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Multiplication table

From Simple English Wikipedia, the free encyclopedia
A multiplication table, by Adam Ries (1490s-1559)
18th century version of Napier's bones, a calculation device similar to an abacus

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.[1] 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.[2] 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.[3]

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 1234567891011121314151617181920
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1234567891011121314151617181920
2 0 246810121416182022242628303234363840
3 0 3691215182124273033363942454851545760
4 0 48121620242832364044485256606468727680
5 0 5101520253035404550556065707580859095100
6 0 6121824303642485460667278849096102108114120
7 0 714212835424956637077849198105112119126133140
8 0 81624324048566472808896104112120128136144152160
9 0 918273645546372819099108117126135144153162171180
10 0 102030405060708090100110120130140150160170180190200
11 0 112233445566778899110121132143154165176187198209220
12 0 1224364860728496108120132144156168180192204216228240
13 0 13263952657891104117130143156169182195208221234247260
14 0 14284256708498112126140154168182196210224238252266280
15 0 153045607590105120135150165180195210225240255270285300
16 0 163248648096112128144160176192208224240256272288304320
17 0 1734516885102119136153170187204221238255272289306323340
18 0 1836547290108126144162180198216234252270288306324342360
19 0 1938577695114133152171190209228247266285304323342361380
20 0 20406080100120140160180200220240260280300320340360380400

Warring States decimal multiplication table

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A group of 21 strips of bamboo from 305 BC from the Warring States period is the world's oldest known decimal multiplication table.[4]

This is a Warring States decimal multiplication table used to find 12 × 34.5.

Examples

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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.

Matrix of multiples of 7
Matrix of multiples of 3
Multiplication table of 6 Illustration Multiplication table of 7 Illustration
6 x 1 = 6
6x1
 7 x 1  = 7
7x1
6 x 2  = 12
6x2
 7 x 2  = 14
7x2
6 x 3 = 18
6x3
 7 x 3 = 21
7x3
6 x 4 = 24
6x4
 7 x 4 = 28
7x4
6 x 5 = 30
6x5
 7 x 5 = 35
7x5
6 x 6 = 36
6x6
 7 x 6 = 42
7x6
6 x 7 = 42
6x7
 7 x 7 = 49
7x7
6 x 8 = 48
6x8
 7 x 8 = 56
7x8
6 x 9 = 54
6x9
 7 x 9 = 63
7x9
6 x 10= 60
6x10
 7 x 10= 70
7x10
6 x 11= 66
6x11
 7 x 11= 77
7x11
6 x 12= 72
6x12
 7 x 12= 84
7x12

Other operations

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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
+ 0 1 2 3 4 5 6 7 8 9 10
0 01234 5 6 7 8 9 10
1 12345 6 7 8 9 10 11
2 23456 7 8 9 10 11 12
3 34567 8 9 10 11 12 13
4 45678 9 10 11 12 13 14
5 56789 10 11 12 13 14 15
6 678910 11 12 13 14 15 16
7 7891011 12 13 14 15 16 17
8 89101112 13 14 15 16 17 18
9 910111213 14 15 16 17 18 19
10 1011121314 15 16 17 18 19 20

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.[5][6] 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.[7] Division tables are used for finding the Quotient in the Long division.

Division tables [8]
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 = 12

 2 ÷ 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 = 12

 3 ÷ 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 = 12

 4 ÷ 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 = 12

 5 ÷ 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 = 12

 6 ÷ 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 = 12

7 ÷ 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 = 12

 8 ÷ 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 = 12

 9 ÷ 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 = 12

 10 ÷ 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 = 12

 11 ÷ 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 = 12

 12 ÷ 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

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  1. ↑ Jane Qiu (January 7, 2014). "Ancient times table hidden in Chinese bamboo strips". Nature News. doi:10.1038/nature.2014.14482. S2CID 130132289.
  2. ↑ "Nine-year-olds should recite times tables by heart, says Schools Minister". The Telegraph. Retrieved 2020-09-29.
  3. ↑ "Which times table do you find the hardest?". 3P Learning. 2014-02-21. Archived from the original on 2020-09-23. Retrieved 2020-09-29.
  4. ↑ Nature article The 2,300-year-old matrix is the world's oldest decimal multiplication table
  5. ↑ "Multiplication & Division Table Charts 0-12 Printable PDF (FREE)" (PDF).
  6. ↑ "How to Complete a Division Table". study.com. Retrieved 2020-09-29.
  7. ↑ McIntosh, Janine; Ramagge, Jacqui. "The Improving Mathematics Education in Schools (TIMES) Project". Australian mathematical sciences institute.
  8. ↑ "Division Tables - From 1 to 12 For Easy Printing: With Customization Options". Helping With Math. 2020-02-28. Retrieved 2020-10-01.
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