Half a loaf is better than no bread to have part of something is better than having nothing at all (compare something is better than nothing). The saying is recorded from the mid 16th century.
the half is better than the whole proverbial saying, mid 16th century, advising economy or restraint. The comparable ‘half is more than the whole’ is found in the writings of the Greek poet Hesiod (c.700 bc).
half mast the position of a flag which is being flown some way below the top of its staff as a mark of respect for a person who has died.
half the truth is often a whole lie something which is partially true can still convey a completely false impression; proverbial saying, mid 18th century.
one half of the world does not know how the other half lives proverbial saying, early 17th century, often used to comment on a lack of communication between neighbouring groups; the saying is found earlier in French, in Rabelais' Pantagruel (1532).
See also two boys are half a boy, do not meet troubles half-way, six of one and half a dozen of the other, well begun is half done at well2.