The nation’s unemployment rate dropped to 5.6% in January to the lowest level in more than two years as companies added just 112,000 new jobs – fewer than expected but enough to keep alive hope for a turnaround in the struggling job market. The jobless rate fell 0.1% last month to the lowest level since October 2001, when it was 5.4%, the Labor Department said Friday. January’s rate matched the 5.6% posted in January 2002. Employers added new jobs last month at a pace not seen in three years. The last time payrolls expanded more than 112,000 was in December 2000, when companies added 124,000 positions.