The earlier answer by dz420 seems to have identified the reason for the difference, which I shall only try to explain in a little more detail, and illustrate with a few examples.
Words like 'X percentage' or 'one third' indicate proportion in your examples and are unlikely to influence the verb form to be used, which depends on the principal noun in each case such as 'population', 'residents' etc.
(1) Since 'residents' is obviously a plural noun, the plural form of the verb is used:
One-third of the residents live below the poverty level.
33.33 percent (one third) of the residents live below the poverty level.
(2) However, collective nouns like population, government, parliament, committee, etc are slightly more complex in that they are usually treated as singular in American English and even in Indian English (which follows the pattern of British English in most other cases), as in
The committee meets every Wednesday
Parliament is now in session
10 percent of the population wants special insurance coverage
One-third of the population of sub-Saharan Africa is undernourished
but the same (type of) words may be treated as singular or plural in British English, and the plural form is more often seen, as in
The government recommend this course of action
Nearly 70 percent of the population still live in the countryside.