Order of Operations

If we read the expression 6 + 4 \cdot 9 - 12 \div 3 from left to right and do each operation as we reach it, we get 10, 90, 78, and finally 26. If we do the multiplication and division first, it becomes 6 + 36 - 4, which equals 38. So the value of an expression depends on the order in which the operations are done. Unless stated otherwise, these rules apply:

I. A series of only additions and subtractions is done in the order they occur.

8 + 12 - 10 + 6 = 20 - 10 + 6 = 10 + 6 = 16

It's incorrect to say 8 + 12 - 10 + 6 = 20 - 16 = 4.

II. A series of only multiplications and divisions is done in the order they occur.

8 \cdot 12 \div 6 \cdot 4 = 96 \div 6 \cdot 4 = 16 \cdot 4 = 64

It's incorrect to say 8 \cdot 12 \div 6 \cdot 4 = 96 \div 24 = 4.

III. In a series with additions, subtractions, multiplications, and divisions, the multiplications and divisions are done first, in order. Then the additions and subtractions are done according to rule I.

6 + 4 \cdot 9 - 12 \div 3 = 6 + 36 - 4 = 38

It's incorrect to say 6 + 4 \cdot 9 - 12 \div 3 = 10 \cdot 9 - 4 = 86.

An expression in parentheses is treated as a single number, and rules I, II, and III apply inside any parentheses too:

(3 + 2)6 = 5 \cdot 6 = 30 8 + (7 - 3)(9 - 6 \div 2) - 4 = 8 + 4 \cdot 6 - 4 = 8 + 24 - 4 = 28

Typing answers: if an answer isn't a whole number, you can type a fraction like 7/3 or a decimal.