document_title: Fraction (mathematics)

question_text: what do you call the line in a fraction

question_tokens: what do you call the line in a fraction

text: Fraction (mathematics)

text: Vocabulary

text: In a fraction, the number of equal parts being described is the numerator (from Latin numerātor, "counter" or "numberer"), and the type or variety of the parts is the denominator (from Latin dēnōminātor, "thing that names or designates").[2] As an example, the fraction 8⁄5 amounts to eight parts, each of which is of the type named "fifth." In terms of division, the numerator corresponds to the dividend, and the denominator corresponds to the divisor.

text: Informally, the numerator and denominator may be distinguished by placement alone but in formal contexts they are always separated by a fraction bar. The fraction bar may be horizontal (as in 1/3), oblique (as in 1/5), or diagonal (as in 1⁄9).[3] These marks are respectively known as the horizontal bar, the slash (US) or stroke (UK), the division slash, and the fraction slash.[n 1] In typography, horizontal fractions are also known as "en" or "nut fractions" and diagonal fractions as "em fractions", based on the width of a line they take up.[3]

text: The denominators of English fractions are generally expressed as ordinal numbers, in the plural if the numerator is not one. (For example, 2⁄5 and 3⁄5 are both read as a number of "fifths".) Exceptions include the denominator 2, which is always read "half" or "halves", the denominator 4, which may be alternatively expressed as "quarter"/"quarters" or as "fourth"/"fourths", and the denominator 100, which may be alternatively expressed as "hundredth"/"hundredths" or "percent". When the denominator is 1, it may be expressed in terms of "wholes" but is more commonly ignored, with the numerator read out as a whole number. (For example, 3/1 may be described as "three wholes" or as simply "three".) When the numerator is one, it may be omitted. (For example, "a tenth" or "each quarter".)

text: The entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. (For example, "two-fifths" is the fraction 2/5 and "two fifths" is the same fraction understood as 2 instances of 1⁄5.) Fractions should always be hyphenated when used as adjectives. Alternatively, a fraction may be described by reading it out as the numerator "over" the denominator, with the denominator expressed as a cardinal number. (For example, 3/1 may also be expressed as "three over one".) The term "over" is used even in the case of solidus fractions, where the numbers are placed left and right of a slash mark. (For example, ½ may be read "one-half", "one half", or "one over two".) Fractions with large denominators that are not powers of ten are often rendered in this fashion (e.g., 1/117 as "one over one hundred seventeen") while those with denominators divisible by ten are typically read in the normal ordinal fashion (e.g., 6/1000000 as "six-millionths", "six millionths", or "six one-millionths").

text: Forms of fractions

text: Simple, common, or vulgar fractions

text:
A simple fraction (also known as a common fraction or vulgar fraction) is a rational number written as a/b or

a
b

{\displaystyle {\tfrac {a}{b}}}

, where a and b are both integers.[7] As with other fractions, the denominator (b) cannot be zero. Examples include

1
2

{\displaystyle {\tfrac {1}{2}}}

,

−

8
5

{\displaystyle -{\tfrac {8}{5}}}

,

−
8

5

{\displaystyle {\tfrac {-8}{5}}}

,

8

−
5

{\displaystyle {\tfrac {8}{-5}}}

, and 3/17. Simple fractions can be positive or negative, proper, or improper (see below). Compound fractions, complex fractions, mixed numerals, and decimals (see below) are not simple fractions, though, unless irrational, they can be evaluated to a simple fraction.

text:
A unit fraction is a common fraction with a numerator of 1, e.g.

1
7

{\displaystyle {\tfrac {1}{7}}}

. Unit fractions can also be expressed using negative exponents, as in 2−1, which represents 1/2, and 2−2, which represents 1/(22) or 1/4.
A dyadic fraction is a common fraction in which the denominator is a power of two, e.g.

1
8

=

1

2

3

{\displaystyle {\tfrac {1}{8}}={\tfrac {1}{2^{3}}}}

.

text: Proper and improper fractions

text: Common fractions can be classified as either proper or improper. When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise.[8][9] In general, a common fraction is said to be a proper fraction if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1.[10][11] It is said to be an improper fraction, or sometimes top-heavy fraction,[12] if the absolute value of the fraction is greater than or equal to 1. Examples of proper fractions are 2/3, –3/4, and 4/9; examples of improper fractions are 9/4, –4/3, and 3/3.

text: Reciprocals and the "invisible denominator"

text:
The reciprocal of a fraction is another fraction with the numerator and denominator exchanged. The reciprocal of

3
7

{\displaystyle {\tfrac {3}{7}}}

, for instance, is

7
3

{\displaystyle {\tfrac {7}{3}}}

. The product of a fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1, that is, numerator and denominator are not equal, is a proper fraction.

text:
When the numerator and denominator of a fraction are equal (

7
7

{\displaystyle {\tfrac {7}{7}}}

, for example), its value is 1, and the fraction therefore is improper. Its reciprocal also has the value 1, and is improper, too.

text:
Any integer can be written as a fraction with the number one as denominator. For example, 17 can be written as

17
1

{\displaystyle {\tfrac {17}{1}}}

, where 1 is sometimes referred to as the invisible denominator. Therefore, every fraction or integer, except for zero, has a reciprocal. The reciprocal of 17 is

1
17

{\displaystyle {\tfrac {1}{17}}}

.

text: Ratios

text: A ratio is a relationship between two or more numbers that can be sometimes expressed as a fraction. Typically, a number of items are grouped and compared in a ratio, specifying numerically the relationship between each group. Ratios are expressed as "group 1 to group 2 ... to group n". For example, if a car lot had 12 vehicles, of which

text:
2 are white,
6 are red, and
4 are yellow,

text: then the ratio of red to white to yellow cars is 6 to 2 to 4. The ratio of yellow cars to white cars is 4 to 2 and may be expressed as 4:2 or 2:1.

text: A ratio is often converted to a fraction when it is expressed as a ratio to the whole. In the above example, the ratio of yellow cars to all the cars on the lot is 4:12 or 1:3. We can convert these ratios to a fraction and say that 4/12 of the cars or ⅓ of the cars in the lot are yellow. Therefore, if a person randomly chose one car on the lot, then there is a one in three chance or probability that it would be yellow.

text: Decimal fractions and percentages

text:
A decimal fraction is a fraction whose denominator is not given explicitly, but is understood to be an integer power of ten. Decimal fractions are commonly expressed using decimal notation in which the implied denominator is determined by the number of digits to the right of a decimal separator, the appearance of which (e.g., a period, a raised period (•), a comma) depends on the locale (for examples, see decimal separator). Thus for 0.75 the numerator is 75 and the implied denominator is 10 to the second power, viz. 100, because there are two digits to the right of the decimal separator. In decimal numbers greater than 1 (such as 3.75), the fractional part of the number is expressed by the digits to the right of the decimal (with a value of 0.75 in this case). 3.75 can be written either as an improper fraction, 375/100, or as a mixed number,

3

75
100

{\displaystyle 3{\tfrac {75}{100}}}

.

text: Decimal fractions can also be expressed using scientific notation with negative exponents, such as 6993602299999999999♠6.023×10−7, which represents 0.0000006023. The 6993100000000000000♠10−7 represents a denominator of 7007100000000000000♠107. Dividing by 7007100000000000000♠107 moves the decimal point 7 places to the left.

text: Decimal fractions with infinitely many digits to the right of the decimal separator represent an infinite series. For example, ⅓ = 0.333... represents the infinite series 3/10 + 3/100 + 3/1000 + ... .

text: Another kind of fraction is the percentage (Latin per centum meaning "per hundred", represented by the symbol %), in which the implied denominator is always 100. Thus, 51% means 51/100. Percentages greater than 100 or less than zero are treated in the same way, e.g. 311% equals 311/100, and −27% equals −27/100.

text: The related concept of permille or parts per thousand (ppt) has an implied denominator of 1000, while the more general parts-per notation, as in 75 parts per million (ppm), means that the proportion is 75/1,000,000.

text: Whether common fractions or decimal fractions are used is often a matter of taste and context. Common fractions are used most often when the denominator is relatively small. By mental calculation, it is easier to multiply 16 by 3/16 than to do the same calculation using the fraction's decimal equivalent (0.1875). And it is more accurate to multiply 15 by 1/3, for example, than it is to multiply 15 by any decimal approximation of one third. Monetary values are commonly expressed as decimal fractions with denominator 100, i.e., with two decimals, for example $3.75. However, as noted above, in pre-decimal British currency, shillings and pence were often given the form (but not the meaning) of a fraction, as, for example 3/6 (read "three and six") meaning 3 shillings and 6 pence, and having no relationship to the fraction 3/6.

text: Mixed numbers

text:
A mixed numeral (also called a mixed fraction or mixed number) is a traditional denotation of the sum of a non-zero integer and a proper fraction (having the same sign). It is used primarily in measurement:

2

3
16

{\displaystyle 2{\tfrac {3}{16}}}

 inches, for example. Scientific measurements almost invariably use decimal notation rather than mixed numbers. The sum is implied without the use of a visible operator such as the appropriate "+". For example, in referring to two entire cakes and three quarters of another cake, the numerals denoting the integer part and the fractional part of the cakes are written next to each other as

2

3
4

{\displaystyle 2{\tfrac {3}{4}}}

 instead of the unambiguous notation

2
+

3
4

.

{\displaystyle 2+{\tfrac {3}{4}}.}

 Negative mixed numerals, as in

−
2

3
4

{\displaystyle -2{\tfrac {3}{4}}}

, are treated like

−
(
2
+

3
4

)
.

{\displaystyle -(2+{\tfrac {3}{4}}).}

 Any such sum of a whole plus a part can be converted to an improper fraction by applying the rules of adding unlike quantities.

text:
This tradition is, formally, in conflict with the notation in algebra where adjacent factors denote a product, without an explicit infix operator. When two algebraic expressions are written next to each other, the operation of multiplication is implied by this general rule:

2
x

{\displaystyle 2x}

 always means the product of

2

{\displaystyle 2}

 and

x

{\displaystyle x}

, even if the value of

x

{\displaystyle x}

 is a fraction. The expression

2

b
c

{\displaystyle 2{\tfrac {b}{c}}}

 for example is not a mixed number, instead, multiplication is expressly required, where

2

b
c

=
2
⋅

b
c

.

