Final answer:
The best estimate for the sum of 12 8/25 and 14 5/9 is 26, as both fractions round down to the nearest whole number.
Step-by-step explanation:
The student is asking for a best estimate of the sum of two mixed numbers: 12 8/25 and 14 5/9. To find this, we can round each number to the nearest whole number and then add them together. The first number, 12 8/25, is approximately 12 because 8/25 is less than half. The second number, 14 5/9, is closer to 14 than to 15 because 5/9 is also less than half. Thus, the best estimate for the sum is 12 + 14, which equals 26.