Which data declaration allows the runtime environment to use fixed-point arithmetic for the expression r = a / b + c?

The correct answer is built on the necessity of employing fixed-point arithmetic for the expression where the variables are involved in division and addition operations. In this scenario, a variable defined as TYPE p (packed decimal) is suitable for representing fixed-point numbers which can preserve precision, especially in financial or high-accuracy calculations.

In the provided option, the declaration of 'r' as TYPE p with DECIMALS 2 indicates that the variable 'r' will hold a value with two decimal places, supporting fixed-point arithmetic. This is critical when performing calculations that may yield fractional results, as it allows the arithmetic operations to handle the precision without leading to rounding issues often associated with floating-point representations.

The other options do not satisfy the requirement for fixed-point arithmetic. For instance, a variable of TYPE f represents floating-point numbers, which can lead to imprecision during arithmetic operations. Furthermore, the data types of 'a', 'b', and 'c' are significant in conjunction with 'r'. In this case, using TYPE i (integer) or TYPE f (floating-point) does not provide the fixed-point handling necessary for operations that include division, as integers will not accommodate fractional results, and floating-point types are detrimentally imprecise when exact decimal