{\displaystyle 2{\tfrac {b}{c}}=2\cdot {\tfrac {b}{c}}.}

text:
For better readability, the multiplication is sometimes made explicit or parentheses are added. So,

2

b
c

{\displaystyle 2{\tfrac {b}{c}}}

 may be written as

text: An improper fraction can be converted to a mixed number as follows:

text:
Divide the numerator by the denominator. In the example,

11
4

{\displaystyle {\tfrac {11}{4}}}

, divide 11 by 4. 11 ÷ 4 = 2 with remainder 3.
The quotient (without the remainder) becomes the whole number part of the mixed number. The remainder becomes the numerator of the fractional part. In the example, 2 is the whole number part and 3 is the numerator of the fractional part.
The new denominator is the same as the denominator of the improper fraction. In the example, they are both 4. Thus

11
4

=
2

3
4

{\displaystyle {\tfrac {11}{4}}=2{\tfrac {3}{4}}}

.

text: Historical notions

text: Egyptian fraction

text:
An Egyptian fraction is the sum of distinct positive unit fractions, for example

1
2

+

1
3

{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{3}}}

. This definition derives from the fact that the ancient Egyptians expressed all fractions except

1
2

{\displaystyle {\tfrac {1}{2}}}

,

2
3

{\displaystyle {\tfrac {2}{3}}}

 and

3
4

{\displaystyle {\tfrac {3}{4}}}

 in this manner. Every positive rational number can be expanded as an Egyptian fraction. For example,

5
7

{\displaystyle {\tfrac {5}{7}}}

 can be written as

1
2

+

1
6

+

1
21

.

{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{6}}+{\tfrac {1}{21}}.}

 Any positive rational number can be written as a sum of unit fractions in infinitely many ways. Two ways to write

13
17

{\displaystyle {\tfrac {13}{17}}}

 are

1
2

+

1
4

+

1
68

{\displaystyle {\tfrac {1}{2}}+{\tfrac {1}{4}}+{\tfrac {1}{68}}}

 and

1
3

+

1
4

+

1
6

+

1
68

{\displaystyle {\tfrac {1}{3}}+{\tfrac {1}{4}}+{\tfrac {1}{6}}+{\tfrac {1}{68}}}

.

text: 'Complex' and 'Compound' fractions

text: Both notions are outdated[13] and nowadays used in no well defined manner, partly even taken synonymously for each other[14] or for mixed numerals.[15] They lost their meaning as technical terms and the attributes "complex" and "compound" tend to be used in their every day meaning of "consisting of parts".

text: Complex fractions

text:
In a complex fraction, either the numerator, or the denominator, or both, is a fraction or a mixed number,[16][17] corresponding to division of fractions. For example,

1
2

1
3

{\displaystyle {\frac {\tfrac {1}{2}}{\tfrac {1}{3}}}}

 and

12

3
4

26

{\displaystyle {\frac {12{\tfrac {3}{4}}}{26}}}

 are complex fractions. To reduce a complex fraction to a simple fraction, treat the longest fraction line as representing division. For example:

text: If, in a complex fraction, there is no unique way to tell which fraction lines takes precedence, then this expression is improperly formed, because of ambiguity. So 5/10/20/40 is not a valid mathematical expression, because of multiple possible interpretations, e.g. as

text: Compound fractions

text:
A compound fraction is a fraction of a fraction, or any number of fractions connected with the word of,[16][17] corresponding to multiplication of fractions. To reduce a compound fraction to a simple fraction, just carry out the multiplication (see the section on multiplication). For example,

3
4

{\displaystyle {\tfrac {3}{4}}}

 of

5
7

{\displaystyle {\tfrac {5}{7}}}

 is a compound fraction, corresponding to

3
4

×

5
7

=

15
28

{\displaystyle {\tfrac {3}{4}}\times {\tfrac {5}{7}}={\tfrac {15}{28}}}

. The terms compound fraction and complex fraction are closely related and sometimes one is used as a synonym for the other. (For example, the compound fraction

3
4

×

5
7

{\displaystyle {\tfrac {3}{4}}\times {\tfrac {5}{7}}}

 is equivalent to the complex fraction

3

/

4

7

/

5

{\displaystyle {\tfrac {3/4}{7/5}}}

.)

text: Arithmetic with fractions

text: Like whole numbers, fractions obey the commutative, associative, and distributive laws, and the rule against division by zero.

text: Equivalent fractions

text:
Multiplying the numerator and denominator of a fraction by the same (non-zero) number results in a fraction that is equivalent to the original fraction. This is true because for any non-zero number

n

{\displaystyle n}

, the fraction

n
n

=
1

{\displaystyle {\tfrac {n}{n}}=1}

. Therefore, multiplying by

n
n

{\displaystyle {\tfrac {n}{n}}}

 is equivalent to multiplying by one, and any number multiplied by one has the same value as the original number. By way of an example, start with the fraction

1
2

{\displaystyle {\tfrac {1}{2}}}

. When the numerator and denominator are both multiplied by 2, the result is

2
4

{\displaystyle {\tfrac {2}{4}}}

, which has the same value (0.5) as

1
2

{\displaystyle {\tfrac {1}{2}}}

. To picture this visually, imagine cutting a cake into four pieces; two of the pieces together (

2
4

{\displaystyle {\tfrac {2}{4}}}

) make up half the cake (

1
2

{\displaystyle {\tfrac {1}{2}}}

).

text:
Dividing the numerator and denominator of a fraction by the same non-zero number will also yield an equivalent fraction. This is called reducing or simplifying the fraction. A simple fraction in which the numerator and denominator are coprime (that is, the only positive integer that goes into both the numerator and denominator evenly is 1) is said to be irreducible, in lowest terms, or in simplest terms. For example,

3
9

{\displaystyle {\tfrac {3}{9}}}

 is not in lowest terms because both 3 and 9 can be exactly divided by 3. In contrast,

3
8

{\displaystyle {\tfrac {3}{8}}}

 is in lowest terms—the only positive integer that goes into both 3 and 8 evenly is 1.

text:
Using these rules, we can show that

5
10

{\displaystyle {\tfrac {5}{10}}}

 =

1
2

{\displaystyle {\tfrac {1}{2}}}

 =

10
20

{\displaystyle {\tfrac {10}{20}}}

 =

50
100

{\displaystyle {\tfrac {50}{100}}}

.

text:
A common fraction can be reduced to lowest terms by dividing both the numerator and denominator by their greatest common divisor. For example, as the greatest common divisor of 63 and 462 is 21, the fraction

63
462

{\displaystyle {\tfrac {63}{462}}}

 can be reduced to lowest terms by dividing the numerator and denominator by 21:

text: The Euclidean algorithm gives a method for finding the greatest common divisor of any two positive integers.

text: Comparing fractions

text: Comparing fractions with the same positive denominator yields the same result as comparing the numerators:

text: If the equal denominators are negative, then the opposite result of comparing the numerators holds for the fractions:

text: If two positive fractions have the same numerator, then the fraction with the smaller denominator is the larger number. When a whole is divided into equal pieces, if fewer equal pieces are needed to make up the whole, then each piece must be larger. When two positive fractions have the same numerator, they represent the same number of parts, but in the fraction with the smaller denominator, the parts are larger.

text:
One way to compare fractions with different numerators and denominators is to find a common denominator. To compare

a
b

{\displaystyle {\tfrac {a}{b}}}

 and

c
d

{\displaystyle {\tfrac {c}{d}}}

, these are converted to

a
⋅
d

b
⋅
d

{\displaystyle {\tfrac {a\cdot d}{b\cdot d}}}

 and

b
⋅
c

b
⋅
d

{\displaystyle {\tfrac {b\cdot c}{b\cdot d}}}

. Then bd is a common denominator and the numerators ad and bc can be compared. This modification of the two fractions is known as "cross multiplying"[citation needed], and it is not necessary to determine the value of the common denominator to compare fractions – one can just compare ad and bc, without evaluating bd, e.g., comparing

2
3

{\displaystyle {\tfrac {2}{3}}}

 ?

1
2

{\displaystyle {\tfrac {1}{2}}}

 gives

4
6

>

3
6

{\displaystyle {\tfrac {4}{6}}>{\tfrac {3}{6}}}

.

text:
For the more laborious question

5
18

{\displaystyle {\tfrac {5}{18}}}

 ?

4
17

,

{\displaystyle {\tfrac {4}{17}},}

 multiply top and bottom of each fraction by the denominator of the other fraction, to get a common denominator, yielding

5
×
17

18
×
17

{\displaystyle {\tfrac {5\times 17}{18\times 17}}}

 ?

18
×
4

18
×
17

{\displaystyle {\tfrac {18\times 4}{18\times 17}}}

. It is not necessary to calculate

18
×
17

{\displaystyle 18\times 17}

 – only the numerators need to be compared. Since 5×17 (= 85) is greater than 4×18 (= 72), the result of comparing is

5
18

>

4
17

{\displaystyle {\tfrac {5}{18}}>{\tfrac {4}{17}}}

.

text: Because every negative number, including negative fractions, is less than zero, and every positive number, including positive fractions, is greater than zero, it follows that any negative fraction is less than any positive fraction. This allows, together with the above rules, to compare all possible fractions.

text: Addition

text: The first rule of addition is that only like quantities can be added; for example, various quantities of quarters. Unlike quantities, such as adding thirds to quarters, must first be converted to like quantities as described below: Imagine a pocket containing two quarters, and another pocket containing three quarters; in total, there are five quarters. Since four quarters is equivalent to one (dollar), this can be represented as follows:

text: Adding unlike quantities

text:
To add fractions containing unlike quantities (e.g. quarters and thirds), it is necessary to convert all amounts to like quantities. It is easy to work out the chosen type of fraction to convert to; simply multiply together the two denominators (bottom number) of each fraction. In case of an integer number apply the invisible denominator

1.

{\displaystyle 1.}

text: For adding quarters to thirds, both types of fraction are converted to twelfths, thus:

text: Consider adding the following two quantities:

text:
First, convert

3
5

{\displaystyle {\tfrac {3}{5}}}

 into fifteenths by multiplying both the numerator and denominator by three:

3
5

×

3
3

=

9
15

{\displaystyle {\tfrac {3}{5}}\times {\tfrac {3}{3}}={\tfrac {9}{15}}}

. Since

3
3

{\displaystyle {\tfrac {3}{3}}}

 equals 1, multiplication by

3
3

{\displaystyle {\tfrac {3}{3}}}

 does not change the value of the fraction.

text:
Second, convert

2
3

{\displaystyle {\tfrac {2}{3}}}

 into fifteenths by multiplying both the numerator and denominator by five:

2
3

×

5
5

=

10
15

{\displaystyle {\tfrac {2}{3}}\times {\tfrac {5}{5}}={\tfrac {10}{15}}}

.

text: Now it can be seen that:

text: is equivalent to:

text: This method can be expressed algebraically:

text: And for expressions consisting of the addition of three fractions:

text:
This method always works, but sometimes there is a smaller denominator that can be used (a least common denominator). For example, to add

3
4

{\displaystyle {\tfrac {3}{4}}}

 and

5
12

{\displaystyle {\tfrac {5}{12}}}

 the denominator 48 can be used (the product of 4 and 12), but the smaller denominator 12 may also be used, being the least common multiple of 4 and 12.

