Multiplication table

A multiplication table is a tool used to learn how to multiply two numbers. The oldest known multiplication tables were written by the Babylonians about 4000 years ago. Many people think it is important to know how to multiply two numbers by heart, usually up to 12 × 12, 30 × 30, 50 × 50, or 100 × 100.

Most children are introduced to the two, five and 10 times tables by year two - at the age of six and seven. Between the age of seven and eight, children start to learn the three, four and eight times tables. The hardest multiplication is 6×8, which students got wrong 63% of the time. This was closely followed by 8×6, then 11×12, 12×8 and 8×12. The easiest multiplication, on the other hand, was 1×12, which students got wrong less than 5% of the time, followed by 1×6 and 9×1.

In a multiplication table, a number on the first column is multiplied by a number on the first row. The number they corner up to is the answer. In the table below, 12 and 9 are multiplied to get 108, using the table. The numbers in bold are squares (numbers multiplied by themselves).

 ×0 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20 0000000000000000000000 101 2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  20 2 46  8  10  12  14  16  18  20  22  24  26  28  30  32  34  36  38  40  30 3  6 9 12  15  18  21  24  27  30  33  36  39  42  45  48  51  54  57  60  40 4  8  12 16 20  24  28  32  36  40  44  48  52  56  60  64  68  72  76  80  50 5  10  15  20 25 30  35  40  45  50  55  60  65  70  75  80  85  90  95  100  60 6  12  18  24  30 36 42  48  54  60  66  72  78  84  90  96  102  108  114  120  70 7  14  21  28  35  42 49 56  63  70  77  84  91  98  105  112  119  126  133  140  80 8  16  24  32  40  48  56 64 72  80  88  96  104  112  120  128  136  144  152  160  90 9  18  27  36  45  54  63  72 81 90  99  108  117  126  135  144  153  162  171  180  100 10  20  30  40  50  60  70  80  90 100 110  120  130  140  150  160  170  180  190  200  110 11  22  33  44  55  66  77  88  99  110 121 132  143  154  165  176  187  198  209  220  120 12  24  36  48  60  72  84  96  108  120  132 144 156  168  180  192  204  216  228  240  130 13  26  39  52  65  78  91  104  117  130  143  156 169 182  195  208  221  234  247  260  140 14  28  42  56  70  84  98  112  126  140  154  168  182 196 210  224  238  252  266  280  150 15  30  45  60  75  90  105  120  135  150  165  180  195  210 225 240  255  270  285  300  160 16  32  48  64  80  96  112  128  144  160  176  192  208  224  240 256 272  288  304  320  170 17  34  51  68  85  102  119  136  153  170  187  204  221  238  255  272 289 306  323  340  180 18  36  54  72  90  108  126  144  162  180  198  216  234  252  270  288  306 324 342  360  190 19  38  57  76  95  114  133  152  171  190  209  228  247  266  285  304  323  342 361 380  200 20  40  60  80  100  120  140  160  180  200  220  240  260  280  300  320  340  360  380 400

 Warring States decimal multiplication table 

A group of 21 strips of bamboo from 305 BC from the Warring States period is the world's oldest known decimal multiplication table.Nature article The 2,300-year-old matrix is the world's oldest decimal multiplication table

 Examples 
The traditional form of multiplication tables are written in columns with complete number sentences, instead of the standard modern grid. This form is also taught in the schools. Some examples of traditional form of multiplication tables are multiplication tables of 6 and 7 given below.

Multiplication table of 6IllustrationMultiplication table of 7Illustration6 x 1  = 6thumb|6x17 x 1  = 7thumb|7x16 x 2  = 12thumb|6x27 x 2  = 14thumb|7x26 x 3  = 18thumb|6x37 x 3  = 21thumb|7x36 x 4  = 24thumb|6x47 x 4  = 28thumb|7x46 x 5  = 30thumb|6x57 x 5  = 35thumb|7x56 x 6  = 36thumb|6x67 x 6  = 42thumb|7x66 x 7  = 42thumb|6x77 x 7  = 49thumb|7x76 x 8  = 48thumb|6x87 x 8  = 56thumb|7x86 x 9  = 54thumb|6x97 x 9  = 63thumb|7x96 x 10= 60thumb|6x107 x 10= 70thumb|7x106 x 11= 66thumb|6x117 x 11= 77thumb|7x116 x 12= 72thumb|6x127 x 12= 84thumb|7x12

 Other operations 

Addition and Division can also have their own tables. Similarly, Subtraction can also have its own table, although it is not commonly used.

