remainder
Word family
Synonym discussion
Sense: noun/1
All four words name what is still present after a portion has been removed, but they differ in register and typical context. 'Rest' is by far the most common in everyday speech and writing — you can almost always swap 'the rest' in for 'the remainder' without sounding strange ('the rest of the day', 'the rest of the cake'). 'Remainder' is slightly more formal and is the natural choice in writing, news, or schedules ('the remainder of the academic year'). 'Balance' is reserved for money or accounts: you pay the balance owing, not the remainder owing. 'Leftovers', usually plural, almost always means uneaten food kept for a later meal. So a quick rule: speak in 'rest', write in 'remainder', invoice in 'balance', and reheat 'leftovers' for dinner.
Common collocations
Etymology
Borrowed into late Middle English from Anglo-French legal vocabulary, where 'remainder' described a future right in property that 'remained' after a prior estate ended. The Anglo-French noun built on the verb 'remain', from Old French 'remaindre', which itself came from the Latin 'remanere', literally 'to stay back' (re- 'back' + manere 'to stay'). The general sense of 'whatever is left over' grew out of this property-law use during the 1500s, and the mathematical sense for the result of an unequal division was added in the 1600s as English mathematical writing expanded.