text: Subtraction

text: The process for subtracting fractions is, in essence, the same as that of adding them: find a common denominator, and change each fraction to an equivalent fraction with the chosen common denominator. The resulting fraction will have that denominator, and its numerator will be the result of subtracting the numerators of the original fractions. For instance,

text: Multiplication

text: Multiplying a fraction by another fraction

text: To multiply fractions, multiply the numerators and multiply the denominators. Thus:

text: To explain the process, consider one third of one quarter. Using the example of a cake, if three small slices of equal size make up a quarter, and four quarters make up a whole, twelve of these small, equal slices make up a whole. Therefore, a third of a quarter is a twelfth. Now consider the numerators. The first fraction, two thirds, is twice as large as one third. Since one third of a quarter is one twelfth, two thirds of a quarter is two twelfth. The second fraction, three quarters, is three times as large as one quarter, so two thirds of three quarters is three times as large as two thirds of one quarter. Thus two thirds times three quarters is six twelfths.

text: A short cut for multiplying fractions is called "cancellation". Effectively the answer is reduced to lowest terms during multiplication. For example:

text: A two is a common factor in both the numerator of the left fraction and the denominator of the right and is divided out of both. Three is a common factor of the left denominator and right numerator and is divided out of both.

text: Multiplying a fraction by a whole number

text: Since a whole number can be rewritten as itself divided by 1, normal fraction multiplication rules can still apply.

text: Multiplying mixed numbers

text: When multiplying mixed numbers, it is considered preferable[citation needed] to convert the mixed number into an improper fraction. For example:

text:
In other words,

2

3
4

{\displaystyle 2{\tfrac {3}{4}}}

 is the same as

8
4

+

3
4

{\displaystyle {\tfrac {8}{4}}+{\tfrac {3}{4}}}

, making 11 quarters in total (because 2 cakes, each split into quarters makes 8 quarters total) and 33 quarters is

8

1
4

{\displaystyle 8{\tfrac {1}{4}}}

, since 8 cakes, each made of quarters, is 32 quarters in total.

text: Division

text:
To divide a fraction by a whole number, you may either divide the numerator by the number, if it goes evenly into the numerator, or multiply the denominator by the number. For example,

10
3

÷
5

{\displaystyle {\tfrac {10}{3}}\div 5}

 equals

2
3

{\displaystyle {\tfrac {2}{3}}}

 and also equals

10

3
⋅
5

=

10
15

{\displaystyle {\tfrac {10}{3\cdot 5}}={\tfrac {10}{15}}}

, which reduces to

2
3

{\displaystyle {\tfrac {2}{3}}}

. To divide a number by a fraction, multiply that number by the reciprocal of that fraction. Thus,

1
2

÷

3
4

=

1
2

×

4
3

=

1
⋅
4

2
⋅
3

=

2
3

{\displaystyle {\tfrac {1}{2}}\div {\tfrac {3}{4}}={\tfrac {1}{2}}\times {\tfrac {4}{3}}={\tfrac {1\cdot 4}{2\cdot 3}}={\tfrac {2}{3}}}

.

text: Converting between decimals and fractions

text:
To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator (this is idiomatically also phrased as "divide the denominator into the numerator"), and round the answer to the desired accuracy. For example, to change ¼ to a decimal, divide

1.00

{\displaystyle 1.00}

 by

4

{\displaystyle 4}

 ("

4

{\displaystyle 4}

 into

1.00

{\displaystyle 1.00}

"), to obtain

0.25

{\displaystyle 0.25}

. To change ⅓ to a decimal, divide

1.000...

{\displaystyle 1.000...}

 by

3

{\displaystyle 3}

 ("

3

{\displaystyle 3}

 into

1.0000...

{\displaystyle 1.0000...}

"), and stop when the desired accuracy is obtained, e.g., at

4

{\displaystyle 4}

 decimals with

0.3333

{\displaystyle 0.3333}

. Note that ¼ can be written exactly with two decimal digits, while the fraction ⅓ cannot be written exactly as a decimal with a finite number of digits. To change a decimal to a fraction, write in the denominator a

1

{\displaystyle 1}

 followed by as many zeroes as there are digits to the right of the decimal point, and write in the numerator all the digits of the original decimal, just omitting the decimal point. Thus

12.3456
=

123456
10000

.

{\displaystyle 12.3456={\tfrac {123456}{10000}}.}

text: Converting repeating decimals to fractions

text: Decimal numbers, while arguably more useful to work with when performing calculations, sometimes lack the precision that common fractions have. Sometimes an infinite repeating decimal is required to reach the same precision. Thus, it is often useful to convert repeating decimals into fractions.

text: The preferred way to indicate a repeating decimal is to place a bar over the digits that repeat, for example 0.789 = 0.789789789… For repeating patterns where the repeating pattern begins immediately after the decimal point, a simple division of the pattern by the same number of nines as numbers it has will suffice. For example:

text: In case leading zeros precede the pattern, the nines are suffixed by the same number of trailing zeros:

text: In case a non-repeating set of decimals precede the pattern (such as 0.1523987), we can write it as the sum of the non-repeating and repeating parts, respectively:

text: Then, convert both parts to fractions, and add them using the methods described above:

text: Alternatively, algebra can be used, such as below:

text:
Let x = the repeating decimal:

x = 0.1523987

Multiply both sides by the power of 10 just great enough (in this case 104) to move the decimal point just before the repeating part of the decimal number:

10,000x = 1,523.987

Multiply both sides by the power of 10 (in this case 103) that is the same as the number of places that repeat:

10,000,000x = 1,523,987.987

Subtract the two equations from each other (if a = b and c = d, then a − c = b − d):

10,000,000x − 10,000x = 1,523,987.987 − 1,523.987

Continue the subtraction operation to clear the repeating decimal:

9,990,000x = 1,523,987 − 1,523
9,990,000x = 1,522,464

Divide both sides by 9,990,00 to represent x as a fraction

x = 1522464/9990000

text: Fractions in abstract mathematics

text:
In addition to being of great practical importance, fractions are also studied by mathematicians, who check that the rules for fractions given above are consistent and reliable. Mathematicians define a fraction as an ordered pair

(
a
,
b
)

{\displaystyle (a,b)}

 of integers

a

{\displaystyle a}

 and

b
≠
0
,

{\displaystyle b\neq 0,}

 for which the operations addition, subtraction, multiplication, and division are defined as follows:[18]

text: These definitions agree in every case with the definitions given above; only the notation is different. Alternatively, instead of defining subtraction and division as operations, the "inverse" fractions with respect to addition and multiplication might be defined as:

text: Furthermore, the relation, specified as

text: is an equivalence relation of fractions. Each fraction from one equivalence class may be considered as a representative for the whole class, and each whole class may be considered as one abstract fraction. This equivalence is preserved by the above defined operations, i.e., the results of operating on fractions are independent of the selection of representatives from their equivalence class. Formally, for addition of fractions

text: and similarly for the other operations.

text:
In case of fractions of integers the fractions with

(
a
,
b
)

{\displaystyle (a,b)}

 coprime are often taken as uniquely determined representatives for their equivalent fractions, which are considered to be the same rational number. This way the fractions of integers make up the field of the rational numbers.

text: More generally, a and b may be elements of any integral domain R, in which case a fraction is an element of the field of fractions of R. For example, polynomials in one indeterminate, with coefficients from some integral domain D, are themselves an integral domain, call it P. So for a and b elements of P, the generated field of fractions is the field of rational fractions (also known as the field of rational functions).

text: Algebraic fractions

text:
An algebraic fraction is the indicated quotient of two algebraic expressions. As with fractions of integers, the denominator of an algebraic fraction cannot be zero. Two examples of algebraic fractions are

3
x

x

2

+
2
x
−
3

{\displaystyle {\frac {3x}{x^{2}+2x-3}}}

 and

x
+
2

x

2

−
3

{\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}}}

. Algebraic fractions are subject to the same field properties as arithmetic fractions.

text:
If the numerator and the denominator are polynomials, as in

3
x

x

2

+
2
x
−
3

{\displaystyle {\frac {3x}{x^{2}+2x-3}}}

, the algebraic fraction is called a rational fraction (or rational expression). An irrational fraction is one that is not rational, as, for example, one that contains the variable under a fractional exponent or root, as in

x
+
2

x

2

−
3

{\displaystyle {\frac {\sqrt {x+2}}{x^{2}-3}}}

.

text:
The terminology used to describe algebraic fractions is similar to that used for ordinary fractions. For example, an algebraic fraction is in lowest terms if the only factors common to the numerator and the denominator are 1 and −1. An algebraic fraction whose numerator or denominator, or both, contain a fraction, such as

1
+

1
x

1
−

1
x

{\displaystyle {\frac {1+{\tfrac {1}{x}}}{1-{\tfrac {1}{x}}}}}

, is called a complex fraction.

text:
The field of rational numbers is the field of fractions of the integers, while the integers themselves are not a field but rather an integral domain. Similarly, the rational expressions are the field of fractions of polynomials. There are different integral domains of polynomials, depending on the integral domain the coefficients of the polynomials are from (e.g. from integers, real numbers, complex numbers, ...). Considering the field of fractions generated by polynomials with real coefficients, radical expressions such as

2

/

2

{\displaystyle \textstyle {\sqrt {2}}/2}

 are also rational fractions, as is the transcendental expression

π

/

2

{\displaystyle \pi /2}

, since all of

2

,
π
,

{\displaystyle {\sqrt {2}},\pi ,}

 and

2

{\displaystyle 2}

 are (constant) polynomials over the reals. These same expressions, however, would not be considered elements of the field of fractions generated by polynomials with integer coefficients. This specific field would contain just the

2

{\displaystyle 2}

 of the three polynomials above, or

1

/

2

{\displaystyle 1/2}

 as fraction, but no radical or transcendental expressions.

text:
The term partial fraction is used when decomposing rational expressions into sums. The goal is to write the rational expression as the sum of other rational expressions with denominators of lesser degree. For example, the rational expression

2
x

x

2

−
1

{\displaystyle {\frac {2x}{x^{2}-1}}}

 can be rewritten as the sum of two fractions:

1

x
+
1

+

1

x
−
1

{\displaystyle {\frac {1}{x+1}}+{\frac {1}{x-1}}}

. This is useful in many areas such as integral calculus and differential equations.

text: Radical expressions

text: A fraction may also contain radicals in the numerator and/or the denominator. If the denominator contains radicals, it can be helpful to rationalize it (compare Simplified form of a radical expression), especially if further operations, such as adding or comparing that fraction to another, are to be carried out. It is also more convenient if division is to be done manually. When the denominator is a monomial square root, it can be rationalized by multiplying both the top and the bottom of the fraction by the denominator:

text: The process of rationalization of binomial denominators involves multiplying the top and the bottom of a fraction by the conjugate of the denominator so that the denominator becomes a rational number. For example:

text: Even if this process results in the numerator being irrational, like in the examples above, the process may still facilitate subsequent manipulations by reducing the number of irrationals one has to work with in the denominator.

text: Typographical variations

text: In computer displays and typography, simple fractions are sometimes printed as a single character, e.g. ½ (one half). See the article on Number Forms for information on doing this in Unicode.

