WASHINGTON — Unemployment rates fell in three-quarters of U.S. states last month, a sign that many parts of the country are experiencing modest job gains.

Unemployment rates fell in 36 states in October and rose in only 5, the Labor Department said today. Rates were unchanged in 9 states. That’s the best showing since April, when rates fell in 39 states.

Nationally, the unemployment rate ticked down to 9 percent in October, from 9.1 percent the previous month. Employers added a modest 80,000 net jobs last month and the previous two months were revised to show much stronger gains.

Still, at least 125,000 jobs a month are needed to keep up with population growth, and at least double that amount to rapidly reduce the unemployment rate.

Nevada had the nation’s highest unemployment rate for the 17th straight month. It was unchanged at 13.4 percent. California had the second-highest rate at 11.7 percent. Mississippi and Michigan had the next highest rates, both at 10.6 percent.

North Dakota reported the nation’s lowest unemployment rate, at 3.5 percent. It was followed by Nebraska, at 4.2 percent.

Unemployment rates in Alabama, Michigan and Minnesota all dropped by a half of a percentage point — the biggest declines among states.

Hawaii, Illinois, Indiana, Louisiana and Oklahoma all reported small increases in their unemployment rates.

Employers added jobs in 39 states. Payrolls declined in 11 states.

Illinois added 30,000 jobs, the most among states. It was followed by California, which added 25,700.

Illinois’ job growth appears to have encouraged many people who had stopped looking for work to resume job searches, increasing the size of the labor force. That caused the unemployment rate to rise, despite the job gain.

Wisconsin reported the biggest job loss, a drop of 9,700, followed by New York, which shed 8,300.

There have been some signs in recent weeks that the economy and hiring may pick up soon. The number of people seeking unemployment benefits fell to a seven-month low last week. Retail sales also grew at a healthy pace in October.

The economy expanded at a 2 percent annual rate in the July-September quarter, the Commerce Department said Tuesday. That was below an earlier estimate of 2.5 percent. But the drop was mostly because companies cut back on their stockpiles of goods, probably because they expected consumer and business demand to slow.

If demand remains steady, businesses may have to boost inventories in the current quarter, leading to stronger growth. Many economists forecast growth will accelerate to about 3 percent in the October-December quarter.