In a corporate setting, clear communication is essential for interpreting financial and operational reports. Suppose you are tasked with writing a section for a company-wide 'Math Literacy' handbook intended for new hires. Write an overview that identifies the specific mathematical terms used to describe the results of the four fundamental arithmetic operations (addition, subtraction, multiplication, and division). Furthermore, describe the various ways multiplication and division are represented in algebraic notation, specifically highlighting how these might look different from the symbols used in basic elementary arithmetic.