text: Scientific publishing distinguishes four ways to set fractions, together with guidelines on use:[19]

text:
special fractions: fractions that are presented as a single character with a slanted bar, with roughly the same height and width as other characters in the text. Generally used for simple fractions, such as: ½, ⅓, ⅔, ¼, and ¾. Since the numerals are smaller, legibility can be an issue, especially for small-sized fonts. These are not used in modern mathematical notation, but in other contexts.
case fractions: similar to special fractions, these are rendered as a single typographical character, but with a horizontal bar, thus making them upright. An example would be

1
2

{\displaystyle {\tfrac {1}{2}}}

, but rendered with the same height as other characters. Some sources include all rendering of fractions as case fractions if they take only one typographical space, regardless of the direction of the bar.[20]
shilling or solidus fractions: 1/2, so called because this notation was used for pre-decimal British currency (£sd), as in 2/6 for a half crown, meaning two shillings and six pence. While the notation "two shillings and six pence" did not represent a fraction, the forward slash is now used in fractions, especially for fractions inline with prose (rather than displayed), to avoid uneven lines. It is also used for fractions within fractions (complex fractions) or within exponents to increase legibility. Fractions written this way, also known as piece fractions,[21] are written all on one typographical line, but take 3 or more typographical spaces.
built-up fractions:

1
2

{\displaystyle {\frac {1}{2}}}

. This notation uses two or more lines of ordinary text, and results in a variation in spacing between lines when included within other text. While large and legible, these can be disruptive, particularly for simple fractions or within complex fractions.

text: History

text: The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on.[22] The Egyptians used Egyptian fractions c. 1000 BC. About 4000 years ago, Egyptians divided with fractions using slightly different methods. They used least common multiples with unit fractions. Their methods gave the same answer as modern methods.[23] The Egyptians also had a different notation for dyadic fractions in the Akhmim Wooden Tablet and several Rhind Mathematical Papyrus problems.

text: The Greeks used unit fractions and (later) continued fractions. Followers of the Greek philosopher Pythagoras (c. 530 BC) discovered that the square root of two cannot be expressed as a fraction of integers. (This is commonly though probably erroneously ascribed to Hippasus of Metapontum, who is said to have been executed for revealing this fact.) In 150 BC Jain mathematicians in India wrote the "Sthananga Sutra", which contains work on the theory of numbers, arithmetical operations, and operations with fractions.

text: A modern expression of fractions known as bhinnarasi seems to have originated in India in the work of Aryabhatta (c. AD 500),[citation needed] Brahmagupta (c. 628), and Bhaskara (c. 1150).[24] Their works form fractions by placing the numerators (Sanskrit: amsa) over the denominators (cheda), but without a bar between them.[24] In Sanskrit literature, fractions were always expressed as an addition to or subtraction from an integer.[citation needed] The integer was written on one line and the fraction in its two parts on the next line. If the fraction was marked by a small circle ⟨०⟩ or cross ⟨+⟩, it is subtracted from the integer; if no such sign appears, it is understood to be added. For example, Bhaskara I writes[25]

text: which is the equivalent of

text: and would be written in modern notation as 61/4, 11/5, and 2−1/9 (i.e., 18/9).

text:
The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200),[24] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence. In his discussion he writes, "... for example, if you are told to write three-fifths and a third of a fifth, write thus,

3

1

5

3

{\displaystyle {\frac {3\quad 1}{5\quad 3}}}

."[26] The same fractional notation—with the fraction given before the integer[24]—appears soon after in the work of Leonardo Fibonacci in the 13th century.[27]

text: In discussing the origins of decimal fractions, Dirk Jan Struik states:[28]

text: "The introduction of decimal fractions as a common computational practice can be dated back to the Flemish pamphlet De Thiende, published at Leyden in 1585, together with a French translation, La Disme, by the Flemish mathematician Simon Stevin (1548–1620), then settled in the Northern Netherlands. It is true that decimal fractions were used by the Chinese many centuries before Stevin and that the Persian astronomer Al-Kāshī used both decimal and sexagesimal fractions with great ease in his Key to arithmetic (Samarkand, early fifteenth century)."[29]

text: While the Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century, J. Lennart Berggren notes that he was mistaken, as decimal fractions were first used five centuries before him by the Baghdadi mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century.[30][n 2]

text: In formal education

text: Pedagogical tools

text: In primary schools, fractions have been demonstrated through Cuisenaire rods, Fraction Bars, fraction strips, fraction circles, paper (for folding or cutting), pattern blocks, pie-shaped pieces, plastic rectangles, grid paper, dot paper, geoboards, counters and computer software.

text: Documents for teachers

text:
Several states in the United States have adopted learning trajectories from the Common Core State Standards Initiative's guidelines for mathematics education. Aside from sequencing the learning of fractions and operations with fractions, the document provides the following definition of a fraction: "A number expressible in the form

a
b

{\displaystyle {\tfrac {a}{b}}}

 where

a

{\displaystyle a}

 is a whole number and

b

{\displaystyle b}

 is a positive whole number. (The word fraction in the standards always refers to a non-negative number.)"[32] The document itself also refers to negative fractions.


document_title: BBC Goal of the Season

question_text: who won premier league goal of the season

root

text: BBC Goal of the Season

text: In English football, the Goal of the Season is an annual competition and award given on BBC's Match of the Day, in honour of the most spectacular goal scored that season. It is typically contested between the winners of the preceding ten Goals of the Month, although the goal can and has come from any game in the regular season, including international qualifiers and friendlies—potentially from the opening league games of the season to the end of the European season UEFA Champions League final. In several instances, the goal has come in the final game of the domestic season, the FA Cup Final, the most recent example of which is Steven Gerrard's last minute goal in 2006. However, in 1980-81 for example the superb goal scored by Ricky Villa in the FA Cup Final replay for Tottenham Hotspur against Manchester City could not be considered as voting had already taken place.[1]

tag: p

text: In general, the winning goal has occurred for an English side within the domestic English league or cups, although these are not particular rules—Kenny Dalglish's goal in 1982–83 for Scotland being an example. The goal usually comes from competitions to which the BBC holds television rights and which are shown under the Match of the Day banner—at present Premier League highlights and FA Cup live matches and highlights —although some have come from the equivalent Sportscene broadcast by BBC Scotland. Due to the lack of BBC European club football coverage, held predominantly by ITV and Sky, no goal of the season has ever been scored in European club competition despite many contenders.

text: Due to a transfer of broadcast rights, the entries for the 2001–02, 2002–03 and 2003–04 seasons were decided on ITV's The Premiership, which have been subsequently recognised by the BBC. When the BBC previously could not show league footage from 1988–89 to 1991–92, the winning goal in each season was scored in the FA Cup which they held the rights to. League rights holder ITV had its own competition during these seasons for Goal of the Season, broadcast on the Saint and Greavsie show. Previously the channels had shared league and cup rights (showing different matches to each other) and for many years ITV broadcast its own Golden Goals competition as an equivalent of Goal of the Season. From 2013–14 season onwards, the Goal of the Season has been chosen by a Twitter poll and the BBC Sport website. Jack Wilshere is the first player to win Goal of the Season in consecutive seasons (2013–14 and 2014–15) since the start of the Premier League.[2] The 1987-88 competition was unique in that all 10 goals shortlisted were scored by Liverpool players.[3] As of 2015-16, this is the only occasion where the contenders were made up entirely of goals scored by players for one club.

text: For several years in the late 2000s, the winner was not subject to public vote due to the 2007 Phone-in scandals. The winning goal was instead decided by pundits in the studio.

text: 2014–15 Goal of the Season controversy[edit]

text: On 24 May 2015, the final day of the 2014–15 season, Match of the Day held an online vote at around 11 pm GMT for the Goal of the Season award. Users were able to vote via the BBC website or via Twitter. The poll was quickly rigged by Arsenal supporters, many from the Far East, resulting in Jack Wilshere winning the award for his final day strike against West Bromwich Albion, despite not being the favourite.[4] Host Gary Lineker expressed surprise as he read out the winner, and pundit Alan Shearer suggested that Charlie Adam should have won the award for his 66-yard effort against Chelsea; fellow pundit Danny Murphy felt former Fulham teammate Bobby Zamora should have won.

text: The incident was labelled a "shambles" by Pete Smith of The Stoke Sentinel[5] who thought that Stoke City's Adam should have won, and a "concerted campaign by Arsenal fans" by Alan Pattullo of The Scotsman,[6] who also believed that the Scottish midfielder was deserving of the award. Mark Brus of Caught Offside also criticized the choice stating that a goal in a meaningless game should not have won Goal of the Season and that Juan Mata's acrobatic effort against Liverpool was worthy of the award.[7]

text: The following season, before the final episode of that season's Match of the Day, the programme's producers changed the rules to prevent a similar situation. The Goal of the Season award has since been decided by the pundits on the show, who will choose the winner based on the top three goals voted for by the public.[8]

text: List of winners[edit]

text:
Season
Scorer
Nationality
For
Against
Stadium
Competition
Date
Commentator
Notes

1970–71
Hunt, ErnieErnie Hunt
 England
Coventry City
Everton
Highfield Road
First Division
3 October 1970
Davies, BarryBarry Davies
[10]

1971–72
Radford, RonnieRonnie Radford
 England
Hereford United
Newcastle United
Edgar Street
FA Cup
5 February 1972
Motson, JohnJohn Motson
[11]

1972–73
Osgood, PeterPeter Osgood
 England
Chelsea
Arsenal
Stamford Bridge
FA Cup
17 March 1973
Coleman, DavidDavid Coleman

1973–74
Mullery, AlanAlan Mullery
 England
Fulham
Leicester City
Craven Cottage
FA Cup
26 January 1974
Motson, JohnJohn Motson
[12]

1974–75
Walsh, MickeyMickey Walsh
 Ireland
Blackpool
Sunderland
Bloomfield Road
Second Division
1 February 1975
Davies, BarryBarry Davies
[13]

1975–76
Francis, GerryGerry Francis
 England
Queens Park Rangers
Liverpool
Loftus Road
First Division
16 August 1975
Motson, JohnJohn Motson
[14]

1976–77
McDermott, TerryTerry McDermott
 England
Liverpool
Everton
Maine Road
FA Cup
23 April 1977
Motson, JohnJohn Motson
[15]

1977–78
Gemmill, ArchieArchie Gemmill
 Scotland
Nottingham Forest
Arsenal
City Ground
First Division
21 January 1978
Coleman, DavidDavid Coleman

1978–79
Kennedy, RayRay Kennedy
 England
Liverpool
Derby County
Baseball Ground
First Division
24 February 1979
Motson, JohnJohn Motson

1979–80
Fashanu, JustinJustin Fashanu
 England
Norwich City
Liverpool
Carrow Road
First Division
9 February 1980
Davies, BarryBarry Davies
[16]

1980–81
Morley, TonyTony Morley
 England
Aston Villa
Everton
Goodison Park
First Division
7 February 1981
Motson, JohnJohn Motson
[17]

