Multiplication table
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In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system.
In
A multiplication table ("times table", as used to teach schoolchildren multiplication) is a grid where rows and columns are headed by the numbers to multiply, and the entry in each cell is the product of the column and row headings.
×
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100
110
120
11
11
22
33
44
55
66
77
88
99
110
121
132
12
12
24
36
48
60
72
84
96
108
120
132
144
So, for example, 3×6=18 by looking up where 3 and 6 intersect.
This table does not give the zeros. That is because any real number times zero is zero.
Multiplication tables vary from country to country. They may have ranges from 1×1 to 10×10, from 2×1 to 9×9, or from 1×1 to 12×12 to quote a few examples.
Traditional use
The traditional rote learning of multiplication was based on memorisation of columns in the table, in a form like
- 1 × 7 = 7
- 2 × 7 = 14
- 3 × 7 = 21
- 4 × 7 = 28
- 5 × 7 = 35
- 6 × 7 = 42
- 7 × 7 = 49
- 8 × 7 = 56
- 9 × 7 = 63
Patterns in the tables
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
For example, for multiplication by 6 a pattern emerges:
2 × 6 = 12 4 × 6 = 24 6 × 6 = 36 8 × 6 = 48 10 × 6 = 60In general:
number × 6 = half_of_number_times_10 + numberThe rule is convenient for even numbers, but also true for odd ones:
1 × 6 = 05 + 1 = 6 2 × 6 = 10 + 2 = 12 3 × 6 = 15 + 3 = 18 4 × 6 = 20 + 4 = 24 5 × 6 = 25 + 5 = 30 6 × 6 = 30 + 6 = 36 7 × 6 = 35 + 7 = 42 8 × 6 = 40 + 8 = 48 9 × 6 = 45 + 9 = 54 10 × 6 = 50 + 10 = 60
In abstract algebra
Multiplication tables can also define binary operations on groups, fields, rings, and other algebraic systems. In such contexts they can be called Cayley tables. For an example, see octonion.
External links
- Printable Tables in [Black and White] or [Color]
- [Learn the Multiplication Table] then [Test Yourself]
- Printable worksheets at [kwizNET Learning System]
- [Arithmetic Operations In Various Number Systems], [Abacus In Various Number Systems], [Soroban In Various Number Systems] and [Suan Pan In Various Number Systems] at cut-the-knot
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