+Addition Table +0123456789100 0  1  2  3  456789101 1  2  3  4  5678910112 2  3  4  5  67891011123 3  4  5  6  789101112134 4  5  6  7  8910111213145 5  6  7  8  91011121314156 6  7  8  9  101112131415167 7  8  9  10  111213141516178 8  9  10  11  121314151617189 9  10  11  12  1314151617181910 10  11  12  13  14151617181920
In mathematics, a division table, like multiplication table, is a mathematical table used to define a division operation for an algebraic system, or to obtain the solution to a certain equation. The division symbol ÷ is used in the division table, known as the obelus. It was first used to signify division in 1659. Mathematicians however, almost never use the ÷ symbol for division. Instead they use fraction notation, called the vinculum. Division tables are used for finding the Quotient in the Long division.
+Division tables 1 ÷ 1 = 1
2 ÷ 1 = 2

3 ÷ 1 = 3

4 ÷ 1 = 4

5 ÷ 1 = 5

6 ÷ 1 = 6

7 ÷ 1 = 7

8 ÷ 1 = 8

9 ÷ 1 = 9

10 ÷ 1 = 10

11 ÷ 1 = 11

12 ÷ 1 = 122 ÷ 2 = 1
4 ÷ 2 = 2

6 ÷ 2 = 3

8 ÷ 2 = 4

10 ÷ 2 = 5

12 ÷ 2 = 6

14 ÷ 2 = 7

16 ÷ 2 = 8

18 ÷ 2 = 9

20 ÷ 2 = 10

22 ÷ 2 = 11

24 ÷ 2 = 123 ÷ 3 = 1
6 ÷ 3 = 2

9 ÷ 3 = 3

12 ÷ 3 = 4

15 ÷ 3 = 5

18 ÷ 3 = 6

21 ÷ 3 = 7

24 ÷ 3 = 8

27 ÷ 3 = 9

30 ÷ 3 = 10

33 ÷ 3 = 11

36 ÷ 3 = 124 ÷ 4 = 1
8 ÷ 4 = 2

12 ÷ 4 = 3

16 ÷ 4 = 4

20 ÷ 4 = 5

24 ÷ 4 = 6

28 ÷ 4 = 7

32 ÷ 4 = 8

36 ÷ 4 = 9

40 ÷ 4 = 10

44 ÷ 4 = 11

48 ÷ 4 = 125 ÷ 5 = 1
10 ÷ 5 = 2

15 ÷ 5 = 3

20 ÷ 5 = 4

25 ÷ 5 = 5

30 ÷ 5 = 6

35 ÷ 5 = 7

40 ÷ 5 = 8

45 ÷ 5 = 9

50 ÷ 5 = 10

55 ÷ 5 = 11

60 ÷ 5 = 126 ÷ 6 = 1
12 ÷ 6 = 2

18 ÷ 6 = 3

24 ÷ 6 = 4

30 ÷ 6 = 5

36 ÷ 6 = 6

42 ÷ 6 = 7

48 ÷ 6 = 8

54 ÷ 6 = 9

60 ÷ 6 = 10

66 ÷ 6 = 11

72 ÷ 6 = 127 ÷ 7 = 1
14 ÷ 7 = 2

21 ÷ 7 = 3

28 ÷ 7 = 4

35 ÷ 7 = 5

42 ÷ 7 = 6

49 ÷ 7 = 7

56 ÷ 7 = 8

63 ÷ 7 = 9

70 ÷ 7 = 10

77 ÷ 7 = 11

84 ÷ 7 = 128 ÷ 8 = 1
16 ÷ 8 = 2

24 ÷ 8 = 3

32 ÷ 8 = 4

40 ÷ 8 = 5

48 ÷ 8 = 6

56 ÷ 8 = 7

64 ÷ 8 = 8

72 ÷ 8 = 9

80 ÷ 8 = 10

88 ÷ 8 = 11

96 ÷ 8 = 129 ÷ 9 = 1
18 ÷ 9 = 2

27 ÷ 9 = 3

36 ÷ 9 = 4

45 ÷ 9 = 5

54 ÷ 9 = 6

63 ÷ 9 = 7

72 ÷ 9 = 8

81 ÷ 9 = 9

90 ÷ 9 = 10

99 ÷ 9 = 11

108 ÷ 9 = 1210 ÷ 10 = 1
20 ÷ 10 = 2

30 ÷ 10 = 3

40 ÷ 10 = 4

50 ÷ 10 = 5

60 ÷ 10 = 6

70 ÷ 10 = 7

80 ÷ 10 = 8

90 ÷ 10 = 9

100 ÷ 10 = 10

110 ÷ 10 = 11

120 ÷ 10 = 1211 ÷ 11 = 1
22 ÷ 11 = 2

33 ÷ 11 = 3

44 ÷ 11 = 4

55 ÷ 11 = 5

66 ÷ 11 = 6

77 ÷ 11 = 7

88 ÷ 11 = 8

99 ÷ 11 = 9

110 ÷ 11 = 10

121 ÷ 11 = 11

132 ÷ 11 = 1212 ÷ 12 = 1
24 ÷ 12 = 2

36 ÷ 12 = 3

48 ÷ 12 = 4

60 ÷ 12 = 5

72 ÷ 12 = 6

84 ÷ 12 = 7

96 ÷ 12 = 8

108 ÷ 12 = 9

120 ÷ 12 = 10

132 ÷ 12 = 11

144 ÷ 12 = 12

References

Category:Arithmetics