1981–82
Regis, CyrilleCyrille Regis
 England
West Bromwich Albion
Norwich City
The Hawthorns
FA Cup
13 February 1982
Parry, AlanAlan Parry
[18][19]

1982–83
Dalglish, KennyKenny Dalglish
 Scotland
Scotland
Belgium
Heysel Stadium, Brussels
Euro 1984 qualifying
15 December 1982
Gubba, TonyTony Gubba

1983–84
Wallace, DannyDanny Wallace
 England
Southampton
Liverpool
The Dell
First Division
16 March 1984
Davies, BarryBarry Davies
[20]

1984–85
Sharp, GraemeGraeme Sharp
 Scotland
Everton
Liverpool
Anfield
First Division
20 October 1984
Motson, JohnJohn Motson
[21]

1985–86
Robson, BryanBryan Robson
 England
England
Israel
Tel Aviv
Friendly
26 February 1986
Davies, BarryBarry Davies

1986–87
Houchen, KeithKeith Houchen
 England
Coventry City
Tottenham Hotspur
Wembley Stadium
FA Cup
16 May 1987
Motson, JohnJohn Motson

1987–88
Aldridge, JohnJohn Aldridge
 Ireland
Liverpool
Nottingham Forest
Hillsborough
FA Cup
9 April 1988
Motson, JohnJohn Motson

1988–89
Aldridge, JohnJohn Aldridge
 Ireland
Liverpool
Everton
Wembley Stadium
FA Cup
20 May 1989
Motson, JohnJohn Motson

1989–90
Wright, IanIan Wright
 England
Crystal Palace
Manchester United
Wembley Stadium
FA Cup
12 May 1990
Motson, JohnJohn Motson

1990–91
Gascoigne, PaulPaul Gascoigne
 England
Tottenham Hotspur
Arsenal
Wembley Stadium
FA Cup
14 April 1991
Davies, BarryBarry Davies

1991–92
Thomas, MickeyMickey Thomas
 Wales
Wrexham
Arsenal
Racecourse Ground
FA Cup
4 January 1992
Gubba, TonyTony Gubba
[22]

1992–93
Atkinson, DalianDalian Atkinson
 England
Aston Villa
Wimbledon
Selhurst Park
Premier League
3 October 1992
Tyldesley, CliveClive Tyldesley
[23]

1993–94
Wallace, RodRod Wallace
 England
Leeds United
Tottenham Hotspur
Elland Road
Premier League
17 April 1994
Sinstadt, GeraldGerald Sinstadt
[24]

1994–95
Le Tissier, MatthewMatthew Le Tissier
 England
Southampton
Blackburn Rovers
Ewood Park
Premier League
10 December 1994
Tyldesley, CliveClive Tyldesley
[25][26]

1995–96
Yeboah, TonyTony Yeboah
 Ghana
Leeds United
Wimbledon
Selhurst Park
Premier League
23 September 1995
Davies, BarryBarry Davies
[24]

1996–97
Sinclair, TrevorTrevor Sinclair
 England
Queens Park Rangers
Barnsley
Loftus Road
FA Cup
25 January 1997
Motson, JohnJohn Motson
[14]

1997–98
Bergkamp, DennisDennis Bergkamp
 Netherlands
Arsenal
Leicester City
Filbert Street
Premier League
27 August 1997
Gubba, TonyTony Gubba
[27]

1998–99
Giggs, RyanRyan Giggs
 Wales
Manchester United
Arsenal
Villa Park
FA Cup
14 April 1999
Champion, JonJon Champion
[27]

1999–2000
Di Canio, PaoloPaolo Di Canio
 Italy
West Ham United
Wimbledon
Upton Park
Premier League
26 March 2000
Brotherton, SimonSimon Brotherton
[28]

2000–01
Bartlett, ShaunShaun Bartlett
 South Africa
Charlton Athletic
Leicester City
The Valley
Premier League
1 April 2001
Champion, JonJon Champion
[29]

2001–02
Bergkamp, DennisDennis Bergkamp
 Netherlands
Arsenal
Newcastle United
St James' Park
Premier League
2 March 2002
Mowbray, GuyGuy Mowbray
[23]

2002–03
Henry, ThierryThierry Henry
 France
Arsenal
Tottenham Hotspur
Highbury
Premier League
16 November 2002
Tyldesley, CliveClive Tyldesley
[30]

2003–04
Hamann, DietmarDietmar Hamann
 Germany
Liverpool
Portsmouth
Anfield
Premier League
17 March 2004
Tyldesley, CliveClive Tyldesley
[31]

2004–05
Rooney, WayneWayne Rooney
 England
Manchester United
Middlesbrough
Old Trafford
FA Cup
29 January 2005
Motson, JohnJohn Motson
[32]

2005–06
Gerrard, StevenSteven Gerrard
 England
Liverpool
West Ham United
Millennium Stadium
FA Cup
13 May 2006
Motson, JohnJohn Motson
[33]

2006–07
Rooney, WayneWayne Rooney
 England
Manchester United
Bolton Wanderers
Old Trafford
Premier League
17 March 2007
Wilson, SteveSteve Wilson
[34]

2007–08
Adebayor, EmmanuelEmmanuel Adebayor
 Togo
Arsenal
Tottenham Hotspur
White Hart Lane
Premier League
15 September 2007
Motson, JohnJohn Motson
[35]

2008–09
Johnson, GlenGlen Johnson
 England
Portsmouth
Hull City
Fratton Park
Premier League
22 November 2008
Brotherton, SimonSimon Brotherton
[36]

2009–10
Figueroa, MaynorMaynor Figueroa
 Honduras
Wigan Athletic
Stoke City
Britannia Stadium
Premier League
12 December 2009
Gubba, TonyTony Gubba
[37]

2010–11
Rooney, WayneWayne Rooney
 England
Manchester United
Manchester City
Old Trafford
Premier League
12 February 2011
Wilson, SteveSteve Wilson
[38]

2011–12
Cissé, PapissPapiss Cissé
 Senegal
Newcastle United
Chelsea
Stamford Bridge
Premier League
2 May 2012
Wilson, SteveSteve Wilson
[39]

2012–13
van Persie, RobinRobin van Persie
 Netherlands
Manchester United
Aston Villa
Old Trafford
Premier League
22 April 2013
Mowbray, GuyGuy Mowbray
[9]

2013–14
Wilshere, JackJack Wilshere
 England
Arsenal
Norwich City
Emirates Stadium
Premier League
19 October 2013
Pearce, JonathanJonathan Pearce
[40]

2014–15
Wilshere, JackJack Wilshere
 England
Arsenal
West Bromwich Albion
Emirates Stadium
Premier League
24 May 2015
Motson, JohnJohn Motson
[9]

2015–16
Alli, DeleDele Alli
 England
Tottenham Hotspur
Crystal Palace
Selhurst Park
Premier League
23 January 2016
Green, AlanAlan Green
[41]

2016–17
Can, EmreEmre Can
 Germany
Liverpool
Watford
Vicarage Road
Premier League
1 May 2017
Martin Fisher
[42]

tag: table


document_title: List of United States Supreme Court Justices by time in office

question_text: who has the shortest tenure on the supreme court

text:
13,358 days
William O. Douglas
from 1939 to 1975

12,614 days
Stephen Johnson Field
from 1863 to 1897

12,611 days
John Paul Stevens
from 1975 to 2010

12,570 days
John Marshall
from 1801 to 1835

12,447 days
Hugo Black
from 1937 to 1971

12,360 days
John Marshall Harlan
from 1877 to 1911

887 days
Howell Edmunds Jackson
from 1893 to 1895

801 days
Robert Trimble
from 1826 to 1828

563 days
John Rutledge
from 1790 to 1791 and in 1795

452 days
James F. Byrnes
from 1941 to 1942

7002167000000000000♠167 days
Neil Gorsuch
since 2017

163 days
Thomas Johnson
from 1792 to 1793

text: A total of 113 Justices have served on the Supreme Court of the United States, the highest judicial body in the United States. Justices have life tenure, and so they serve until they die in office, resign or retire, or are impeached and removed from office (which has never happened; the one impeached Justice was acquitted). The longest-serving member of the current court is Associate Justice Anthony Kennedy, with a term to date of 7004108110000000000♠10,811 days (29 years). For the 104 non-incumbent justices, the mean length of service was 6,112 days (16.7 years) with a standard deviation of 3,620 days (9.9 years). The median length of service was 5,740 days (15.7 years). Their period of service ranges from William O. Douglas's 13,358 days (36 years) on the Court to the 163-day tenure of Thomas Johnson.

text: A nominee who was confirmed by the United States Senate but declined to serve, such as Robert H. Harrison, or who died before taking his seat, such as Edwin M. Stanton, is not considered to have served as a Justice.[1][2] The Term Start date is the day the Justice took the oath of office,[1] with the Term End date being the date of the Justice's death, resignation, or retirement.[1] A highlighted row indicates that the Justice is currently serving on the Court.[3]

text: Justices[edit]

text:
*Chief Justice
†Term as Associate Justice and Chief Justice combined

text:
Rank by
length
of term
Justice
Term
in
days
Term Start[1]
Term End[1]

1
Douglas, William O.William O. Douglas
7004133580000000000♠13,358
000000001939-04-17-0000April 17, 1939
000000001975-11-12-0000November 12, 1975

2
Field, Stephen JohnsonStephen Johnson Field
7004126140000000000♠12,614
000000001863-05-20-0000May 20, 1863
000000001897-12-01-0000December 1, 1897

3
Stevens, John PaulJohn Paul Stevens
7004126110000000000♠12,611
000000001975-12-19-0000December 19, 1975
000000002010-06-29-0000June 29, 2010

4
Marshall, JohnJohn Marshall*
7004125700000000000♠12,570
000000001801-02-04-0000February 4, 1801
000000001835-07-06-0000July 6, 1835

5
Black, HugoHugo Black
7004124470000000000♠12,447
000000001937-08-19-0000August 19, 1937
000000001971-09-17-0000September 17, 1971

6
Harlan, John MarshallJohn Marshall Harlan
7004123600000000000♠12,360
000000001877-12-10-0000December 10, 1877
000000001911-10-14-0000October 14, 1911

7
Brennan, Jr., William J.William J. Brennan, Jr.
7004123300000000000♠12,330
000000001956-10-16-0000October 16, 1956
000000001990-07-20-0000July 20, 1990

8
Rehnquist, WilliamWilliam Rehnquist*
7004122930000000000♠12,293†
000000001972-01-07-0000January 7, 1972
000000002005-09-03-0000September 3, 2005†

9
Story, JosephJoseph Story
7004122730000000000♠12,273
000000001812-02-03-0000February 3, 1812
000000001845-09-10-0000September 10, 1845

10
Wayne, James MooreJames Moore Wayne
7004118600000000000♠11,860
000000001835-01-14-0000January 14, 1835
000000001867-07-05-0000July 5, 1867

11
McLean, JohnJohn McLean
7004114060000000000♠11,406
000000001830-01-11-0000January 11, 1830
000000001861-04-04-0000April 4, 1861

