apportion

[uh-pawr-shuhn, uh-pohr-]
verb (used with object)
to distribute or allocate proportionally; divide and assign according to some rule of proportional distribution: to apportion expenses among the three men.

Origin:
1565–75; < Middle French apportionner, equivalent to ap- ap-1 + portionner to portion

apportionable, adjective
apportioner, noun
nonapportionable, adjective
unapportioned, adjective
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World English Dictionary
apportion (əˈpɔːʃən)
 
vb
(tr) to divide, distribute, or assign appropriate shares of; allot proportionally: to apportion the blame
 
ap'portionable
 
adj
 
ap'portioner
 
n

Collins English Dictionary - Complete & Unabridged 10th Edition
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Etymonline
Word Origin & History

apportion
1570s, from M.Fr. apportionner, from O.Fr. aporcioner, from a- "to" + portioner "to divide into portions," from portion "share, portion" (see portion). Apportionment is attested from 1620s.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
It is too soon to point fingers at individuals or apportion blame precisely.
Their report will no doubt apportion blame and recommend changes in maintenance
  procedures.
To apportion blame to one partner or another in this marriage is, as ought by
  now to be evident, pointless.
It is a complicated thing, they said, to apportion compensation in a bear
  market.
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