Total profit greater than 100 % Newspapers like Forbes, CNet, WSJ and many other say that it is possible to have total profit of industry more than 100 %.

Examples:


  Apple and Samsung account for more than 100% of industry profits
  because other makers broke even or lost money
  
  Samsung and Apple combined to take 106% percent of the industry's
  profits. How do they take more than 100%? Well, it's a quirk of the
  fact that everyone else in the industry is losing money, or breaking
  even. Apple has 65% of the industry's profits, and Samsung has 41%.


Source: Business Insider: Apple And Samsung Have 106% Of The Smartphone Industry's Profits 

I can't imagine that. Profit means positive value. Negative value is loss. Is it possible to count loss into total industry profit?

When I create an example like this:


  Company A - loss 100
  Company B - loss 100
  Company C - profit 10
  Company D - loss 10
  = total "profit" -200.


Company C would take -5 % of industry profits.
Company D would take 5 % ...

How it is possible that big newspapers use such irrational math?
I think this is just a reflection of the casual language of the popular press. What appears to be in dispute in this question is if profits can be negative or if that case is properly referred to as losses.  I agree that in many contexts this is at best a confusing usage. Most dictionary definitions are clearly implying that profits must be positive (e.g., "A financial gain", "Advantage", "Benefit", or "income in excess of costs"). 

I'm comfortable thinking about negative profits as being a synonym for losses. Industry profits can be thought of as the sum of profits and losses of individual firms just like a firm's profits can be thought of as the sum of profits and losses of subsidiary firms. That seems uncontroversial, at least if this total is positive but that doesn't seem like a standard usage. If we accept that profits can be negative and this aggregate is negative we have weird things happening like firms with positive profits making a negative fraction of total profits. Nothing wrong with the math here, but the math may be telling you something difficult to translate into words. If firm level profits were by definition positive then in @denesp's example Apple and Samsung's share of profits would be 100 percent. 

The more technical term for a variable that when positive is profits and when negative is losses is Net Income. Wikipedia's page on Net Income says:


  In the context of the presentation of financial statements, the IFRS
  Foundation defines net income as synonymous with profit and loss.


I'd avoid the confusion and not refer to losses as negative profits. Instead I would use the term Net Income.  Let's fix that Business Insider quote to use net income:


  Apple and Samsung account for more than 100% of industry net income
  because other makers broke even or lost money
  
  Samsung and Apple combined to take 106% percent of the industry's
  net income. How do they take more than 100%? Well, it's a quirk of the
  fact that everyone else in the industry is losing money, or breaking
  even. Apple has 65% of the industry's net income, and Samsung has 41%.


Now let's use @denesp's example:

Company / Net Income 
Apple / \$53 
Samsung / \$53 
Other / -\$6 
Total / \$100

Everything looks good to me here after the change in terms.