8) Order of Operations

1. Parentheses have the highest precedence and can be used to force an expression to evaluate in the order you want. Since expressions in parentheses are evaluated first, 2 * (3-1) is 4, and(1+1)**(5-2) is 8. You can also use parentheses to make an expression easier to read, as in(minute * 100) / 60, even though it doesn’t change the result.
2. Exponentiation has the next highest precedence, so 2**1+1 is 3 and not 4, and 3*1**3 is 3 and not 27. Can you explain why?
3. Multiplication and both division operators have the same precedence, which is higher than addition and subtraction, which also have the same precedence. So 2*3-1 yields 5 rather than 4, and5-2*2 is 1, not 6.
4. Operators with the same precedence are evaluated from left-to-right. In algebra we say they areleft-associative. So in the expression 6-3+2, the subtraction happens first, yielding 3. We then add 2 to get the result 5. If the operations had been evaluated from right to left, the result would have been 6-(3+2), which is 1.

Note

Due to some historical quirk, an exception to the left-to-right left-associative rule is the exponentiation operator **. A useful hint is to always use parentheses to force exactly the order you want when exponentiation is involved: