Final answer:
The best estimate of the sum of -14 and 1/9 and -2 and 9 / 10 is -17, achieved by rounding both numbers to the nearest whole number and then adding them together.
Step-by-step explanation:
The student has asked for the best estimate of the sum of two numbers: -14 and 1/9 and -2 and 9 / 10. To estimate this, we can round each number to the nearest whole number and add them together. -14 and 1/9 rounds to -14, and -2 and 9/10 rounds to -3. Adding these together, -14 + (-3) gives us -17 as the best estimate. It's important to remember this is an estimate and not the exact sum of the two numbers.