The House voted yesterday to extend for five years the federal government's major education aid programs, after cutting back increases in impact aid to avoid a confrontation with the White House.

The Elementary and Secondary Education Act, costing $46.8 billion over the five-year period and $10.3 billion to 20 vote. The bill now goes to the Senate.

Latest extimates show the government bears about 8 percent of the cost of running the nation's school system. Federal budget extimates predict outlays of about $10.1 billion for fiscal

The major change made in the bill on the floor yesterday was a move by Education and Labor Committee Chairman Rep. Carl Perkins (D.Ky.) to cut impact aid increases in the bill by some $215 million.

Perkins said the move was made to work off a presidential veto and the figure amounted to a "compromise" with the administration.

The administraion had wanted to cut impact aid by some $76 million to $735 million. But the committee ignored its pleas and added increases amounting to about $127 million for some categories of impact aid and $110 million for children who live in public housing.

The cut means the Washington area will not get an expected $16 million windfall that would have gone to Maryland, Virginia and the District of Columbia under the bill, but the area will not lose any money, since the cut contained a "hold harmless" provision that protects recipients of aid from getting less than they did the previous year.

According to Rep. Herbert Harris (D-Va), the area will stay at its current level. "The administration was urging a cut of considerably more," Harris said. "We would have liked to have gotten more money, but I think we did well to hold it at its current level."

The cut eliminated a committee provision that would have allowed children whose parents work on a federal installation, such as the Pentagon, but live in another state, such as Maryland, to be counted for inpact aid.

It reduced the amount of money for children whose parents work on a federal installation but live in a different county.

Perkins' move to cut $215 million was adopted by a voice vote. But a move by Minority Whip Robert Michel (R-III.), to cut the $110 million increase for children in low-rent public housing was defeated by a voice vote.

The idea of impact aid is to offset the burden placed on local school districts by government employes who work at tax-exempt federal installations.

The aid is compensation for the fact that the workers' families use local services but their employer does'nt pay the taxes that usually support such services.

Recent presidents however, have all tried to cut impact aid, which has grown from $29 million in fiscal 1951 to $770 million in fiscal 1978.

The other major change in the bill is one the committee made in the formula for distributing compensatory education money. Under 1974 provisions, the committee de-emphasized the number of poor children in a district as a basis for distributing the funds. This bill restores the emphasis on the number of poor children, with the result that big cities will get more of the $6.3 billion for FY '79 authorized for compensatory education.

The bill also seeks to reduce paper work in applying for federal aid, and it for the first time allows states grants to develop minimum standards of proficiency tests and remedial programs for those who fail such tests.