What does this mean: 'I strip all spaces and stuff out of the string upfront.' ???

Make whitesspace optional with \s* and add a few more tests:

my @valid_strings = (
    ['240 x 240 x 2/3600',   'Sample'],
    ['10000 x 240 x 2/3600', 'Max number'],
    ['1 x 240 x 2/3600',     'Min number'],
    ['120x240x2/3600',       'Number sans whitespace'],
    ['120x240x2 / 3600',     'Fraction with whitespace'],
);

my $number = qr/10000|[1-9]\d{0,3}/;
my $valid  = qr{\b$number\s*x\s*$number\s*x\s*$number\s*/\s*$number\b}
+;
#my $valid  = qr{\A$number\s*x\s*$number\s*x\s*$number\s*/\s*$number\z
+};
#my $valid  = qr{^$number\s*x\s*$number\s*x\s*$number\s*/\s*$number$};

my @invalid_strings = (
    ['240 * 240 x 2/3600',    'Missing operator'],
    ['10001 x 240 x 2/3600',  'number exceeds max'],
    ['100 x 10001 x 2/3600',  'number exceeds max'],
    ['100 x 10001 x 2/10001', 'number exceeds max'],
    ['240x240x10001/3600',    'number exceeds max'],
    ['0 x 240 x 2/3600',      'number less than minimum'],
    ['240 x 240 x 2/0',       'Cannot divide by zero'],
    ['240 x 240 x 0/3600',    'Numerator cannot be zero'],
);
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