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1
HiepQH
Ho Chi Minh
89
2
Phung Dang Khoi
Ha Noi
89
3
HoanNguyen
Ho Chi Minh
88
4
Đăng Khôi Phùng
Ha Noi
86
5
Phùng Đăng Khôi
Ho Chi Minh
85
6
Asterohnefos
Ha Noi
77
7
hoàn phạm long
Ha Noi
77
8
Albert E
Ha Noi
72
9
Phuc Giang
Ho Chi Minh
72
11
& LEARN PLAY
Ho Chi Minh
71
12
Minh Tran Nhat
Ha Noi
67
13
Hoàn Phạm Long
Da Nang
64
14
Le Tuan Minh
Ho Chi Minh
63
15
haly68
Ho Chi Minh
63
16
Anh Minh Tran Ngoc
Ho Chi Minh
63
17
User
Ha Noi
62
18
tran nhat minh
Ha Noi
61
19
User
Tây Ninh
59
20
User
Ha Noi
58
21
User
Ha Noi
58
22
User
Ho Chi Minh
58
23
lionel messi
Ha Noi
58
24
User
Ho Chi Minh
56
25
User
Ha Noi
56
26
User
Ha Noi
56
29
Gia Hung Vu
Ha Noi
55
30
User
Ho Chi Minh
54
31
MINH NHAT
Ho Chi Minh
51
32
Kumar
Ho Chi Minh
49
33
User
Ha Noi
49
34
User
Ho Chi Minh
46
35
User
Ho Chi Minh
46
36
User
Ha Noi
43
37
Cong Le Chi
Tiền Giang
43
38
User
Ho Chi Minh
42
39
Quang Minh Ngô
Ha Noi
41
40
Giakhanh Duongmac
Ha Noi
41
41
User
Ho Chi Minh
40
42
Super Nicholas The MLG BACON HAIR
Ho Chi Minh
40
43
User
Quảng Ninh
40
44
User
Ha Noi
40
45
dz
Ha Noi
39
46
User
Ho Chi Minh
38
48
User
Ho Chi Minh
38
49
Cuong
Ha Noi
37
50
User
Ha Noi
36
51
User
Ho Chi Minh
36
52
User
Ho Chi Minh
36
53
Đặng Như
Ho Chi Minh
35
54
User
Lai Châu
35
55
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Lâm Ðồng
35
56
User
Ha Noi
35
57
Phan Hân
Ho Chi Minh
35
58
User
Ho Chi Minh
34
59
User
Ho Chi Minh
34
60
User
Ha Noi
34
61
User
Ho Chi Minh
34
62
User
Ha Noi
33
63
User
Ha Noi
33
64
User
Ha Noi
33
65
Kalyn Nguyễn
Da Nang
32
66
User
Ho Chi Minh
32
67
User
Ho Chi Minh
30
68
Nguyet Nguyen
Ha Noi
30
69
User
Ha Noi
30
70
User
Ha Noi
30
71
User
Ho Chi Minh
29
73
Oanh Nguyen
Da Nang
29
74
User
Ho Chi Minh
28
75
User
Ho Chi Minh
28
76
User
Ha Noi
27
77
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An Giang
27
78
Thay Giao Ba
Ho Chi Minh
27
79
User
Ho Chi Minh
27
80
Chris
Ha Noi
26
81
Duy Tran
Hai Phong
26
82
User
Ha Noi
25
83
User
Lai Châu
25
84
User
Ha Noi
25
85
User
Ho Chi Minh
24
86
User
Ho Chi Minh
24
87
User
Ho Chi Minh
24
88
User
Lai Châu
24
89
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Khánh Hòa
24
90
tomcoi
Ha Noi
24
91
User
Tiền Giang
23
92
User
Ha Noi
23
93
Norman
Ho Chi Minh
23
94
User
Ho Chi Minh
23
95
User
Ho Chi Minh
23
96
User
Ho Chi Minh
22
97
User
Ho Chi Minh
21
98
User
Ha Noi
21
100
User
Bình Dương
21
101
User
Ho Chi Minh
21
102
Blingbling Annie
Ha Noi
21
103
User
Ha Noi
20
104
User
Ho Chi Minh
20
105
User
Ha Noi
20
106
User
Ha Noi
19
107
User
Ho Chi Minh
19
108
User
Ho Chi Minh
19
109
Luatuadua
Ha Noi
19
110
User
Quảng Nam
19
111
User
Ha Noi
18
112
Mai Phuong HA
Ho Chi Minh
18
113
User
Ha Noi
18
114
Le Tien
Ho Chi Minh
17
115
User
Ho Chi Minh
17
116
Nguyen Ha Ngo
Ho Chi Minh
17
117
User
An Giang
17
118
Ngọc Tiến Nguyễn
Ho Chi Minh
17
119
User
Ho Chi Minh
17
120
User
Ho Chi Minh
17
121
User
Ho Chi Minh
17
122
User
Ho Chi Minh
17
123
User
Ho Chi Minh
17
124
User
Ho Chi Minh
16
125
User
Nghệ An
16
126
User
Bình Dương
16
127
Huy Vũ Lê
Ha Noi
16
128
Hoàng Phạm
Ha Noi
16
129
User
Ho Chi Minh
16
130
Phan Minh Hoàng
Ho Chi Minh
16
131
User
Ho Chi Minh
16
132
User
Ho Chi Minh
16
134
User
Ha Noi
15
135
User
Ho Chi Minh
15
136
User
Ho Chi Minh
14
137
User
Ho Chi Minh
14
138
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Sóc Trăng
14
139
User
Ha Noi
14
140
User
Ho Chi Minh
14
141
Quang Tran
Ho Chi Minh
14
142
User
Ho Chi Minh
14
143
User
Ha Noi
13
144
User
Ho Chi Minh
13
145
User
Bình Dương
13
146
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Ho Chi Minh
13
147
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Ho Chi Minh
13
148
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Ho Chi Minh
13
149
712a
Nghệ An
13
150
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Ho Chi Minh
13
151
Anonymous
Ho Chi Minh
13
152
Nam Hoang
Ho Chi Minh
13
153
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Ho Chi Minh
13
154
Hax.exe
Ho Chi Minh
12
155
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Hưng Yên
12
156
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Ha Noi
12
157
Andrew Nguyen
Ho Chi Minh
12
158
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Ha Noi
12
159
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Ðồng Nai
12
160
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Da Nang
12
161
Mzanh kun
Ho Chi Minh
12
162
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Ho Chi Minh
12
163
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Ho Chi Minh
12
164
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Ha Noi
12
165
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Ho Chi Minh
11
166
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Bình Dương
11
167
User
Ho Chi Minh
11
168
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Ho Chi Minh
11
169
duy le
Ha Noi
11
170
User
Ho Chi Minh
11
171
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Ho Chi Minh
11
172
User
Ho Chi Minh
11
173
User
Ha Noi
11
174
Vinh
Ha Noi
11
175
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Ho Chi Minh
10
176
Minh Nam Phan
Ho Chi Minh
10
177
Nhân Lê
Ho Chi Minh
10
178
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Ho Chi Minh
10
179
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Ho Chi Minh
10
180
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Ho Chi Minh
10
181
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Ho Chi Minh
10
182
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Ho Chi Minh
10
183
Kane Karry
Can Tho
10
184
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Kiến Giang
10
185
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An Giang
10
186
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Tây Ninh
10
187
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Bình Định
10
188
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Ha Noi
10
189
User
Ho Chi Minh
10
190
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Ho Chi Minh
10
191
Nhân
Ho Chi Minh
9
192
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Ho Chi Minh
9
193
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Ho Chi Minh
