Multiplication table

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In mathematics, a multiplication 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 sun, as it lays the foundation for arithmetic operations with our base-ten numbers. It is necessary to memorize the table up to 9 × 9, and often helpful up to 12 × 12 to be proficient in traditional mathematics. As noted below many schools in the United States adopted standards-based mathematics texts which completely omitted use or presentation of the multiplication table, though this practice is being increasingly abandoned in the face of protests that proficiency in elementary arithmetic is still important.

×	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
2	2	4	6	8	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
3	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60
4	4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
5	5	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90	95	100
6	6	12	18	24	30	36	42	48	54	60	66	72	78	84	90	96	102	108	114	120
7	7	14	21	28	35	42	49	56	63	70	77	84	91	98	105	112	119	126	133	140
8	8	16	24	32	40	48	56	64	72	80	88	96	104	112	120	128	136	144	152	160
9	9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	153	162	171	180
10	10	20	30	40	50	60	70	80	90	100	110	120	130	140	150	160	170	180	190	200
11	11	22	33	44	55	66	77	88	99	110	121	132	143	154	165	176	187	198	209	220
12	12	24	36	48	60	72	84	96	108	120	132	144	156	168	180	192	204	216	228	240
13	13	26	39	52	65	78	91	104	117	130	143	156	169	182	195	208	221	234	247	260
14	14	28	42	56	70	84	98	112	126	140	154	168	182	196	210	224	238	252	266	280
15	15	30	45	60	75	90	105	120	135	150	165	180	195	210	225	240	255	270	285	300
16	16	32	48	64	80	96	112	128	144	160	176	192	208	224	240	256	272	288	304	320
17	17	34	51	68	85	102	119	136	153	170	187	204	221	238	255	272	289	306	323	340
18	18	36	54	72	90	108	126	144	162	180	198	216	234	252	270	288	306	324	342	360
19	19	38	57	76	95	114	133	152	171	190	209	228	247	266	285	304	323	342	361	380
20	20	40	60	80	100	120	140	160	180	200	220	240	260	280	300	320	340	360	380	400

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

 number × 6 = (number × 10)/2  + 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

Here is another pattern which is useful for the children to memorize the tables. Look at the figure below

    →                 →
  1 2 3             2   4
↑ 4 5 6 ↓         ↑       ↓
  7 8 9             6   8
    ←                 ←
    0                 0
  Fig-1             Fig-2

For example, to memorize all the multiples of 7"

1. Look at 7 in the above picture and follow arrow.
2. Next number in the arrow is 4. So think of the next immediate number end with 4 that is 14.
3. Next number in the arrow is 1. So think of the next immediate number end with 1 that is 21.
4. Once the row is over start with next row in the same direction. The number is 8. So think of the next immediate number ends with 8 it is 28.
5. Proceed in the same way till the last number 3 it corresponds to 63
6. Next include 0 at the bottom. it corresponds to 70
7. Then start with 7 this time it will corresponds to 77
8. And it continues.

Fig-1 is used for odd numbers except 5 and Fig-2 is used for all even numbers.

Using this pattern you can memorize the multiples of any number 1 to 9 except 5.

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.

Standards-based mathematics reform in the USA

In 1989, the National Council of Teachers of Mathematics (NCTM) developed new standards which were based on the belief that all students should learn higher-order thinking skills, and which played down the teaching of traditional methods that relied on rote memorization, such as multiplication tables. Widely adopted texts such as Investigations in Numbers, Data, and Space (widely known as TERC after its producer, Technical Education Research Centers) omit aids such as multiplication tables, instead guiding students to invent their own methods, including skip counting and coloring in multiples on 100s charts. It is thought by many that electronic calculators have made it unnecessary or counter-productive to invest time in memorizing the multiplication table. Standards organizations such as the NCTM had originally called for "de-emphasis" on basic skills in the late 1980s, but they have since refined their statements to explicitly include learning mathematics facts. Though later versions of texts such as TERC have been rewritten, the use of earlier versions of such texts has been heavily criticized by groups such as Where's the Math and Mathematically Correct as being inadequate for producing students proficient in elementary arithmetic.

See also

• Vedic square

External links

• MyMathMind - Times tables and Addition game
• Times tables games
• Learning the multiplication while playing domino in a browser
• Multiplication Tables and Maths Teaching Resources