A multiplication table, by Adam Ries (1490s-1559)18th century version of Napier's bones, a calculation device similar to an abacus
A multiplication table is a tool used to learn how to multiply two numbers. The oldest known multiplication tables were written by the Babylonians about 4000 years ago.[1] Many people think it is important to know how to multiply two numbers by heart, usually up to 12 × 12, 30 × 30, 50 × 50, or 100 × 100.
Most children are introduced to the two, five and 10 times tables by year two - at the age of six and seven. Between the age of seven and eight, children start to learn the three, four and eight times tables.[2] The hardest multiplication is 6×8, which students got wrong 63% of the time. This was closely followed by 8×6, then 11×12, 12×8 and 8×12. The easiest multiplication, on the other hand, was 1×12, which students got wrong less than 5% of the time, followed by 1×6 and 9×1.[3]
In a multiplication table, a number on the first column is multiplied by a number on the first row. The number they corner up to is the answer. In the table below, 12 and 9 are multiplied to get 108, using the table. The numbers in bold are squares (numbers multiplied by themselves).
×
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
3
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
4
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
6
0
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
96
102
108
114
120
7
0
7
14
21
28
35
42
49
56
63
70
77
84
91
98
105
112
119
126
133
140
8
0
8
16
24
32
40
48
56
64
72
80
88
96
104
112
120
128
136
144
152
160
9
0
9
18
27
36
45
54
63
72
81
90
99
108
117
126
135
144
153
162
171
180
10
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
11
0
11
22
33
44
55
66
77
88
99
110
121
132
143
154
165
176
187
198
209
220
12
0
12
24
36
48
60
72
84
96
108
120
132
144
156
168
180
192
204
216
228
240
13
0
13
26
39
52
65
78
91
104
117
130
143
156
169
182
195
208
221
234
247
260
14
0
14
28
42
56
70
84
98
112
126
140
154
168
182
196
210
224
238
252
266
280
15
0
15
30
45
60
75
90
105
120
135
150
165
180
195
210
225
240
255
270
285
300
16
0
16
32
48
64
80
96
112
128
144
160
176
192
208
224
240
256
272
288
304
320
17
0
17
34
51
68
85
102
119
136
153
170
187
204
221
238
255
272
289
306
323
340
18
0
18
36
54
72
90
108
126
144
162
180
198
216
234
252
270
288
306
324
342
360
19
0
19
38
57
76
95
114
133
152
171
190
209
228
247
266
285
304
323
342
361
380
20
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
340
360
380
400
Warring States decimal multiplication table
A group of 21 strips of bamboo from 305 BC from the Warring States period is the world's oldest known decimal multiplication table.[4]
This is a Warring States decimal multiplication table used to find 12 × 34.5.
Examples
The traditional form of multiplication tables are written in columns with complete number sentences, instead of the standard modern grid. This form is also taught in the schools. Some examples of traditional form of multiplication tables are multiplication tables of 6 and 7 given below.
Addition and Division can also have their own tables. Similarly, Subtraction can also have its own table, although it is not commonly used.
Addition Table
+
0
1
2
3
4
5
6
7
8
9
10
0
0
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
11
2
2
3
4
5
6
7
8
9
10
11
12
3
3
4
5
6
7
8
9
10
11
12
13
4
4
5
6
7
8
9
10
11
12
13
14
5
5
6
7
8
9
10
11
12
13
14
15
6
6
7
8
9
10
11
12
13
14
15
16
7
7
8
9
10
11
12
13
14
15
16
17
8
8
9
10
11
12
13
14
15
16
17
18
9
9
10
11
12
13
14
15
16
17
18
19
10
10
11
12
13
14
15
16
17
18
19
20
In mathematics, a division table, like multiplication table, is a mathematical table used to define a divisionoperation for an algebraic system, or to obtain the solution to a certain equation.[5][6] The division symbol ÷ is used in the division table, known as the obelus. It was first used to signify division in 1659. Mathematicians however, almost never use the ÷ symbol for division. Instead they use fraction notation, called the vinculum.[7] Division tables are used for finding the Quotient in the Long division.
