Final answer:
To estimate the value of the expression 34/8 - 16/3 - 14/9, simplify each fraction to the nearest whole number, then subtract to get -2 and 5/6. Among the given choices, the closest estimate is -2 1/2 (Option B).
Step-by-step explanation:
To find the best estimate for the value of the expression 34/8 - 16/3 - 14/9, we can perform the calculation step by step. First, we can simplify each fraction:
- 34/8 is approximately equal to 4 (since 32 is the nearest multiple of 8 to 34).
- 16/3 is approximately equal to 5 and 1/3 (since 15 is the multiple of 3 nearest to 16).
- 14/9 is approximately 1 and 1/2 (since 9 is the multiple of 9 nearest to 14).
Now we perform the subtraction:
- 4 - (5 + 1/3) = 4 - 5 - 1/3 = -1 - 1/3
- -1 - 1/3 - 1 and 1/2 = -1 - 1/3 - 3/2
- To combine -1/3 and -3/2, we find a common denominator:
-1/3 - 3/2 = -2/6 - 9/6 = -11/6 = -1 and 5/6 - Finally, we combine -1 - 1 and 5/6 to get the estimate: -2 and 5/6
Looking at the answer choices, the estimate that comes closest is -2 1/2 (Option B), even though it is not as close as the calculation we just performed. However, among the provided options, it is the one that best fits.