12
White, ByronByron White
7004113960000000000♠11,396
000000001962-04-16-0000April 16, 1962
000000001993-06-28-0000June 28, 1993

13
Washington, BushrodBushrod Washington
7004112520000000000♠11,252
000000001799-02-04-0000February 4, 1799
000000001829-11-26-0000November 26, 1829

14
Johnson, WilliamWilliam Johnson
7004110460000000000♠11,046
000000001804-05-07-0000May 7, 1804
000000001834-08-04-0000August 4, 1834

15
Kennedy, AnthonyAnthony Kennedy
7004108110000000000♠10,811
000000001988-02-18-0000February 18, 1988
000000002017-09-24-0000Incumbent

16
Scalia, AntoninAntonin Scalia
7004107320000000000♠10,732
000000001986-09-26-0000September 26, 1986
000000002016-02-13-0000February 13, 2016

17
Holmes, Oliver WendellOliver Wendell Holmes
7004106270000000000♠10,627
000000001902-12-08-0000December 8, 1902
000000001932-01-12-0000January 12, 1932

18
Taney, Roger B.Roger B. Taney*
7004104250000000000♠10,425
000000001836-03-28-0000March 28, 1836
000000001864-10-12-0000October 12, 1864

19
Miller, Samuel FreemanSamuel Freeman Miller
7004103110000000000♠10,311
000000001862-07-21-0000July 21, 1862
000000001890-10-13-0000October 13, 1890

20
Catron, JohnJohn Catron
7004102560000000000♠10,256
000000001837-05-01-0000May 1, 1837
000000001865-05-30-0000May 30, 1865

21
Nelson, SamuelSamuel Nelson
7004101360000000000♠10,136
000000001845-02-27-0000February 27, 1845
000000001872-11-28-0000November 28, 1872

22
White, Edward DouglassEdward Douglass White*
7003992900000000000♠9,929†
000000001894-03-12-0000March 12, 1894
000000001921-05-19-0000May 19, 1921†

23
McKenna, JosephJoseph McKenna
7003984000000000000♠9,840
000000001898-01-26-0000January 26, 1898
000000001925-01-05-0000January 5, 1925

24
Van Devanter, WillisWillis Van Devanter
7003964700000000000♠9,647
000000001911-01-03-0000January 3, 1911
000000001937-06-02-0000June 2, 1937

25
McReynolds, James ClarkJames Clark McReynolds
7003960800000000000♠9,608
000000001914-10-12-0000October 12, 1914
000000001941-01-31-0000January 31, 1941

26
Thomas, ClarenceClarence Thomas
7003946800000000000♠9,468
000000001991-10-23-0000October 23, 1991
000000002017-09-24-0000Incumbent

27
O'Connor, Sandra DaySandra Day O'Connor
7003889400000000000♠8,894
000000001981-09-25-0000September 25, 1981
000000002006-01-31-0000January 31, 2006

28
Blackmun, HarryHarry Blackmun
7003882100000000000♠8,821
000000001970-06-09-0000June 9, 1970
000000001994-08-03-0000August 3, 1994

29
Ginsburg, Ruth BaderRuth Bader Ginsburg
7003881100000000000♠8,811
000000001993-08-10-0000August 10, 1993
000000002017-09-24-0000Incumbent

30
Marshall, ThurgoodThurgood Marshall
7003876500000000000♠8,765
000000001967-10-02-0000October 2, 1967
000000001991-10-01-0000October 1, 1991

31
Frankfurter, FelixFelix Frankfurter
7003861100000000000♠8,611
000000001939-01-30-0000January 30, 1939
000000001962-08-28-0000August 28, 1962

32
Clifford, NathanNathan Clifford
7003858600000000000♠8,586
000000001858-01-21-0000January 21, 1858
000000001881-07-25-0000July 25, 1881

33
Grier, Robert CooperRobert Cooper Grier
7003857500000000000♠8,575
000000001846-08-10-0000August 10, 1846
000000001870-01-31-0000January 31, 1870

34
Breyer, StephenStephen Breyer
7003845300000000000♠8,453
000000001994-08-03-0000August 3, 1994
000000002017-09-24-0000Incumbent

35
Duvall, GabrielGabriel Duvall
7003845300000000000♠8,453
000000001811-11-23-0000November 23, 1811
000000001835-01-14-0000January 14, 1835

36
Stewart, PotterPotter Stewart
7003829800000000000♠8,298
000000001958-10-14-0000October 14, 1958
000000001981-07-03-0000July 3, 1981

37
Brandeis, LouisLouis Brandeis
7003828800000000000♠8,288
000000001916-06-05-0000June 5, 1916
000000001939-02-13-0000February 13, 1939

38
Bradley, Joseph P.Joseph P. Bradley
7003797500000000000♠7,975
000000001870-03-23-0000March 23, 1870
000000001892-01-22-0000January 22, 1892

39
Fuller, MelvilleMelville Fuller*
7003793800000000000♠7,938
000000001888-10-08-0000October 8, 1888
000000001910-07-04-0000July 4, 1910

40
Stone, Harlan F.Harlan F. Stone*
7003772100000000000♠7,721†
000000001925-03-02-0000March 2, 1925
000000001946-04-22-0000April 22, 1946†

41
Gray, HoraceHorace Gray
7003755300000000000♠7,553
000000001882-01-09-0000January 9, 1882
000000001902-09-15-0000September 15, 1902

42
Cushing, WilliamWilliam Cushing
7003752700000000000♠7,527
000000001790-02-02-0000February 2, 1790
000000001810-09-13-0000September 13, 1810

43
Thompson, SmithSmith Thompson
7003741300000000000♠7,413
000000001823-09-01-0000September 1, 1823
000000001843-12-18-0000December 18, 1843

44
Brewer, David JosiahDavid Josiah Brewer
7003738500000000000♠7,385
000000001890-01-06-0000January 6, 1890
000000001910-03-28-0000March 28, 1910

45
Day, William R.William R. Day
7003719600000000000♠7,196
000000001903-03-02-0000March 2, 1903
000000001922-11-13-0000November 13, 1922

46
Reed, Stanley FormanStanley Forman Reed
7003696500000000000♠6,965
000000001938-01-31-0000January 31, 1938
000000001957-02-25-0000February 25, 1957

47
Swayne, Noah HaynesNoah Haynes Swayne
7003693700000000000♠6,937
000000001862-01-27-0000January 27, 1862
000000001881-01-24-0000January 24, 1881

48
Todd, ThomasThomas Todd
7003685400000000000♠6,854
000000001807-05-04-0000May 4, 1807
000000001826-02-07-0000February 7, 1826

49
Souter, DavidDavid Souter
7003683800000000000♠6,838
000000001990-10-09-0000October 9, 1990
000000002009-06-29-0000June 29, 2009

50
Daniel, Peter VivianPeter Vivian Daniel
7003671600000000000♠6,716
000000001842-01-10-0000January 10, 1842
000000001860-05-31-0000May 31, 1860

51
Clark, Tom C.Tom C. Clark
7003650100000000000♠6,501
000000001949-08-24-0000August 24, 1949
000000001967-06-12-0000June 12, 1967

52
Burger, Warren E.Warren E. Burger*
7003630400000000000♠6,304
000000001969-06-23-0000June 23, 1969
000000001986-09-26-0000September 26, 1986

53
Hughes, Charles EvansCharles Evans Hughes*
7003621400000000000♠6,214†
000000001910-10-10-0000October 10, 1910
February 24, 1930*
000000001916-06-10-0000June 10, 1916
June 30, 1941*

54
Butler, PiercePierce Butler
7003616200000000000♠6,162
000000001923-01-02-0000January 2, 1923
000000001939-11-16-0000November 16, 1939

55
Harlan II, John MarshallJohn Marshall Harlan II
7003602300000000000♠6,023
000000001955-03-28-0000March 28, 1955
000000001971-09-23-0000September 23, 1971

56
Livingston, Henry BrockholstHenry Brockholst Livingston
7003590100000000000♠5,901
000000001807-01-20-0000January 20, 1807
000000001823-03-18-0000March 18, 1823

57
Warren, EarlEarl Warren*
7003574000000000000♠5,740
000000001953-10-05-0000October 5, 1953
000000001969-06-23-0000June 23, 1969

58
Powell, Lewis FranklinLewis Franklin Powell
7003564900000000000♠5,649
000000001972-01-07-0000January 7, 1972
000000001987-06-26-0000June 26, 1987

59
Brown, Henry BillingsHenry Billings Brown
7003562100000000000♠5,621
000000001891-01-05-0000January 5, 1891
000000001906-05-28-0000May 28, 1906

60
Chase, SamuelSamuel Chase
7003561300000000000♠5,613
000000001796-02-04-0000February 4, 1796
000000001811-06-19-0000June 19, 1811

61
Sutherland, GeorgeGeorge Sutherland
7003558600000000000♠5,586
000000001922-10-02-0000October 2, 1922
000000001938-01-17-0000January 17, 1938

62
Roberts, OwenOwen Roberts
7003553800000000000♠5,538
000000001930-06-02-0000June 2, 1930
000000001945-07-31-0000July 31, 1945

63
McKinley, JohnJohn McKinley
7003530500000000000♠5,305
000000001838-01-09-0000January 9, 1838
000000001852-07-19-0000July 19, 1852

64
Baldwin, HenryHenry Baldwin
7003520700000000000♠5,207
000000001830-01-18-0000January 18, 1830
000000001844-04-21-0000April 21, 1844

65
Davis, DavidDavid Davis
7003519800000000000♠5,198
000000001862-12-10-0000December 10, 1862
000000001877-03-04-0000March 4, 1877

66
Waite, MorrisonMorrison Waite*
7003513300000000000♠5,133
000000001874-03-04-0000March 4, 1874
000000001888-03-23-0000March 23, 1888

67
Peckham, Rufus WheelerRufus Wheeler Peckham
7003503900000000000♠5,039
000000001896-01-06-0000January 6, 1896
000000001909-10-24-0000October 24, 1909

68
Paterson, WilliamWilliam Paterson
7003492900000000000♠4,929
000000001793-03-11-0000March 11, 1793
000000001806-09-09-0000September 9, 1806

69
Jackson, Robert H.Robert H. Jackson
7003483800000000000♠4,838
000000001941-07-11-0000July 11, 1941
000000001954-10-09-0000October 9, 1954

70
Burton, Harold HitzHarold Hitz Burton
7003476000000000000♠4,760
000000001945-10-01-0000October 1, 1945
000000001958-10-13-0000October 13, 1958

71
Roberts, JohnJohn Roberts*
7003437800000000000♠4,378
000000002005-09-29-0000September 29, 2005
000000002017-09-24-0000Incumbent

72
Alito, SamuelSamuel Alito
7003425400000000000♠4,254
000000002006-01-31-0000January 31, 2006
000000002017-09-24-0000Incumbent

73
Blatchford, SamuelSamuel Blatchford
7003411300000000000♠4,113
000000001882-04-03-0000April 3, 1882
000000001893-07-07-0000July 7, 1893