9
194
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Thanh Hóa
9
195
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Ho Chi Minh
9
196
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Ho Chi Minh
9
197
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Ho Chi Minh
9
198
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Ha Noi
9
199
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Ha Noi
9
200
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Ha Noi
9
201
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Ho Chi Minh
9
202
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Ho Chi Minh
9
203
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Ho Chi Minh
9
204
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Phú Yên
9
205
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Ha Noi
9
206
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Ho Chi Minh
9
207
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Nam Ðịnh
9
208
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9
209
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An Giang
9
210
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Ho Chi Minh
8
211
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Phú Yên
8
212
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Ha Noi
8
213
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Ha Noi
8
214
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Phú Yên
8
215
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Ho Chi Minh
8
216
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Ha Noi
8
217
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Long An
8
218
Deebster
Ha Noi
8
219
Nguyen Dang Hoang Duy
Ho Chi Minh
8
220
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Ho Chi Minh
8
221
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Ho Chi Minh
8
222
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Ha Noi
7
223
Vân Anh
Ho Chi Minh
7
224
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Ho Chi Minh
7
225
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Ho Chi Minh
7
226
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Ho Chi Minh
7
227
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Ha Noi
7
228
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Ho Chi Minh
7
229
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Ho Chi Minh
7
230
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Ha Noi
7
231
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Ha Noi
7
232
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Ho Chi Minh
7
233
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Ho Chi Minh
6
234
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Ho Chi Minh
6
235
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Khánh Hòa
6
236
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Hai Phong
6
237
Star The Fist
Cao Bằng
6
238
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Ho Chi Minh
6
239
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Ha Noi
6
240
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Ha Noi
6
241
Luận Hà
Ha Noi
6
242
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Ho Chi Minh
6
243
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Ho Chi Minh
6
244
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Ho Chi Minh
6
245
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Ðồng Nai
6
246
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Ho Chi Minh
6
247
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Ha Noi
6
248
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Ha Noi
6
249
User
Ha Noi
5
250
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Ha Noi
5
251
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Khánh Hòa
5
252
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Can Tho
5
253
Nguyen Anh
Quảng Trị
5
254
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Ha Noi
5
256
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Ho Chi Minh
5
257
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Nam Ðịnh
5
258
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Ha Noi
5
259
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Ho Chi Minh
5
260
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Vĩnh Long
5
261
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Ho Chi Minh
5
262
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Ho Chi Minh
5
263
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Ha Noi
5
264
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5
265
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Ho Chi Minh
5
266
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Ha Noi
5
268
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Quảng Nam
5
270
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Ho Chi Minh
5
271
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Ho Chi Minh
5
272
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Ha Noi
5
273
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Ho Chi Minh
5
274
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Ha Noi
5
275
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Ho Chi Minh
4
276
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Ho Chi Minh
4
277
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Ho Chi Minh
4
278
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Ho Chi Minh
4
279
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Ho Chi Minh
4
280
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Da Nang
4
281
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Ho Chi Minh
4
282
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Ha Noi
4
283
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Ho Chi Minh
4
284
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Ho Chi Minh
4
285
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Ho Chi Minh
4
286
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Ha Noi
4
287
Vu Dinh An
Ha Noi
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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Ha Noi
4
294
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Ha Noi
4
295
