quotient

• n.

• 商

　 　 　

WordNet

1. the number obtained by division
2. the ratio of two quantities to be divided

PrepTutorEJDIC

1. 割り算の答え,商

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2017/12/04 05:35:18」(JST)

wiki en

[Wiki en表示]

For other uses, see Quotient (disambiguation).

See also: Division (mathematics), Fraction (mathematics), and Ratio

Calculation results
Addition (+)
$$ summand + summand addend (broad sense) + addend (broad sense) augend + addend (strict sense) } = {\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{summand}}\,+\,{\text{summand}}\\\scriptstyle {\text{addend (broad sense)}}\,+\,{\text{addend (broad sense)}}\\\scriptstyle {\text{augend}}\,+\,{\text{addend (strict sense)}}\end{matrix}}\right\}\,=\,}	$$ sum {\displaystyle \scriptstyle {\text{sum}}}
Subtraction (−)
$$ minuend − subtrahend = {\displaystyle \scriptstyle {\text{minuend}}\,-\,{\text{subtrahend}}\,=\,}	$$ difference {\displaystyle \scriptstyle {\text{difference}}}
Multiplication (×)
$$ factor × factor multiplicand × multiplier } = {\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplicand}}\,\times \,{\text{multiplier}}\end{matrix}}\right\}\,=\,}	$$ product {\displaystyle \scriptstyle {\text{product}}}
Division (÷)
$$ dividend divisor   numerator denominator } = {\displaystyle \scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\\scriptstyle {\text{ }}\\\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,}	$$ fraction quotient ratio {\displaystyle {\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}}
Modulo (mod)
$$ dividend mod divisor = {\displaystyle \scriptstyle {\text{dividend}}{\bmod {\text{divisor}}}\,=\,}	$$ remainder {\displaystyle \scriptstyle {\text{remainder}}}
Exponentiation
$$ base exponent = {\displaystyle \scriptstyle {\text{base}}^{\text{exponent}}\,=\,}	$$ power {\displaystyle \scriptstyle {\text{power}}}
nth root (√)
$$ radicand degree = {\displaystyle \scriptstyle {\sqrt[{\text{degree}}]{\scriptstyle {\text{radicand}}}}\,=\,}	$$ root {\displaystyle \scriptstyle {\text{root}}}
Logarithm (log)
$$ log base ⁡ ( antilogarithm ) = {\displaystyle \scriptstyle \log _{\text{base}}({\text{antilogarithm}})\,=\,}	$$ logarithm {\displaystyle \scriptstyle {\text{logarithm}}}

The quotient of 12 apples by 3 apples is 4.

In arithmetic, a quotient (from Latin: quotiens "how many times", pronounced /ˈkwoʊʃənt/) is the quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as a fraction or a ratio. For example, when dividing twenty (the dividend) by three (the divisor), the quotient is six and two thirds. In this sense, a quotient is the ratio of a dividend to its divisor.

Notation

Main article: Division (mathematics) § Notation

The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole.

$$$$

 
   
     
       
         
           
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               ←
               
                 dividend  or  numerator
               
             
           
           
             
             
               
               ←
               
                 divisor  or  denominator
               
             
           
         
       
       
         
           }
         
       
       ←
       
         quotient
       
     
   
   {\displaystyle {\dfrac {1}{2}}\quad {\begin{aligned}&\leftarrow {\text{dividend  or  numerator}}\\&\leftarrow {\text{divisor  or  denominator}}\end{aligned}}{\Biggr \}}\leftarrow {\text{quotient}}}
 

Integer part definition

The quotient is also less commonly defined as the greatest whole number of times a divisor may be subtracted from a dividend without the remainder becoming negative. For example, the divisor three may be subtracted up to six times from the dividend twenty before the remainder becomes negative: 20-3-3-3-3-3-3 ≥ 0, while 20-3-3-3-3-3-3-3 < 0. In this sense, a quotient is the integer part of the ratio of two numbers.

Quotient of two integers

Main article: Rational number

The definition of a rational number is the quotient of two integers (as long as the denominator is not a zero).

More formal definitions:

A real number r is rational if, and only if, it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational.

Even more formally:

if r is a real number, then r is rational ⇔ ∃ integers a and b such that $r={\frac {a}{b}}$ and $b\neq 0$

The existence of irrational numbers – numbers that are not a quotient of two integers – was first discovered in geometry in such things as the ratio of the diagonal of a square to the side.

More general "quotients"

Outside of arithmetic, many branches of mathematics have borrowed the word "quotient" to describe structures built by breaking larger structures into pieces. Given a set with an equivalence relation defined on it, a "quotient set" may be created which contains those equivalence classes as elements. A quotient group may be formed by breaking a group into a number of similar cosets, while a quotient space may be formed in a similar process by breaking a vector space into a number of similar linear subspaces.

See also

• Left quotient / Right quotient
• Quotient category
• Quotient graph
• Quotient group
• Quotient module
• Quotient object
• Quotient ring
• Quotient set
• Quotient space (linear algebra)
• Quotient space (topology)
• Quotient type
• Quotition and partition

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リンク元

「知能指数」

「知能指数」

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quotient

英

intelligence quotient IQ

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知能検査

-IQ