2.8. Order of Operations¶
When more than one operator appears in an expression the order of evaluation depends on the rules of precedence. A complete explanation of precedence can get complicated, but just to get you started:
Multiplication and division happen before addition and subtraction. So
2 * 3  1
yields 5, not 4, and2 / 3  1
yields 1, not 1 (remember that in integer division2/3
is 0).If the operators have the same precedence they are evaluated from left to right. So in the expression
minute * 100 / 60
, the multiplication happens first, yielding5900 / 60
, which in turn yields 98. If the operations had gone from right to left, the result would be 59 * 1 which is 59, which is wrong.Any time you want to override the rules of precedence (or you are not sure what they are) you can use parentheses. Expressions in parentheses are evaluated first, so
2 * (3  1) is 4
. 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.
Observe the output of the code below to see how the placement of parentheses can change the result of a calculation.

Q2: Match the expression to its correct output. Don't forget to consider integer
division!
Try again!
 (6*4)+1
 25
 6*(4+1)
 30
 (6/4)+1
 2
 6/(4+1)
 1
Note
The following module will walk you through an example of the rules of precedence. Answer the questions in order to check what you remember about the order of operations!
1 + 2 * ( 10  2 ) / 4
Once you’ve submitted your answer for Question 3A, click on Question 3B below.
1 + 2 * 8 / 4
Once you’ve submitted your answer for Question 3B, click on Question 3C below.
1 + 16 / 4
Once you’ve submitted your answer for Question 3C, click on Question 3D below.
1 + 5
is the only operation remaining. I’m not going to ask you any questions
about it. However, it’s important that you can wrap you head around the fact that
the +
operator appeared first in the calculation, but it was the last
operator to be evaluated. The order of operations can be kind of confusing
at times, but I think you’ve got a good grasp of the concept!