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Ho Chi Minh
4
297
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3
298
QTSon
Ha Noi
3
299
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Ho Chi Minh
3
300
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3
301
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3
302
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3
303
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3
304
Minh Trung
Ha Noi
3
306
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3
307
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3
309
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Ha Noi
3
310
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3
311
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3
312
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Ha Noi
3
313
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3
314
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3
315
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3
316
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Ho Chi Minh
3
317
minh quang phạm
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3
319
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2
320
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2
321
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2
322
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2
324
MrSteve
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2
325
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2
326
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Ha Noi
2
327
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Ha Noi
2
328
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2
329
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2
330
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2
331
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2
332
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2
333
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2
334
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2
335
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2
337
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2
338
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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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Ha Noi
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
Thuận Quách
Ha Noi
2
353
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Ha Noi
2
354
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Ha Noi
2
355
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Ho Chi Minh
2
356
User
Ha Noi
2
357
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Ho Chi Minh
2
358
User
Ho Chi Minh
2
359
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Ho Chi Minh
1
360
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Ha Noi
1
361
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Hai Phong
1
362
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Ha Noi
1
363
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Ho Chi Minh
1
364
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Ho Chi Minh
1
365
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Ho Chi Minh
1
367
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Ha Noi
1
368
tuanorm
Ho Chi Minh
1
369
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Ha Noi
1
370
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1
371
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Ha Noi
1
372
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1
373
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1
374
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1
375
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1
376
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1
378
haly68
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1
379
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1
380
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1
381
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1
382
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Ha Noi
1
383
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1
384
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1
385
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1
386
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1
387
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1
388
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Ha Noi
1
389
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1
390
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Ho Chi Minh
1
391
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Ho Chi Minh
1
392
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Ho Chi Minh
1
393
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Ho Chi Minh
1
394
User
Ho Chi Minh
1
395
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Ha Noi
1
396
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Ho Chi Minh
1
398
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Ha Noi
1
399
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1
401
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1
402
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Ha Noi
1
403
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1
404
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Ho Chi Minh
1
405
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Ho Chi Minh
1
406
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Ho Chi Minh
1
407
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1
408
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Vĩnh Long
1
410
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Ho Chi Minh
1
411
User
Ho Chi Minh
1
412
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Ho Chi Minh
1
413
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Khánh Hòa
1
414
User
Ho Chi Minh
1
415
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Da Nang
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 math practice, you'll be able to predict what the tips will say—you'll have learned mental math!


