how can properties of operations be used to subtract expressions

Properties of operations can be used to subtract expressions  because If you don't, you'll get the wrong answer, because you'll perform the solution steps in the wrong order. Also The Order of Operations provides us with a fixed approach to solving algebraic expressions. Without them, it would be impossible to get the same results because everyone would solve algebraic expressions in their own unique way. With the Order of Operations, everyone who solves a given problem will arrive at the same solution(s). This is what makes it possible to tackle problems like predicting the orbit path of Mars so we can land a probe on it...or develop software that does your math homework for you.;)