I'm sure there are better ways than the one I'm about to suggest.

Firstly you've used a regexp to clean up the input, very good, you're protecting yourself against potentially nasty input from the source.. because real-world programmers know real-world people try and stick anything into our machines!

Perhaps you could make the regexp ensure the operator is only one of the four specified operations and then performing an eval on the reconstructed operation?

e.g.

$Problem =~ /(\d+)    # one or more digits
             \s*      # zero or more whitespace
             ([-+\/*]) # operator (1 char only)
             \s*      # zero or more whitespace
             (\d+)/x; # one or more digits
my $Number1    = $1;
my $Number2    = $3;
my $Operator   = $2;

my $Answer;

my $Code = "$1 $2 $3"; # we're confident this is safe
$Answer = eval "$Code";
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Of course if statements should be littered about to ensure the regexp actually matches etc.

Update: as wfsp pointed out below I have now escaped the forward slash in the regexp because the forward slash is the regexp delimiter.