Get Better at Mental Math

The ability to quickly perform mental calculations offers advantages in certain circumstances. But even without applications, getting better at mental math is a great way to stimulate one’s mind. It develops better number sense and intuition for quantifying the world around us. Practicing mental calculation will strengthen your foundation for learning more advanced maths topics.

Nonetheless, the tangible benefits of improving at mental math are many. It is certainly expected that educated people are able to do simple arithmetic without having to pull out a calculator. An inability to do so may reflect poorly on you, while being well-practiced in mental calculation will leave your contemporaries impressed. In many scientific and technical circles, mental math ability is even more highly regarded.

For students, mental calculation speed will often have a direct impact on math and science test scores. At all grade levels, it is not sufficient to know how to solve math problems when tests have a time limit on them. The highest-scoring test takers are able to answer questions both correctly and efficiently. Improving mental math skills will only benefit a student’s academic career.

Calculating the solution to an arithmetic problem in your head is often faster than pulling out a device to tell you the answer. For example, figuring out how much to tip a server at a restaurant is a straightforward arithmetic problem that many people are unable to perform without a calculator. By training your brain to solve basic math problems, you can save time in situations like these.

Mental math can also be relied upon when calculation devices are not available. Even with the conveniences of modern life, we occasionally find ourselves without access to our cell phones or other capable devices. A mind skilled in mental math is always available to you.

Finally, getting better at mental math enables a quick estimate and sanity check on results obtained from calculators. While computers are extremely reliable at solving math problems, there is always the risk of incorrectly inputting the problem to the computer. By getting better at mental mathematics, you will develop an intuition for whether the results of calculators make sense.

In fact, the ability to estimate is often sufficient to avoid using calculators altogether. While the use of computers is widespread, estimation is an increasingly valued skill in many industries. There are many situations where complex math will eventually be required, but a preliminary estimate is needed quickly. A major boost to productivity!


Use a Math Trainer

Mental math ability is a lot like physical fitness training. You may be out of shape in the beginning, but with diligent training you can and will improve. Initially you might not enjoy the exercise, but you will reap significant rewards for your effort. As you become more fit, you’ll begin to enjoy the activity much more. If you are serious about it, your mental calculation fitness could become a source of energy, galvanizing you to face the challenges of life with enthusiasm.

In physical training, you break down the fibers in your muscles during a workout session. Your muscles actually sustain tiny tears during resistance training exercises. While you rest afterwards, your body repairs the damage, rebuilding the fibers thicker and stronger.

A similar process is believed to occur for cognitive tasks. A 2016 study found "extensive evidence that brain-training interventions improve performance on the trained tasks".1 Therefore you can expect training your brain to answer mental math questions will lead to improved performance over time.

In the context of physical fitness, a "trainer" often refers to a trained professional who guides the workout and recovery process. Personal trainers are tasked with assessing a trainee's level of ability, prescribing an exercise regimen, and offering feedback as the training goes along. The word "trainer" could also refer to a system that automates the role of a personal trainer. Many aerobic exercise machines today offer interactive training programs with feedback and analysis of a user's performance.

A math trainer is needed for optimal math fitness. Like in physical fitness, the trainer should be compatible with users at a variety of skill levels and should guide them to the next level. It should give an accurate assessment of a user's strengths and weakness, as well as offer helpful feedback on where to focus one's efforts. Learning the ropes of mental maths with a math trainer should be a seamless, rewarding journey to ever-greater abilities.


Mental Calculation

Mental calculation, or mental math, is performing arithmetical calculations without the aid of tools or supplies. As opposed to using a calculator or pencil and paper, mental math is performed entirely in one’s head.

People use mental calculation when computation aides are not available, when it is faster to do so, or when they wish to practice math, show off, or participate in mental math competitions. Most people perform basic mental calculation using elementary arithmetic on a daily basis. An inability to calculate mentally is a serious obstacle to many common tasks.

