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# Multiplication table

(Redirected from Multiplication tables)

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, 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.

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. For an example, see octonion.