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Multiplication table

From Academic Kids

In mathematics, a multiplication table is used to define a multiplication operation for an algebraic system.

Contents

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, 51=5.

Multiplication tables vary from country to country. They may have ranges from 11 to 1010, from 21 to 99, or from 11 to 1212 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)

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