Final answer:
After rounding each fraction to the nearest whole number, the expression (34/8 - 16/3) - 19/9 simplifies to (4 - 5) - 2, giving an estimation of -3. Thus, the best estimate for the value of the expression is -3.
Step-by-step explanation:
The question asks to estimate the value of the expression: (34/8 - 16/3) - 19/9. To estimate, we can round each fraction to the nearest whole number. So, 34/8 is approximately 4 (since 4.25 rounds to 4), 16/3 is approximately 5 (since 5.33 rounds to 5), and 19/9 is approximately 2 (since 2.11 rounds to 2).
Now, substituting the rounded numbers into the expression, we have: (4 - 5) - 2, which simplifies to -1 - 2. This simplification yields a final estimation of -3.
Therefore, the best estimate for the value of the expression is -3, which corresponds to option a.