The Prince George's County school board has officially adopted a pared-down budget of $308.4 million for the 1981-82 academic year, but some of its toughest spending decisions may be still ahead.

It took a decision to close 43 schools, nearly 100 hours of public hearings and much anguished pleading with County Executive Lawrence J. Hogan and the County Council to set the final budget, which school officials say is as lean as a $20 steak, with just a little gravy.

But because the board has not yet come to terms with the system's 6,000 increasingly restless teachers, who are demanding a raise, it has not finally decided how the money will be spent. When a settlement is reached the board will almost certainly be forced to give up some or all of the little bit of gravy left in the budget -- a planned reduction of class sizes that would be made possible by adding teacher positions.

The teachers' present contract expires July 31. If no agreement is reached by that time, the board may be forced unilaterally to set a salary level, bringing on a confrontation with the teachers.

"This board of education has done what it has to do by law," warned assistant superintendent Ed Felegy, who said the administration nevertheless will resume negotiations with the teachers soon. "Come Aug. 1, there has to be a salary schedule set in the computer."

The executive board and representative council of the teachers' union three weeks ago rejected the most recent contract proposal.Superintendent Edward J. Feeney offered a 10.5 percent cumulative wage increase -- 9 percent in cash during the first year. The teachers, who asked for a 42.5 percent pay raise last November, now say they want at least a real 10 percent increase for next year. They also want the sizes of their classes made subject to formal grievance procedures.

But school administrators insist they cannot concede an inch on the principle of who controls class sizes.

"Class size is an issue of educational policy, which the board sets," said Felegy, who is in charge of personnel for the schools. "Were it a grievable issue, if the dispute was not resolved at my level, then it goes to arbitration. You get a third party coming in. . . The board cannot give up that authority."

The budget was a $293.6 million gleam in Feeney's eye when he first proposed it to the school board last December. The superintendent stressed that his "bare bones" document provided only enough money to keep up with increased operating costs and proposed few new programs or improvements. The proposal did not allow for a teachers' raise because negotiations were still in progress at that time.

The school board then added $19 million to the budget: $10.7 million reserved for a settlement with the teachers, $4.8 million for a settlement negotiated with unionized non-teaching personnel and $3.5 million for a reduction of class sizes by adding 122 elementary and 62 secondary teaching positions. Of the $19 million, $2 million is in the form of savings to be realized by closing schools.

Current elementary classes average 28 pupils. The proposal pushed by board members Angelo Castelli and Norman Saunders would set a maximum of 25 for classes in first through third grades and 28 for fourth, fifth and sixth graders, and would increase staffing at the secondary level.

When the resulting $310 million budget was submitted to County Executive Hogan, he promptly cut it to $299 million -- removing, he said, unnecessary expenditures caused by waste, mismanagement and a too-generous provision for the teacher settlement. The County Council then restored all but $1.5 million of Hogan's cuts when it approved the county's $630 million budget on May 23.

The council accounted for $1 million of the shortfall by allowing for a smaller pay raise to substitute teachers, postponing improvements to the heating plants in some schools, and making some optimistic assumptions about faculty attrition. "And then they said 'there's another half million more that we're not giving you, and we're not telling you what category to cut," said assistant superintendent Felegy.

He estimated that the superintendent's latest offer to the teachers would cost $13.5 million, approximately $1.5 million less than the settlement recommended by arbitrator Arvid Anderson. Felegy insisted the offer could be met within the budget, but said other budget categories would have to be cut by $2.8 million to do it and the class size item, the second most important concern of the teachers, would be the first to go.

"It all depends on where you slice it. If you want to slice the cost-of-living increase large, you have to slice something else small," said Felegy. "Clearly those issues are related; the arbitrator took note of that."

Teachers' union president John Sisson said the money to meet the teachers' demands can be found in the budget without sacrificing additional insrtructional programs or class size, but he would not be specific.

"I have some ideas in my head but at this point I can't say what they are," said the embattled union president. Sisson is caught between the surprising resolve of the 300 teacher representatives, who voted overwhelmingly not to send the school system's latest contract to the rank and file, and his more conservative board of directors, nearly half of whom voted to override the representatives' decision. The addition of two new, vocal members to the board of directors on July 1 could tip the balance toward the hardline position, however.

Schools spokesman Brian Porter warned, however, that it would be "wishful thinking on the part of teachers to believe that the board of education would be willing to gut its instructional programs to fund a huge salary increase."

Meanwhile, a grass-roots petition drive is seeking the signatures of 1,200 teachers in a bid to force the union's board of directors to send the contract offer to a membership vote. School officials and some union insiders feel that a majority of the rank and file would find the offer fair, in light of the tight fiscal posture of the county, state and federal governments.

Other observers, including some close to negotiations, say the petition campaign is the work of the more conservative elements in the union hierarchy, who are trying to "sell out" the wishes of the representative council. These observers, who oppose the latest offer, say fewer than 200 signatures have been collected, and the campaign will fall.

The union leadership will return next week from the National Educators Association conference in Minneapolis. At that time a new negotiating team, headed by Sisson and perhaps including National Education Association negotiator David Graham, will meet the school system representatives. Sisson said he was not sure whether the representative council would have to approve the next offer before it would be sent to the rank and file for a vote.