Final answer:
The question involves evaluating a mixed arithmetic and algebraic expression with fractions and signs. After simplifying fractions and finding a common denominator, the resulting value (approximately 4.3295) is not among the provided options, indicating a possible error in the original problem or the answer choices.
Step-by-step explanation:
The question asks to evaluate the following expression: 4 - 2/16 - (-16/11 + 16/16). Let's break down the expression step by step.
Firstly, simplify the fractions within the parentheses:
- -16/11 remains as it is, since it cannot be simplified further.
- 16/16 is equal to 1.
So, inside the parentheses, we have: -16/11 + 1. To add 1 to -16/11, we need to find a common denominator, which is 11, so we get:
-16/11 + 11/11 = (-16 + 11)/11 = -5/11
Now, let's look at the expression outside:
4 - 2/16 simplifies to 4 - 1/8 because 2/16 can be reduced by dividing both the numerator and the denominator by 2. Then, 4 can be written as 32/8 to have a common denominator with 1/8, resulting in:
32/8 - 1/8 = (32 - 1)/8 = 31/8
Finally, combine the two parts:
31/8 - (-5/11)
The subtraction of a negative number is equivalent to addition:
31/8 + 5/11
Now, find a common denominator for both fractions, which is 88, and add them together:
(31 * 11)/88 + (5 * 8)/88 = (341 + 40)/88 = 381/88
To simplify this, divide 381 by 88, which gives us approximately 4.3295, which is not among the provided options, thus indicating an error in the original question or the provided options.