Montgomery County Council agreed yesterday to lower property tax rates by as much as 37 cents for each $100 of assessed value, but most property tax bills will go down only slightly because of rapidly rising assessments in the area.

The owner of a typical $80,000 house whose assessment rose about 10 percent over last year would get a tax bill that was about $17 lower than in 1979. The owner of a $100,000 house would pay about $22 less.

The drop in the tax rate, approved by an informal 5-to-2 vote during a council work session yesterday, comes as a result of a budget surplus of $27 million. About $12 million of that figure had not been expected.

County Executive Charles Gilchrist had recommended that the council use $15 million of the surplus to drop the tax rate even further. But council members, noting that at least part of the surplus would probably be used to pay rising gasoline an utility costs, decided to devote only $12 million to tax relief and to keep $15 million available for next year.

If the council passes the tax rate bill in the form agreed on yesterday, county property owners will pay $3.22 for each $100 of assessed value next year compared with $3.59 per $100 last year. That compares with a rate of $3.04 per $100 in Prince George's County (down 27 cents from 1979).

In Virginia the tax rate is much lower than Maryland - residents will pay $1.54 per $100 in Fairfax County for $1980. Because Virginia home-owners are assessed at 100 percent of their property's value as opposed to 45 percent in Maryland, Fairfax and Montgomery homeowners pay almost the same in taxes. Fairfax's projected tax bills for 1980, are expected to be slightly higher than Montgomery's, about $34 more on an $80,000 house.

The property tax rate varies in different parts of Montgomery County because some areas receive fewer county services than others. Thus, those in rural areas have a lower tax rate than those in urbanized areas.

The tax cuts throughout the county will range from as low as 31 cents (about 8 percent) in some rural areas to as high as 37 cents (about 10 percent) in most down-county areas. State law prohibits assessment increases of more than 15 percent and the increases this year are expected to be between 7 and 10 percent.

The largest tax cut in recent memory, according to deputy budget director William Treeworgy, was in 1966 when the tax rate was dropped 9 cents - a cut of about 3 percent.

The council will take final action on the tax cut bill for 1980 during its regular session on Tuesday. Although the cut is slightly less than Gilchrist recommended, the executive is not expected to take any action to try and amend yesterday's vote.

Council members warned yesterday that this year's drop is almost undoubtedly a one-time phenomenon brought about by the unexpected $12 million surplus. With a number of county contracts expiring in the coming year the remaining $15 million surplus is expected to disappear quickly.

Only council members Rose Crenca and Scott Fosler agreed with the Gilchrist recommendation that would have dropped the tax rate further.

Other local jurisdictions have also voted decreases in property tax rates for next year - Prince George's, Arlington, Alexandria and Fairfax - only to have the decrease wiped out by rising property assessments.

Late yesterday Gilchrist said he was "generally pleased," with the council action noting that the council came "within an eyelash of going along with my recommendation."

This year's tax rate will go to fund a $599.4 million operating budget for 1980 that cuts the size of the county's administrate office for the first time in 15 years. The council cut 35 vacant positions from the central government work force complement of 5,313.

In one of their most substantial reductions in the amounts sought by the various county agencies, the executive and council refused to appropriate $1.73 million for 65 new teachers and related instructional costs for the public schools. The school board had sought the positions to reduce class size.