Manor Care Inc. of Silver Spring, one of the nation's largest nursing home companies, yesterday announced a 3-for-2 stock split, its seventh split in the past five years.

Chairman Stewart Bainum Sr. said the split was intended to give a wider distribution to the company's stock. Frequent stock splits have been a key element in Manor Care's effort to attract investors.

The split will be distributed Sept. 30 to stockholders of record Sept. 16. It will increase the number of outstanding common shares to 39.8 million, prompting the board of directors this week to raise the number of authorized common shares from 40 million to 80 million.

At the same time, the board authorized an increase in the number of preferred shares from 500,000 to 5 million, although at present no preferred shares are outstanding.

Companies that split their stocks do so for several reasons. It lowers the price of a stock, presumably making it more attractive to investors who prefer lower-priced issues. At yesterday's closing price of $25.50, the post-split price of Manor Care stock would be $17. A split also creates additional shares, making the "float," or pool, of shares available for trading larger. That is an advantage for institutional investors who prefer to buy stocks that are widely held and can be bought and sold without creating wide swings in the share price.

Manor Care's record of growth continued through fiscal 1985, ending May 31. The company earned $30.2 million ($1.14 a share) on revenues of $454.4 million. Manor Care operates 154 health care facilities containing 19,600 beds. It also operates or franchises 624 Quality Inns.