One way of looking at gerundives is to consider them to be reductions of subordinate clauses. To see the full relationship among main clauses, subordinate clauses, and gerundives, consider the following two main clauses:
(1) Sam went to the store for bread, bacon, and tomatoes. On the way there, he saw the accident.Subordinating a Main Clause
You can combine these two main clauses by subordinating one of them, using a subordinating conjunction:
(2a) When Sam was going to the store for bread, bacon, and tomatoes, he saw the accident.Note that, in addition to using the subordinating conjunction, I changed the tense from the simple past "went" to the progressive "was going." As a result, I could eliminate "On the way there." Note also that the subordinate clause can be placed either before or after the main clause S/V/C pattern.
Semi-reducing the Subordinate Clause
Some writers will instinctively feel that version two is wordy because the subject of the two clauses are identical in meaning. This repetition can be eliminated by deleting the subject and the "helping" verb in the subordinate clause. The result is called a semi-reduced clause:
(3a) When going to the store for bread, bacon, and tomatoes, Sam saw the accident.Note that since "Sam" is more specific than "he," I moved "Sam" to the main clause and eliminated "he." Option 3b is an acceptable sentence, but it is weaker than 3a because some readers may tend to chunk "when going" to "accident" rather than to "Sam."
Full Reduction of the Subordinate Clause -- a Gerundive
Semi-reduced clauses are called that because often a further reduction is possible. If the ellipsed subject of the subordinate clause is also named in the main clause, one can delete the subordinating conjunction, thereby creating a gerundive:
(4a) Going to the store for bread, bacon, and tomatoes, Sam saw the accident.Note that 4b is not an acceptable sentence because when the subordinate conjunction is also deleted, most readers will tend to chunk the gerundive "going" to "accident."