Solidity Weirdness

solidity-weirdness.sol

  function test(uint256 a) public pure returns (uint256) {
    uint256 fooERROR = 2 * 997 / 1000;  // ERROR: Type rational_const 997 / 500 is not implicitly convertible to expected type uint256. Try converting to type ufixed16x3 or use an explicit conversion.
    uint256 fooOK = a * 997 / 1000; // this works... somehow
    uint256 fooERROR2 = a * (997 / 1000); // Operator * not compatible with types uint256 and rational_const 997 / 1000
  }