Multiplication table
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In mathematics, a multiplication table is used to define a multiplication operation for an algebraic system.
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In basic arithmetic
A multiplication 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.
| × | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
This table does not give the ones and zeros. That is because:
- Anything times zero is zero.
- Anything times one is itself. For example, 5×1=5.
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 x 7 = 7
- 2 x 7 = 14
- 3 x 7 = 21
- 4 x 7 = 28
- 5 x 7 = 35
- 6 x 7 = 42
- 7 x 7 = 49
- 8 x 7 = 56
- 9 x 7 = 63
- 10 x 7 = 70
- 11 x 8 = 88
- 12 x 9 =
Patterns in the tables
For example, for multiplication by 6 a pattern emerges:
2 x 6 = 12 4 x 6 = 24 6 x 6 = 36 8 x 6 = 48 10 x 6 = 60
In general:
number x 6 = half_of_number_times_10 + number
The rule is convenient for even numbers, but also true for odd ones:
1 x 6 = 05 + 1 = 6 2 x 6 = 10 + 2 = 12 3 x 6 = 15 + 3 = 18 4 x 6 = 20 + 4 = 24 5 x 6 = 25 + 5 = 30 6 x 6 = 30 + 6 = 36 7 x 6 = 35 + 7 = 42 8 x 6 = 40 + 8 = 48 9 x 6 = 45 + 9 = 54 10 x 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
For practicing multiplication, free printable worksheets are available at: kwizNET Learning System (http://www.kwiznet.com/p/takeQuiz.php?ChapterID=1297&Method=Worksheet&NQ4P=3&NQ=24)
- Arithmetic Operations In Various Number Systems (http://www.cut-the-knot.org/blue/SysTable.shtml)
- Abacus In Various Number Systems (http://www.cut-the-knot.org/Curriculum/Arithmetic/Abacus.shtml)
- Soroban In Various Number Systems (http://www.cut-the-knot.org/Curriculum/Arithmetic/Soroban.shtml)
- Suan Pan In Various Number Systems (http://www.cut-the-knot.org/Curriculum/Arithmetic/SuanPan.shtml)nl:Tafels van vermenigvuldiging