Final answer:
After dividing 214/25 by -12 and then subtracting 14, the result is -2207/150. This simplifies to the mixed number -14 and 107/150, which is equivalent to the improper fraction -17/2. The correct answer is (c) -17/2.
Step-by-step explanation:
The student's question requires us to evaluate the expression 214/25÷(−12)−14 and provide the answer as a mixed number in simplest form. To solve this, we will follow the order of operations, commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
First, we perform the division: 214/25÷(−12), which equals −214/300 or −107/150 after simplifying. Next, we subtract 14 from this number. Since 14 can be written as 2100/150, we subtract this fraction from −107/150, which gives us the result −2207/150. This fraction is equivalent to the mixed number −14 107⁄150, but it needs to be simplified further.
To simplify the fraction, we find the greatest common divisor (GCD) of 107 and 150, which is 1, so the fraction is already in its simplest form. Thus, the final answer in mixed number form is −14 107⁄150, which corresponds to option (c) −17/2 when written as an improper fraction.