74
Pitney, MahlonMahlon Pitney
7003394000000000000♠3,940
000000001912-03-18-0000March 18, 1912
000000001922-12-31-0000December 31, 1922

75
Strong, WilliamWilliam Strong
7003392800000000000♠3,928
000000001870-03-14-0000March 14, 1870
000000001880-12-14-0000December 14, 1880

76
Shiras, Jr., GeorgeGeorge Shiras, Jr.
7003378700000000000♠3,787
000000001892-10-10-0000October 10, 1892
000000001903-02-23-0000February 23, 1903

77
Murphy, FrankFrank Murphy
7003345200000000000♠3,452
000000001940-02-05-0000February 5, 1940
000000001949-07-19-0000July 19, 1949

78
Iredell, JamesJames Iredell
7003344800000000000♠3,448
000000001790-05-12-0000May 12, 1790
000000001799-10-20-0000October 20, 1799

79
Hunt, WardWard Hunt
7003330500000000000♠3,305
000000001873-01-09-0000January 9, 1873
000000001882-01-27-0000January 27, 1882

80
Wilson, JamesJames Wilson
7003324200000000000♠3,242
000000001789-10-05-0000October 5, 1789
000000001798-08-21-0000August 21, 1798

81
Taft, William HowardWilliam Howard Taft*
7003312900000000000♠3,129
000000001921-07-11-0000July 11, 1921
000000001930-02-03-0000February 3, 1930

82
Chase, Salmon P.Salmon P. Chase*
7003306500000000000♠3,065
000000001864-12-15-0000December 15, 1864
000000001873-05-07-0000May 7, 1873

83
Sotomayor, SoniaSonia Sotomayor
7003296900000000000♠2,969
000000002009-08-08-0000August 8, 2009
000000002017-09-24-0000Incumbent

84
Campbell, John ArchibaldJohn Archibald Campbell
7003294100000000000♠2,941
000000001853-04-11-0000April 11, 1853
000000001861-04-30-0000April 30, 1861

85
Matthews, StanleyStanley Matthews
7003286600000000000♠2,866
000000001881-05-17-0000May 17, 1881
000000001889-03-22-0000March 22, 1889

86
Vinson, Fred M.Fred M. Vinson*
7003263300000000000♠2,633
000000001946-06-24-0000June 24, 1946
000000001953-09-08-0000September 8, 1953

87
Kagan, ElenaElena Kagan
7003260500000000000♠2,605
000000002010-08-07-0000August 7, 2010
000000002017-09-24-0000Incumbent

88
Sanford, Edward TerryEdward Terry Sanford
7003257400000000000♠2,574
000000001923-02-19-0000February 19, 1923
000000001930-03-08-0000March 8, 1930

89
Minton, ShermanSherman Minton
7003256000000000000♠2,560
000000001949-10-12-0000October 12, 1949
000000001956-10-15-0000October 15, 1956

90
Rutledge, Wiley BlountWiley Blount Rutledge
7003239900000000000♠2,399
000000001943-02-15-0000February 15, 1943
000000001949-09-10-0000September 10, 1949

91
Woods, William BurnhamWilliam Burnham Woods
7003232000000000000♠2,320
000000001881-01-05-0000January 5, 1881
000000001887-05-14-0000May 14, 1887

92
Cardozo, Benjamin N.Benjamin N. Cardozo
7003230800000000000♠2,308
000000001932-03-14-0000March 14, 1932
000000001938-07-09-0000July 9, 1938

93
Curtis, Benjamin RobbinsBenjamin Robbins Curtis
7003218200000000000♠2,182
000000001851-10-10-0000October 10, 1851
000000001857-09-30-0000September 30, 1857

94
Woodbury, LeviLevi Woodbury
7003217200000000000♠2,172
000000001845-09-23-0000September 23, 1845
000000001851-09-04-0000September 4, 1851

95
Clarke, John HessinJohn Hessin Clarke
7003217000000000000♠2,170
000000001916-10-09-0000October 9, 1916
000000001922-09-18-0000September 18, 1922

96
Blair, JohnJohn Blair
7003209100000000000♠2,091
000000001790-02-02-0000February 2, 1790
000000001795-10-25-0000October 25, 1795

97
Jay, JohnJohn Jay*
7003207900000000000♠2,079
000000001789-10-19-0000October 19, 1789
000000001795-06-29-0000June 29, 1795

98 (tie)
Lamar, Lucius Quintus CincinnatusLucius Quintus Cincinnatus Lamar
7003183200000000000♠1,832
000000001888-01-18-0000January 18, 1888
000000001893-01-23-0000January 23, 1893

98 (tie)
Whittaker, Charles EvansCharles Evans Whittaker
7003183200000000000♠1,832
000000001957-03-25-0000March 25, 1957
000000001962-03-31-0000March 31, 1962

100
Lamar, Joseph RuckerJoseph Rucker Lamar
7003182500000000000♠1,825
000000001911-01-03-0000January 3, 1911
000000001916-01-02-0000January 2, 1916

101
Barbour, Philip PendletonPhilip Pendleton Barbour
7003175000000000000♠1,750
000000001836-05-12-0000May 12, 1836
000000001841-02-25-0000February 25, 1841

102
Ellsworth, OliverOliver Ellsworth*
7003174200000000000♠1,742
000000001796-03-08-0000March 8, 1796
000000001800-12-15-0000December 15, 1800

103
Lurton, Horace HarmonHorace Harmon Lurton
7003165100000000000♠1,651
000000001910-01-03-0000January 3, 1910
000000001914-07-12-0000July 12, 1914

104
Moody, William HenryWilliam Henry Moody
7003143400000000000♠1,434
000000001906-12-17-0000December 17, 1906
000000001910-11-20-0000November 20, 1910

105
Moore, AlfredAlfred Moore
7003137500000000000♠1,375
000000001800-04-21-0000April 21, 1800
000000001804-01-26-0000January 26, 1804

106
Fortas, AbeAbe Fortas
7003131800000000000♠1,318
000000001965-10-04-0000October 4, 1965
000000001969-05-14-0000May 14, 1969

107
Goldberg, ArthurArthur Goldberg
7003102800000000000♠1,028
000000001962-10-01-0000October 1, 1962
000000001965-07-25-0000July 25, 1965

108
Jackson, Howell EdmundsHowell Edmunds Jackson
7002887000000000000♠887
000000001893-03-04-0000March 4, 1893
000000001895-08-08-0000August 8, 1895

109
Trimble, RobertRobert Trimble
7002801000000000000♠801
000000001826-06-16-0000June 16, 1826
000000001828-08-25-0000August 25, 1828

110
Rutledge, JohnJohn Rutledge*
7002563000000000000♠563†
000000001790-02-15-0000February 15, 1790
July 1, 1795*
000000001795-12-28-0000March 5, 1791
December 28, 1795*

111
Byrnes, James F.James F. Byrnes
7002452000000000000♠452
000000001941-07-08-0000July 8, 1941
000000001942-10-03-0000October 3, 1942

112
Gorsuch, NeilNeil Gorsuch
7002167000000000000♠167
000000002017-04-10-0000April 10, 2017
000000002017-09-24-0000Incumbent

113
Johnson, ThomasThomas Johnson
7002163000000000000♠163
000000001792-08-06-0000August 6, 1792
000000001793-01-16-0000January 16, 1793


document_title: Kami

question_text: japanese for spirits these are associated with shintoism

text: Kami

text: Etymology[edit]

text: Kami is the Japanese word for a god, deity, divinity, or spirit.[4] It has been used to describe mind (心霊), God (ゴッド), supreme being (至上者), one of the Shinto deities, an effigy, a principle, and anything that is worshipped.[5]

text: Although deity is the common interpretation of kami, some Shinto scholars argue that such a translation can cause a misunderstanding of the term.[6][page needed] The wide variety of usage of the word kami can be compared to the Sanskrit Deva and the Hebrew Elohim, which also refer to God, gods, angels, or spirits.

text: Some etymological suggestions are:

text:
Kami may, at its root, simply mean spirit, or an aspect of spirituality. It is written with the kanji 神, Sino-Japanese reading shin or jin. In Chinese, the character means deity.[7]
In the Ainu language, the word kamuy refers to an animistic concept very similar to Japanese kami. The matter of the words' origins is still a subject of debate; several hypotheses about their similarities exist: the Japanese word was borrowed from the Jomon/Ainu language, or are cognates of an extremely distant common ancestor.[8]
In his Kojiki-den, Motoori Norinaga gave a definition of kami: "...any being whatsoever which possesses some eminent quality out of the ordinary, and is awe-inspiring, is called kami."[9]

tag: ul

text: Because Japanese does not normally distinguish grammatical number in nouns (the singular and plural forms of nouns in Japanese are the same), it is sometimes unclear whether kami refers to a single or multiple entities. When a singular concept is needed, -kami (神) or -kamisama (神様) is used as a suffix.[citation needed] The logograms for kami-sama are those used for shén yàng in Pŭtōnghuà;[10][page needed] 'kami-sama can be used for a divinity, or for an outstanding human, such as Tezuka Osamu, "the god of manga."[citation needed] The term generally used to refer to multiple kami is kamigami.[3]:210–211

text: Gender is also not implied in the word kami, and as such it can be used to reference either male or female. The word megami (女神), the use of female kami is a fairly new tradition.[citation needed]

text: History[edit]

text: While Shinto has no founder, no overarching doctrine, and no religious texts, the Kojiki (the Ancient Chronicles of Japan), written in 712 CE, and the Nihonshoki (Chronicles of Japan), written in 720 CE, contain the earliest record of Japanese creation myths. The Kojiki also includes descriptions of various kami.[3]:39

text: In the ancient Shinto traditions there were five defining characteristics of kami:[11]

text:
Kami are of two minds. They can nurture and love when respected, or they can cause destruction and disharmony when disregarded. Kami must be appeased in order to gain their favor and avoid their wrath. Traditionally, kami possess two souls, one gentle (nigi-mitama) and the other assertive (ara-mitama); additionally, in Yamakage Shinto, kami have two additional souls that are hidden: one happy (sachi-mitama) and one mysterious (kushi-mitama).[3]:130
Kami are not visible to the human realm. Instead, they inhabit sacred places, natural phenomena, or people during rituals that ask for their blessing.
They are mobile, visiting their places of worship, of which there can be several, but never staying forever.
There are many different varieties of kami. There are 300 different classifications of kami listed in the Kojiki, and they all have different functions, such as the kami of wind, kami of entryways, and kami of roads.
Lastly, all kami have a different guardianship or duty to the people around them. Just as the people have an obligation to keep the kami happy, the kami have to perform the specific function of the object, place, or idea they inhabit.

