Multiplication table

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

In basic arithmetic

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

For example, for multiplication by 6 a pattern emerges: 2 × 6 = 12 4 × 6 = 24 6 × 6 = 36 8 × 6 = 48 10 × 6 = 60

In general: number × 6 = half_of_number_times_10 + number

The 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

Elementary arithmetic

×	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

×	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

Gourt Home::Gourt :: Multiplication table

In basic arithmetic

Traditional use

Patterns in the tables

In abstract algebra

External links

×	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