Multiplication table

In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.

The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9.

The oldest known multiplication tables were used by the Babylonians about 4000 years ago. However, they used a base of 60. The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China’s Warring States period. “Table of Pythagoras” on Napier’s bones.
— Wikipedia

×	0	1	2	3	4	5	6	7	8	9	10	11	12
0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9	10	11	12
2	0	2	4	6	8	10	12	14	16	18	20	22	24
3	0	3	6	9	12	15	18	21	24	27	30	33	36
4	0	4	8	12	16	20	24	28	32	36	40	44	48
5	0	5	10	15	20	25	30	35	40	45	50	55	60
6	0	6	12	18	24	30	36	42	48	54	60	66	72
7	0	7	14	21	28	35	42	49	56	63	70	77	84
8	0	8	16	24	32	40	48	56	64	72	80	88	96
9	0	9	18	27	36	45	54	63	72	81	90	99	108
10	0	10	20	30	40	50	60	70	80	90	100	110	120
11	0	11	22	33	44	55	66	77	88	99	110	121	132
12	0	12	24	36	48	60	72	84	96	108	120	132	144

Basically multiplication table is set of multiply operations between two numbers. And there no difference which number is first or second, because it’s following Commutative Associative and Distributive Laws property.

Half of the table is a mirror image of the other (diagonal line from top left to bottom right), and you can memorize first part (small number x big number).

You can find that some operations are repeated in the multiplication table and that operations are the patterns.

Better to learn mutliplication table in chunks:

• Columns: 1-5, Rows: 1-5
• Columns: 6-9, Rows: 1-5
• Columns: 1-5, Rows: 6-9. It’s mostly same as previous, but learn/practice it too.
• Columns: 6-9, Rows: 6-9

Patterns

Multiples of even numbers or even and odd numbers are always even numbers. 2x, 4x, 6x, 8x, 10x, 5x6, 9x8, etc.

2× is just doubling the number, 2x2=4, 2x3=6, 2x4=8, 5x2=10, 6x2=12, etc.

5× has a pattern: 5, 10, 15, 20, etc. It ends in either 0 or 5.

9× has a pattern, too: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90. Now, notice how the “ones” place goes down: 9, 8, 7, 6, …? And at the same time, the “tens” place goes up: 1, 2, 3,…? Well, your hands can help! Example: to multiply 9 by 8: hold your 8th finger down, and you can count “7” and “2” … the answer is 72.

10× is maybe the easiest of them all … just put a zero after it.

11× is mostly easy: from 11×2 to 11×9 you just put the two digits together. 11×2=22, 11×3=33, …, 11×9=99 and 11×11=121, 11×12=132

2x12 → double 2x12 → 24 3×12=36 4×12=48 5x12 → ends in 0, 60 (pattern above) 6×12=72 7×12=84 8×12=96 9×12=108 10x12 → add 0, 120

TODO: more patterns Multiplication Tips and Tricks

Training

• Math Trainer - Multiplication

• Multiplication Quiz Interactive multiplication quiz written by me, very simple! Can be found here