The Montgomery County Board of Education voted last night to eliminate 81 school system jobs, an unprecedented reduction intended to offset major cuts in the school budget imposed by the County Council.

By eliminating the jobs, 45 of which are currently filled, the school system will partly absorb $17 million worth of cuts and enable teachers and other workers to receive higher salaries than the council intended.

Virtually all of the positions cut will come from the school system's area and central offices, primarily administrative and clerical jobs. Superintendent Harry Pitt, who recommended the cuts, said he had tried to preserve jobs actually in schools.

As a result, the board's decision essentially represents a trade-off: straining the administration to furnish teachers and other workers with somewhat larger raises than County Council members thought necessary.

At a special Board of Education meeting last night, Pitt said, "I want to make clear to the public we are reducing services . . . . To sit here and say we are making these cuts and it is not going to have any impact is utterly {ridiculous}."

School board President Robert E. Shoenberg said the school system would try to fit the 45 displaced employees into other jobs for which they are qualified. "Nobody is going to be out on the streets," Shoenberg said.

But school spokesman Brian Porter added, "some may bag it, some may retire."

"I'm not thrilled about these cuts. I certainly don't think any of them are a great idea," Pitt told school board members.

Deciding how to balance the $703 million 1990-91 budget was the final chore in what has been an unusually arduous spring for the 102,000-student school system, which has traditionally viewed itself as one of the nation's best -- and relatively financially secure.

But in the face of an election-year taxpayers' revolt, disputes over how much money the school system needs, and how the money should be spent, have spread acrimony among Montgomery's school officials, county political leaders and education unions.

The school board's displeasure was reflected in the fact that, for the first time in recent memory, members adopted the budget on a close vote, 4 to 3. "It was just a general expression of unhappiness," Shoenberg said afterward. "We had sort of a nice budget that did a lot of nice things, then we had to cut the imagination out of it."

This spring, for only the second time in Montgomery history, the County Council furnished less money than the school system needed to cover new contracts negotiated last winter with the Montgomery County Education Association and the Montgomery County Council of Supporting Services Employees.

The school board, in turn, voted last month to renegotiate the two contracts to spare deeper cuts in other parts of the school system's budget.

Last night, the board voted to ratify the revised contracts for Montgomery's 7,200 teachers and 6,500 bus drivers, secretaries and other support workers. Both unions already have approved the new agreements.

Teachers will receive a 6 percent raise next year, 1 percent less than they negotiated initially, while the workers will get a pay increase of 6.5 percent under a renegotiated contract that is similar to their original one.

Health benefits have been weakened in both contracts.

In choosing to revise the contracts, a decision that infuriated union members, several school board members said they thought that was the only way to prevent substantial layoffs.

But the board's decision last night means that even the lowered raises could not spare the loss of jobs entirely. The renegotiated contracts will cost $5.8 million more than the council envisioned.

The biggest single reduction is the elimination of all 24 curriculum specialists and four gifted-education specialists who work in the school system's area offices, a savings of $1.2 million.

In addition, the board made a $227,000 reduction in pay for summertime work, and a $108,000 cut in grants to let schools try innovative projects.

The cuts included nearly $1 million of the $7.4 million in improvements that school officials had expected to make in educational programs.

The board decided not to hire half of the new lunchroom aides who would have freed teachers from the chore, and to abandon three new jobs that would have let the school system start an alternative program for disruptive middle-school students. The school system also will not hire six teaching assistants who would have worked in large kindergarten classes.