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Definition of apportion : To divide and assign in just proportion; to divide and distribute proportionally; to portion out; to allot; as, to apportion undivided rights; to apportion time among various employments.

Synonyms:

dole out, sell, grant, consider, grapple, take, parcel out, trade, collect, set apart, make do, dish out, plow, cope, carry on, cover, shell out, make out, mete out, partake, partake in, portion out, care, look at, get by, destine, select, appoint, address, administer, lot, award, measure out, divvy up, admeasure, manage, deal out, handle, conduct, treat, contend

distribute, ration, parcel, earmark, allocate, partition, measure, divide, cut, budget, slice, set, portion, study atallot, allow, deal, give, dispense, segment, split, share, assign, allot, mete

dismember, halve, compartmentalize, chunk, piece, zone, subdivide

Usage examples:

• There were so many more important arrests to be made that the overworked police of Monsieur de Maupas had only been able to apportion to him a bungler whom Colville had easily outwitted. - "The Last Hope", Henry Seton Merriman.
• His eyes wandered down to the carving- table, where Brother Biscoe stood ready, as his turn was, to direct and apportion the helpings. - "Brother Copas", Sir Arthur Thomas Quiller-Couch.
• Calculate, balance, and apportion. - "Kept for the Master's Use", Frances Ridley Havergal.