Question 761054
You should explain your question more thoroughly.  This appears unrelated to arithmetic progressions.


You asked how 9 years and 4 months is {{{28/3}}}.  Starting from the mixed unitted number, you could change all into the number of months.

9 years is {{{9*12=111}}} months.
4 more months gives 115 months.


You suggest a denominator of 12 from the mixed units and a denominator of 3 is shown on your right-side member number.  Four months is {{{(1/3)}}} of a year.  If 9 years were cut into denominations of 3 equal parts, then {{{9*3=27}}}.
One more denomination would be 28 of these denominations.  Now, {{{28/3=9&1/3}}}.
That must be what you are looking for.