When the Frederick County Board of Commissioners approved last week a $64.9 million budget for fiscal 1984, county commissioners exchanged handshakes, pleased that they had kept property taxes down and increased the budget by only 5.9 percent.

But the county's 1,500 schoolteachers were not pleased to learn that their request for a 5 percent cost-of-living raise had been voted down. The new budget gives the teachers the same 2 1/2 percent cost-of-living increase granted all county employes. On top of that, they will get the 2.4 percent annual raise all county workers can expect during the fiscal year.

Teachers had sought a 7 1/2 percent cost-of-living increase, but in negotiations concluded in March had agreed to 5 percent. That tentative settlement with the school board needed the county commissioners' approval, however, and last week the commissioners opted instead to pay only 2.4 percent.

The teachers association intends to reopen negotiations. According to Donald Koons, chief negotiator for the school system, state law requires the county system to discuss salaries since a tentative agreement with the teachers had been reached.

Galen R. Clagett, president of the Board of Commissioners said, "The agreement isn't legally binding. Any discussion on pay raises is between the schoolteachers and the school system, not the county Board of Commissioners."

If a 5 percent cost-of-living increase is ultimately approved, said Charles Smith, vice president of the Board of Commissioners, the money--roughly $1 million--will have to come out of the school board budget. That would mean firing an unspecified number of teachers or cutting programs, he said.

The county budget can't be changed now, Smith said, because the county code states that funds can't be transferred from capital improvements to operations.

The teachers contend there is a $600,000 surplus from the county's food services account, and $300,000 left over from the capital budget that could be tapped.

Kenneth R. Coffey, a county board aide, said the commissioners felt that a 5 percent cost-of-living increase on top of the merit step raises would have been "totally overwhelming and unfair to other county employes."

Teacher association officials, however, pointed out that starting salaries are lower in Frederick than in neighboring Howard and Montgomery counties. Frederick teachers start at $13,150, while Montgomery next year will pay its teachers $14,820 to start. About 30 percent of the Frederick teachers are paid the beginning salary, said Daniel Gadra, head of the county schools' personnel office.

In passing the operating budget, the commissioners allocated the largest share, $33.9 million, to the school board, mainly for salaries and programs; and $1.38 million for Frederick Community College. The commissioners set aside $16.8 million for capital improvements, with half of that going for renovation of Linganore High School and for a middle school in the southern part of the county.

Property taxes will remain at $2.25 per $100 of assessed valuation.

Water and sewerage rates are to be set at a meeting of the commissioners Tuesday. They will also consider a 5 to 10 percent amusement tax then.