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| In [[arithmetic]], '''quotition''' is one of two ways of viewing fractions and division, the other being '''partition'''.
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| In '''quotition division''' one asks how many parts there are; in '''partition division''' one asks what the size of each part is.
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| For example, the expression
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| : <math> 6 \div 2</math> | |
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| can be construed in either of two ways:
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| * "How many parts of size 2 must be added to get 6?" (Quotition division)
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| : One can write
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| :: <math> 6 = \underbrace{2+2+2}_{\text{3 parts}}. </math>
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| : Since it takes 3 parts, the conclusion is that
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| :: <math> 6 \div 2 = 3. \, </math>
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| * "What is the size of 2 equal parts whose sum is 6?". (Partition division)
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| : One can write
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| :: <math> 6 = \underbrace{3+3}_{\text{2 parts}}. </math>
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| : Since the size of each part is 3, the conclusion is that
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| :: <math> 6 \div 2 = 3.</math>
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| It is a fact of elementary theoretical mathematics that the numerical answer is always the same either way: 6 ÷ 2 = 3. This is essentially equivalent to the [[commutative law|commutativity]] of [[multiplication]].
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| [[Division (mathematics)|Division]] involves thinking about a whole in terms of its parts. One frequent division notion, a natural number of equal parts, is known as ''partition'' to educators.
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| The basic concept behind partition is ''sharing''. In sharing a whole entity becomes an integer number of equal parts.
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| What quotition concerns is explained by removing the word ''integer'' in the last sentence. Allow ''number'' to be ''any fraction'' and you have quotition instead of partition.
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| ==See also==
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| * [[List of partition topics]]
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| ==References==
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| <references />
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| {{Refbegin}}
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| *{{cite book|last=Klapper|first=Paul|title=The teaching of arithmetic: A manual for teachers|year=1916|page=202}}
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| *{{cite book|last=Solomon|first=Pearl Gold|title=The math we need to know and do in grades preK–5 : concepts, skills, standards, and assessments|year=2006|publisher=Corwin Press|location=Thousand Oaks, Calif.|isbn=9781412917209|pages=105–106|edition=2nd}}
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| {{Refend}}
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| ==External links==
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| * [http://extranet.edfac.unimelb.edu.au/DSME/arithmetic/FTACDROM1.1/fractions/operations/divfract.shtml A University of Melbourne web page] shows what to do when the fraction is a [[ratio]] of [[integers]] or [[Rational number|rational]].
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| [[Category:Arithmetic]]
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