Prahova
15
132
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Prahova
15
133
User
Cluj
14
134
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Bucureşti
14
135
George Cristian Pruteanu
Bucureşti
13
136
User
Cluj
13
137
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Bihor
13
138
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Prahova
13
139
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13
140
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12
141
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12
142
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12
143
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12
144
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Bucureşti
12
145
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12
146
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Iaşi
12
147
Edina
Arad
11
148
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11
149
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Cluj
11
150
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Iaşi
10
151
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10
152
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Cluj
10
153
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Cluj
10
154
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Arad
10
155
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Arad
10
156
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Arad
10
157
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Bucureşti
10
158
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Bucureşti
10
159
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10
160
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10
161
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Iaşi
9
162
Nagy Imola
Cluj
9
163
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Bucureşti
9
164
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9
165
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Arad
9
166
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9
167
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Iaşi
9
168
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Bucureşti
9
169
Andrea Molnar
Cluj
8
170
User
Bucureşti
8
171
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Cluj
8
172
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Arad
8
173
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Bucureşti
8
174
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Mureş
8
175
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8
176
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Bucureşti
8
177
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8
178
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Iaşi
8
179
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Iaşi
7
180
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Timiş
7
181
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Cluj
7
182
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Bucureşti
7
183
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7
184
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Iaşi
7
185
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7
186
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Bucureşti
7
187
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Bucureşti
7
188
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Prahova
7
189
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7
190
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7
191
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7
192
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7
193
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6
194
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6
195
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6
196
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6
197
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6
198
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6
199
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6
200
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6
201
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6
202
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6
203
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6
204
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6
205
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Bucureşti
5
206
OliNonstopGamer
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5
207
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5
208
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5
209
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5
210
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5
211
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5
212
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5
213
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5
214
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5
215
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5
216
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5
217
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5
218
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5
219
User
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5
220
User
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4
221
User
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4
222
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4
223
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4
224
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4
225
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4
226
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4
227
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4
228
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4
229
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4
230
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4
231
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4
232
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4
233
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4
234
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4
235
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4
236
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4
237
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4
238
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4
239
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Bucureşti
3
240
Alexa Mateias
Bucureşti
3
241
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Alba
3
242
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3
243
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3
244
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3
245
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3
246
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3
247
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3
248
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Cluj
3
249
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3
250
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3
251
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3
252
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Timiş
3
253
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Bucureşti
3
254
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3
255
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3
256
User
Iaşi
3
257
User
Ilfov
3
258
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Constanţa
2
259
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2
260
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Cluj
2
261
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2
262
Covaciu Claudia
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2
263
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2
264
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Arad
2
265
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2
266
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2
267
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2
268
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2
269
User
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2
270
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2
271
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2
272
User
Botoşani
2
273
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2
274
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2
275
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2
276
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2
277
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2
278
User
Ilfov
2
279
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Ilfov
2
280
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Ilfov
2
281
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Bucureşti
2
282
User
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2
283
User
Constanţa
1
284
User
Prahova
1
285
User
Dolj
1
286
User
Arad
1
287
User
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1
288
User
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1
289
User
Arad
1
290
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Bucureşti
1
291
Dimitrie
Arad
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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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