Filed by Blackrock Diversified Income Strategies Fund, Inc.

pursuant to Rule 425 of the Securities Act of 1933, as amended

and deemed filed pursuant to Rule 14a-6

under the Securities and Exchange Act of 1934, as amended

Subject Company: BlackRock Floating Rate Income Strategies Fund, Inc.

Commission File No. 811-21413

----- PLEASE VOTE NOW -----

VOTING NOW HELPS LOWER OVERALL PROXY COSTS AND ELIMINATES

FURTHER MAILINGS AND PHONE CALLS

Time is running short and the Special Meeting is rapidly approaching. According to our records your vote has not yet been received. The special shareholder meeting is to be held at the offices of BlackRock Advisors, LLC, 1 University Square Drive, Princeton, NJ 08540-6455, on Thursday, September 13, 2012 at 9:00 A.M. (Eastern time).

Stockholders of BlackRock Floating Rate Income Strategies Fund II, Inc. (“FRB”) and Blackrock Diversified Income Strategies Fund, Inc. (“DVF”) are being asked to consider the reorganization of their Fund with and into BlackRock Floating Rate Income Strategies Fund, Inc. (“FRA” and together with FRB and DVF, the “Funds”) (the “Reorganizations”), a fund with the same or substantially similar (but not identical) investment objectives and investment policies. Stockholders of FRA are being asked to consider the issuance of additional shares of common stock of FRA (the “Issuances”) in connection with the Reorganizations.

The Board of Directors of each Fund believes the proposal applicable to its respective

Fund is in the best interests of that Fund and its stockholders and unanimously

recommends that you vote “FOR” such proposal.

The proposals were independently reviewed by Institutional Shareholder Services (“ISS”), recognized as one of the leading independent proxy advisory firms in the nation. ISS supports and recommends voting “FOR” the proposals. Hundreds of major institutional investment firms, mutual funds, and other fiduciaries throughout the country rely upon ISS’ expertise, research and ultimately their recommendations. For 25 years, ISS has been a leading provider of independent proxy research to institutional investors. ISS recommends that its clients vote “FOR” the proposals.

Your vote is important, no matter how large or small your holdings may be. We urge you to vote “FOR” the proposal(s) by completing, signing and dating the enclosed proxy card and promptly mailing it in the enclosed postage-paid envelope. Alternatively, you may vote by phone or internet by following the instructions on the enclosed card.

If you hold your shares in a brokerage or bank account (in “street name”), your broker or bank cannot vote your shares (as they have in past annual meetings) unless you complete, sign, date and return the enclosed proxy voting form. Voting now will minimize the expenses incurred with further reminder mailings and solicitations calls.

If you have questions or need assistance in voting your shares, please call Georgeson Inc. at 1-866-856-2826.

Thank you for voting!