The state Labor Department says New Jersey’s unemployment rate dropped slightly in October as monthly job losses slowed. The jobless rate for October was 9.7 percent, down one-tenth of a percent from September. That’s lower that the national rate of 10.2 percent. Figures released Wednesday show private sector employment fell by 4,400 jobs last month while government employment rose by 2,600. The new report also revised the state’s job loss figure for September, from 12,700 jobs to 10,600. The biggest losses in October came in the business and professional sectors, where employment fell by 3,600 jobs. Financial activities shed 3,000 jobs. The biggest gains came in construction and manufacturing, which each added 1,600 jobs. AP