tag: ol

text: Kami are an ever-changing concept, but their presence in Japanese life has remained constant. The kami’s earliest roles were as earth-based spirits, assisting the early hunter-gatherer groups in their daily lives. They were worshipped as gods of earth (mountains) and sea. As the cultivation of rice became increasingly important and predominant in Japan, the kami’s identity shifted to more sustaining roles that were directly involved in the growth of crops; roles such as rain, earth, and rice.[11] This relationship between early Japanese people and the kami was manifested in rituals and ceremonies meant to entreat the kami to grow and protect the harvest. These rituals also became a symbol of power and strength for the early emperors.[12] See Niiname-sai (i.e., 新嘗祭, which also reads as Shinjō-sai).

text: There is a strong tradition of myth-histories in the Shinto faith; one such myth details the appearance of the first emperor, grandson of the Sun Goddess Amaterasu. In this myth, when Amaterasu sent her grandson to earth to rule, she gave him five rice grains, which had been grown in the fields of heaven (Takamagahara). This rice made it possible for him to transform the "wilderness".[12]

text: Social and political strife have played a key role in the development of new sorts of kami, specifically the goryo-shin (the sacred spirit kami). The goryo are the vengeful spirits of the dead whose lives were cut short, but they were calmed by the devotion of Shinto followers and are now believed to punish those who do not honor the kami.[12]

text: The pantheon of kami, like the kami themselves, is forever changing in definition and scope. As the needs of the people have shifted, so too have the domains and roles of the various kami. Some examples of this are related to health, such as the kami of small pox whose role was expanded to include all contagious diseases, or the kami of boils and growths who has also come to preside over cancers and cancer treatments.[12]

text: In the ancient animistic religions, kami were understood as simply the divine forces of nature. Worshippers in ancient Japan revered creations of nature which exhibited a particular beauty and power such as waterfalls, mountains, boulders, animals, trees, grasses, and even rice paddies. They strongly believed the spirits or resident kami deserved respect.

text: in 927 CE, the Engi-shiki (延喜式, literally, Procedures of the Engi Era) was promulgated in fifty volumes. This, the first formal codification of Shinto rites and norito (liturgies and prayers) to survive, became the basis for all subsequent Shinto liturgical practice and efforts. It listed all of the 2,861 Shinto shrines existing at the time, and the 3,131 official-recognized and enshrined kami.[13] The number of kami has grown and far exceeded this figure through the following generations as there are over 2,446,000 individual kami enshrined in Tokyo's Yasukuni Shrine alone.[14]

text: Shinto belief[edit]

text: Kami are the central objects of worship for the Shinto faith. The ancient animistic spirituality of Japan was the beginning of modern Shinto, which became a formal spiritual institution later, in an effort to preserve the traditional beliefs from the encroachment of imported religious ideas. As a result, the nature of what can be called kami is very general and encompasses many different concepts and phenomena.

text: Some of the objects or phenomena designated as kami are qualities of growth, fertility, and production; natural phenomena like wind and thunder; natural objects like the sun, mountains, rivers, trees, and rocks; some animals; and ancestral spirits. Included within the designation of ancestral spirits are spirits of the ancestors of the Imperial House of Japan, but also ancestors of noble families as well as the spirits of the ancestors of all people, which when they died were believed to be the guardians of their descendants.[3]:150

text: There are other spirits designated as kami as well. For example, the guardian spirits of the land, occupations, and skills; spirits of Japanese heroes, men of outstanding deeds or virtues, and those who have contributed to civilization, culture, and human welfare; those who have died for the state or the community;[citation needed] and the pitiable dead. Not only spirits superior to man can be considered kami; spirits that are considered pitiable or weak have also been considered kami in Shinto.

text: The concept of kami has been changed and refined since ancient times, although anything that was considered to be kami by ancient people will still be considered kami in modern Shinto. Even within modern Shinto, there are no clearly defined criteria for what should or should not be worshipped as kami. The difference between modern Shinto and the ancient animistic religions is mainly a refinement of the kami-concept, rather than a difference in definitions.[citation needed]

text: Although the ancient designations are still adhered to, in modern Shinto many priests also consider kami to be anthropomorphic spirits, with nobility and authority. One such example is the mythological figure Amaterasu-ōmikami, the sun goddess of the Shinto pantheon. Although these kami can be considered deities, they are not necessarily considered omnipotent or omniscient, and like the Greek Gods, they had flawed personalities and were quite capable of ignoble acts. In the myths of Amaterasu, for example, she could see the events of the human world, but had to use divination rituals to see the future.

text: There are considered to be three main variations of kami: amatsu-kami (the heavenly deities), kunitsu-kami (the gods of the earthly realm), and ya-o-yorozu no kami (八百万の神, countless kami). ("八百万" literally means eight million, but idiomatically it expresses "uncountably many" and "all around"—like many East Asian cultures, the Japanese often use the number 8, representing the cardinal and ordinal directions, to symbolize ubiquity.) These classifications of kami are not considered strictly divided, due to the fluid and shifting nature of kami, but are instead held as guidelines for grouping them.[3]:56

text: The ancestors of a particular family can also be worshipped as kami. In this sense, these kami are worshipped not because of their godly powers, but because of a distinctive quality or virtue. These kami are celebrated regionally, and several miniature shrines (hokora) have been built in their honor. In many cases, people who once lived are thus revered; an example of this is Tenjin, who was Sugawara no Michizane (845-903 CE) in life.

text: Within Shinto it is believed that the nature of life is sacred, because the kami began human life. Yet people cannot perceive this divine nature, which the kami created, on their own; therefore, magokoro, or purification, is necessary in order to see the divine nature.[15] This purification can only be granted by the kami. In order to please the kami and earn magokoro, Shinto followers are taught to uphold the four affirmations of Shinto.

text: The first affirmation is to hold fast to tradition and the family. Family is seen as the main mechanism by which traditions are preserved. For instance, in marriage or birth, tradition is potentially observed and passed onto future generations. The second affirmation is to have a love of nature. Nature objects are worshipped as sacred, because the kami inhabit them. Therefore, to be in contact with nature means to be in contact with the gods. The third affirmation is to maintain physical cleanliness. Followers of Shinto take baths, wash their hands, and rinse out their mouths often. The last affirmation is to practice matsuri, which is the worship and honor given to the kami and ancestral spirits.[15]

text: Shinto followers also believe that the kami are the ones who can either grant blessings or curses to a person. Shinto believers desire to appease the evil kami to "stay on their good side", and also to please the good kami. In addition to practicing the four affirmations daily, Shinto believers also wear omamori to aid them in remaining pure and protected. Mamori are charms that keep the evil kami from striking a human with sickness or causing disaster to befall them.[15]

text: The kami are both worshipped and respected within the religion of Shinto. The goal of life to Shinto believers is to obtain magokoro, a pure sincere heart, which can only be granted by the kami.[16] As a result, Shinto followers are taught that humankind should venerate both the living and the nonliving, because both possess a divine superior spirit within: the kami.[17][page needed]

text: Ceremonies and festivals[edit]

text: One of the first recorded rituals we know of is Niiname-sai,[12] the ceremony in which the Emperor offers newly harvested rice to the kami to secure their blessing for a bountiful harvest. A yearly festival, Niiname-sai is also performed when a new Emperor comes to power, in which case it is called Onamesai. In the ceremony the Emperor offers crops from the new harvest to the kami, including rice, fish, fruits, soup, and stew. The Emperor first feasts with the deities, then the guests. The feast could go on for some time; for example, the Showa Emperor's feast spanned two days.[12]

text: Visitors to a Shinto shrine follow a purification ritual before presenting themselves to the kami. This ritual begins with hand washing, and swallowing and later spitting a small amount of water in front of the shrine to purify the body, heart, and mind. Once this is complete they turn their focus to gaining the kami’s attention. The traditional method of doing this is to bow twice, clap twice and bow again, alerting the kami to their presence and desire to commune with them. During the last bow, the supplicant offers words of gratitude and praise to the kami; if they are offering a prayer for aid they will also state their name and address. After the prayer and/or worship they repeat the two bows, two claps and a final bow in conclusion.[3]:197

text: Shinto practitioners also worship at home. This is done at a kamidana (household shrine), on which an ofuda (kami name card or charm card) with the name of their protector or ancestral kami is positioned. Their protector kami is determined by their or their ancestors’ relationship to the kami.[3]:28, 84

text: Ascetic practices, shrine rituals and ceremonies, and Japanese festivals are the most public ways that Shinto devotees celebrate and offer adoration for the kami. Kami are celebrated during their distinct festivals that usually take place at the shrines dedicated to their worship. Many festivals involve believers, who are usually intoxicated, parading, sometimes running, toward the shrine while carrying mikoshi (portable shrines) as the community gathers for the festival ceremony. Yamamoto Guji, the high priest at the Tsubaki Grand Shrine, explains that this practice honors the kami because "it is in the festival, the matsuri, the greatest celebration of life can be seen in the world of Shinto and it is the people of the community who attend festivals as groups, as a whole village who are seeking to unlock the human potential as children of kami."[2] During the New Year Festival, families purify and clean their houses in preparation for the upcoming year. Offerings are also made to the ancestors so that they will bless the family in the future year.[citation needed]

text: Shinto ceremonies are so long and complex that in some shrines it can take ten years for the priests to learn them.[citation needed] The priesthood was traditionally hereditary. Some shrines have drawn their priests from the same families for over a hundred generations.[18] It is not uncommon for the clergy to be female priestesses.[18] The priests may be assisted by miko, young unmarried women acting as shrine maidens.[19] Neither priests nor priestesses live as ascetics; in fact, it is common for them to be married,[18] and they are not traditionally expected to meditate. Rather, they are considered specialists in the arts of maintaining the connection between the kami and the people.[18]

text: In addition to these festivals, ceremonies marking rites of passage are also performed within the shrines. Two such ceremonies are the birth of a child and the Shichi-Go-San. When a child is born they are brought to a shrine so that they can be initiated as a new believer and the kami can bless them and their future life. The Shichi-Go-San (the Seven-Five-Three) is a rite of passage for five-year-old boys and three- or seven-year-old girls. It is a time for these young children to personally offer thanks for the kami’s protection and to pray for continued health.[20]

text: Many other rites of passage are practiced by Shinto believers, and there are also many other festivals. The main reason for these ceremonies is so that Shinto followers can appease the kami in order to reach magokoro.[16]:205 Magokoro can only be received through the kami. Ceremonies and festivals are long and complex because they need to be perfect to satisfy the kami. If the kami are not pleased with these ceremonies, they will not grant a Shinto believer magokoro.

text: Notable kami[edit]

text:
Amaterasu Omikami, the sun goddess
Ebisu one of seven gods of fortune
Hachiman, the god of war
Inari Okami, the god of rice and agriculture
Izanagi-no-Mikoto, the first man
Izanami-no-Mikoto, the first woman
Kotoamatsukami, the primary kami trinity
Omoikane, the deity of wisdom
Sarutahiko Okami, the kami of earth
Susanoo-no-mikoto, the sea and storms god
Tenjin the poetry god
Tsukuyomi, the moon god
Ryūjin, the Japanese dragon god of sea and storms

text: In popular culture[edit]