The PEMDAS rule states that operations in parentheses must be performed first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. Parentheses group elements together and specify the order of operations. Multiplication combines equal groups, division splits a quantity into equal parts, addition combines quantities, and subtraction removes from a total quantity. Several example calculations are provided to demonstrate applying the PEMDAS rule.