Final answer:
The largest possible value for the decimal a.b + c.d with each letter representing a different digit from 1 to 9 is 18.3, obtained by using the largest possible digits in a descending order (9 for 'a', 7 for 'b', 8 for 'c', and 6 for 'd').
Step-by-step explanation:
In mathematics, specifically number theory, there's a question about finding the largest possible value for the decimal a.b + c.d, where 'a', 'b', 'c', and 'd' are different digits from 1 to 9, inclusive. To achieve this, we should select the largest digits for 'a' and 'c' since they will be in the unit and tenth place, respectively, making the biggest impact on the overall sum. As 'b' and 'd' are in the hundredth place, we should then choose the next largest remaining digits for them.
So, the largest value for 'a' would be 9 since it is the largest digit. The next largest value for 'c' would then be 8. Lastly, we should pick 7 and 6 for 'b' and 'd', respectively. Therefore, the maximum value for a.b + c.d is 9.7 + 8.6 which equals 18.3.