Los Angeles County’s jobs picture was mixed in November as the county added more than 16,000 jobs but the unemployment rate shot up to a record 12.9 percent as more residents re-entered the job market to search for work, according to state figures released Friday.

The county’s unemployment rate reached its highest rate in modern history, rising from a revised 12.6 percent in October and 12.3 percent in November of last year, according to the state Employment Development Department. The labor force grew by a total of 29,000 jobs, indicating more people have re-entered the workforce. Some labor force growth is typical in November as people look seasonal work; adjusting for this, the labor force still grew by 8,000 jobs.

California’s unemployment rate was 12.4 percent in November, unchanged from October. The national unemployment rate rose to 9.8 percent in November from 9.6 percent in October.

The unemployment rate in each of the county’s two largest cities, Los Angeles and Long Beach, was 14.3 percent in November, meaning one in seven residents was out of work.

The picture was brighter on the payroll jobs front, which uses a different survey. Employers in Los Angeles County added 16,500 jobs, led by seasonal hires in the retail sector. Adjusting for the typical surge in holiday season hiring, the total number of payroll jobs in L.A. County was unchanged in November from October, according to calculations by Los Angeles-based Beacon Economics.

Other sectors adding jobs included professional and business services, local government and entertainment. Leisure and hospitality, which had been a strong area throughout most of the year, lost the most payroll jobs in November, down 2,000. Other industries posting slight losses were construction and financial activities.

In the year-over-year figures, the county lost 15,000 payroll jobs from November 2009, a drop of 0.4 percent. This year-over-year figure is way down from a year ago, when the loss in jobs was more than 100,000. That indicates the local job market is stabilizing.

The entertainment sector added 11,000 jobs over the last 12 months, leading the job gainers. Private education and health services added 9,000 jobs, while leisure and hospitality added 8,000 jobs.

Those gains were offset by losses in the government sector as local governments slashed 16,000 jobs from their payrolls. Manufacturing companies shed nearly 10,000 jobs, while construction jobs dropped by 8,000.