In many areas of the world.

which sentence correcs the fragment by including it in the subject?

• have you lived in many areas of the world.
• in many areas of the world, sheep outnumber people.
• cities in many areas of the world have hosted the olympics.

The sentence that corrects the fragment by including it in the subject is the last example: 
Cities in many areas of the world have hosted the Olympics.
Cities is the subject, and in many areas is included in it. 

Cain was a man from the bible. cain and abel were brothers but cain was extremely  jealous of able and while abel was in the fields gathering wheat (i think that's what he was doing) cain came behind him and killed him.  genesis 4: 2  now abel kept flocks, and cain worked the soil.  3  in the course of time cain brought some of the fruits of the soil as an offering  to the  lord.4  and abel also brought an offering—fat portions  from some of the firstborn of his flock.  the  lord  looked with favor on abel and his offering,  5  but on cain and his offering he did not look with favor. so cain was very angry, and his face was downcast.

6  then the  lord  said to cain, “why are you angry?   why is your face downcast?   7  if you do what is right, will you not be accepted? but if you do not do what is right, sin is crouching at your door;   it desires to have you, but you must rule over it.”

8  now cain said to his brother abel, “let’s go out to the field.”  while they were in the field, cain attacked his brother abel and killed him.

i hope this you! : )