You can put this solution on YOUR website! You should explain your question more thoroughly. This appears unrelated to arithmetic progressions.
You asked how 9 years and 4 months is . Starting from the mixed unitted number, you could change all into the number of months.
9 years is 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 of a year. If 9 years were cut into denominations of 3 equal parts, then .
One more denomination would be 28 of these denominations. Now, .
That must be what you are looking for.