Algorithm A2 is clearly better, since it performs fewer mathematical operations.
Which is far from true in the real world. Fewer operations is not equal to better, unless you assume that all operations perform exactly the same way (unrealistic) and the way you compose them (e.g. order of operations, even when commutative) doesn't affect performance (again: unrealistic). For example the x86 LOOP instruction is infamously known to be worse than multiple x86 instructions needed for manual loop. The difficulty of proper measurement gets higher when probability and/or multiple threads are involved.
In your very simple scenario it may be as you say because of the simplicity 10 divs + 5 adds vs 5 divs + 3 adds. But it still is possible that a compiler/cpu will optimize the first one better. We don't know what those algorithms actually are. For example what if those 10 divs are performed on constants and thus a compiler can simply replace them with a single constant? The devil is in details.
Finally it is very dangerous to generalize it to more complicated scenarios. The real world example is quick sort, which is known to even have worse complexity than other sorting algorithms, yet it is widely used, because in many practical situations it outperforms its (theoretically faster) competition.
Is there a mathematical/computational way to clearly show that algorithm $A_2$ offers computational time/cost advantages over algorithm $A_1$?
Typically people will benchmark algorithms (or rather their concrete implementations) in order to truely determine whether they perform better/worse. You will often see such benchmarks directly in published papers. Note that this is hard to do well, because there are so many factors one has to take into account (like for example cache locality, compiler optimizations, cpu optimizations, OS affecting runtime, etc.).
That being said some people do precise runtime analysis (as machine-independent as possible), e.g. Don Knuth in his book series “The Art of Computer Programming” or Robert Sedgewick in "Algorithms". However it is rather rare. At the end of the day we care more about practical application rather than theoretical numbers.