These words refer to what exists as a superfluous quantity once the needed or used portion of something has been subtracted. Left-over is relatively informal in pointing to any such entity, concrete or abstract. Often, it suggests a survival from an earlier period: an idea that was a left-over from the Victorian era. It particularly pertain to food not eaten at a given meal, suggesting something saved to be eaten later or prepared in a different way; in this use, it is often plural: observing that they’d probably be eating left-overs from the Christmas dinner for the next month. Residue is much more formal and points more exclusively to actual material left-overs , but with the suggestion that these are wasted or unusable portions: scraping the residue of food from the plates before putting them under water. Most specifically, the word refers to dregs or to insoluble matter left behind by the filtration or evaporation of a liquid: hard water that leaves a chalky residue when it is boiled away. Surplus indicates something in excess of need, but, in contrast with residue , this amount might be perfectly usable and possibly beneficial: agreeing to share any surplus funds after all expenses were paid. The word is particularly used to indicate stored farm produce or excess military supplies: grain silos for storing the season’s wheat surplus ; labelling the older-model binoculars as surplus .

The remaining words are much more general, having fewer connotations about the nature of the left-over. Remainder and balance can both point to the amount left after subtracting one sum from another; the former often appears in the context of arithmetic, the latter in accounting. Both can be used more generally to suggest a partial quantity viewed in separation from the whole for any reason: grating half the carrots and dicing the remainder ; They burned the obviously outdated books before deciding what to do with the balance . The only distinction here is that balance has a more formal tone and can sometimes sound out of place beyond its natural context of accounting.

Rest is the most general and informal of all these words; it can refer to anything that remains outside some designated amount.

• He asked John to come with him and told the rest of the boys to stay where they were; I wondered how I’d live through the rest of the week; Only one of her reasons really mattered, and the rest were wide of the mark.