In U.S. schools, mental calculation is taught only for the most elementary arithmetic, such as single-digit addition and multiplication of two numbers between 0 and 12. To solve addition problems involving multiple digits, you are taught to add columns of digits from right to left, carrying the tens digit if the column sum exceeds 9. For example, how would you approach this addition problem?

Example of two-digit
addition problem

If you were trained like many of us were, you’d add the right column to obtain 12. Since that’s two digits, you’d write the 2 under the right column and carry the 10 by writing a 1 above the left column. Finally, you’d add the two tens digits and the carried 1 to obtain the answer, 52.

To solve an addition problem mentally, it’s best to add the columns from left to right. In our example, you could add the tens digit of the second number, 30, to the first number, 14, to obtain 44. This is easier than the full problem because you’re just doing one mental calculation and tacking on the 4 from the 14 as the singles digit. Then you’d add the remaining ones digit of the second number, 8, to 44 to arrive at the answer, 52.

Which approach seems simpler to you? Can you do the first approach without pulling out a pencil and paper? It turns out the same advantages of left-to-right addition apply to much larger numbers as well. It’s unlikely that difficult addition problems can be solved right to left without needing to write it all out, which of course is more time consuming.

Mental math should be distinguished from the memorization of math facts such as multiplication tables. A foundation of memorized answers to simple math problems will make mental math easier, but performing maths in your head requires both memorized facts and the manipulation of numbers and operations to solve problems. This combination of skill and memory allows us to solve far more complex math questions than can be answered with readily-memorized math facts.

Many mental math tricks are specific to particular numbers or types of problems, usually dependent on the base of the number system used. In the decimal numeral system, for example, it is trivially easy to multiply by 10—just add a 0 to the end of the number. This mental math trick wouldn’t work in the hexadecimal numeral system, though, because the base is 16 instead of 10.

Therefore mental calculation is the ability to manipulate complex arithmetic problems in such a way that they can be resolved using simple memorized math facts.


Arithmetic

Arithmetic is the branch of mathematics concerning basic number operations: addition, subtraction, multiplication, and division. As kids, we are taught to do arithmetic because real-world math problems depend on a mastery of elementary arithmetic. Higher-level study of arithmetic and the integers, or whole numbers, is known as number theory.

Though the math kids initially study is arithmetic, the word is rarely used in this context anymore. Originally it comes from the Greek arithmos, meaning “number”. It has however been included in the “three Rs” of elementary Western education: reading, writing, and arithmetic.

There is evidence prehistoric humans were using arithmetic as hunter-gatherers. Archaeologists have uncovered a tally stick, believed to be over 20,000 years old, which may exhibit the earliest known sequences of prime numbers. An understanding of prime numbers, which are only divisible by themselves and the number 1, requires knowledge of the operation in arithmetic known as division.

From tally marks came base-10 numerals such as those used in Egypt over 5,000 years ago. Number systems based on 10 probably arose because humans have ten “digits” as fingers on their hands (or toes on their feet). A later advance in arithmetic was positional notation, which allowed the same symbols to represent different magnitudes depending on their position in the written number. These numeral systems allowed complex arithmetic to be communicated, recorded, and applied to the challenges faced by our ancestors.

The basic operation of arithmetic is addition. It combines two or more numbers into one, the sum of the terms. The terms can be added in any order, which is known as the commutative property of arithmetic. On a number line, the sum of two numbers is the total distance from zero covered by both numbers.

The inverse arithmetical operation of addition is subtraction. It finds the difference between two numbers. Subtraction is not commutative because the order of the numbers determines whether the answer is positive or negative. On a number line, the difference between two numbers is the distance between their positions.

A second basic operation of arithmetic is multiplication, which scales a number by another number. This second number is called a factor. Like addition, multiplication is commutative—you can change the order of the factors and still get the same answer. Multiplication on a number line can be viewed as adding the first number a total number of times equal to the second factor.

Finally, division is an arithmetical operation that is essentially the inverse of multiplication. Rather than scaling a number, it is divided into a number of pieces equal to the second number. Dividing by the number 0 is not defined in arithmetic because dividing something into zero pieces is impossible.

Basic arithmetic allows us to evaluate the answers to an unlimited number of mathematical expressions. Arithmetical expressions can be purely mathematical, as in 2 + 2, or they can represent quantities in the physical world, such as two items plus two more. Understanding the laws of arithmetic is tremendously powerful.


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