NEW YORK — The trustee in the Bernard Madoff fraud started sending out nearly $356 million in checks last week to investors cheated in the giant Ponzi scheme, bringing the total reimbursements so far to over $7.2 billion.

With his fifth payment to Madoff’s victims, trustee Irving Picard said the total recoveries given to victims with approved claims amounts to almost 50 percent of the estimated $17.6 billion lost in Wall Street’s largest fraud.

As the latest round of checks went out Friday, 1,160 accounts out of 2,216 have been reimbursed in full on their original investments, Picard said. The smallest payment sent out was for $431, with the largest being about $67.1 million, he said.

Since Madoff’s investment firm folded in December 2008, Picard has been on a worldwide quest to recover funds to give back to investors.

So far, he and his law firm BakerHostetler have located and recovered through litigation some $10.55 billion in customer monies.

The claims eligible to share in the recovery are those that are approved as “net losers,” meaning they invested more money with Madoff than they took out. “Net winners,” customers who took out of their accounts more than they invested, have had to pay back the difference and are not eligible to recover anything.

The nonprofit Securities Investor Protection Corporation has also advanced $823.7 million to approved customers, an amount included in the $7.2 billion repaid. SIPC also pays Picard’s fees.