The time complexity of the Counting Sort algorithm is linear and is famous for sorting non-negative integers (0-positive). It runs well for a possible small difference between the smallest and largest number in the input data series to avoid redundant unused memory space. So far studied in the literature, the traditional counting sort algorithm may also be applied to sort all integers (negative-0-positive) in such a way that positive and negative integers will be dealt with separately to sort. In this paper, we propose a integrated form of counting sort algorithm to sort all real numbers, and we call it the “negative fractional counting sort” method that can efficiently sort arrays with negative and positive integers along with fractional numbers. While the input array has been extended from the integer range 0 to K to the fractional range from –ve fractional number to +ve fractional number, the time complexity remains linear. The proposed method involves separately sorting the negative and positive components of the array, followed by an innovative merging process. This integrated approach eliminates the need for additional arrays or multiple sorting passes, thus optimizing memory usage and computational efficiency. Experimental results demonstrate the algorithm's capability to sort mixed numeric arrays effectively, with performance metrics indicating minimal execution time. Our contribution offers a versatile and efficient sorting solution, extending the practical utility of Counting Sort to a broader spectrum of real-world data scenarios.