The number of people filing new claims for unemployment benefits fell slightly last week, in line with the recent moderate pace of job growth, the U.S. government reported Thursday. The Labor Department said initial jobless claims fell 9,000 to 346,000 last week. The four-week moving average, considered a better measure of labor-market trends because it smoothes weekly fluctuations, fell 2,750 to 345,750, near the five-year low of 338,000 that the measure hit last month. Jobless claims are a gauge of layoffs. Since March, they have fluctuated between 340,000 and 360,000, a level consistent with steady hiring. Employers added 175,000 new jobs in May, nearly matching the average monthly gain for the past year.