Precedence is just a way of avoiding ambiguity in an operation without brackets.
x+n*y ... how do we know whether the person who wrote that operation means add xn to x then multiply by y; or do they mean multiply y by n then add to x. We know because of precedence. With no brackets we have to do the multiplication first, so it is "multiply n by y then add to x" that is meant.
If, conversely, what the person writing teh operation wants to express is "add n to x then multiply the whole thing by y" then they would have to write:
(x+n)*y ... the addition in the brackets has to be done *before* the multiplication, so we can override precedence with brackets.
Of course in the first example we could express "multiply n by y then add to x" as:
x+(n*y) ... but the brackets are superfluous, because of the precedence of multiplication over addition. We already know we have to multiply first, so we don't need the brackets to tell us.
Next week, partial differential equations and hyperplanes. Remember to bring your sextants and plumb lines. I'm just off to get a new tank top.
