Multiplication table

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

Table of contents

1 In basic arithmetic
2 Traditional use
3 Patterns in the tables
4 In abstract algebra
5 External link

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.

A table of multiplication is one of the number from 1 through 10 multiplied by 1 through 10.

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

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 = 50

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.

External link

For practicing multiplication, free printable worksheets are available at: kwizNET Learning System

×	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

×	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

×	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