PEMDAS is P, E, MD, AS; multiplication and division have the same precedence, and the same goes for addition and subtraction. When a division operator appears before multiplication, division goes first.

The order Python operators are executed in is governed by the operator precedence, and follow the same rules. Operators with higher precedence are executed before those with lower precedence, but operators have matching precedence when they are in the same group.

For 10-7//2*3+1, you have 2 classes of operators, from lowest to higest:

• +, - (correlating with AS == addition and subtraction)
• *, @, /, //, % (correlating with MD, so multiplication and division).

So // and * are executed first; multiplication and division fall in the same group, not a set order here (MD doesn't mean multiplication comes before division):

10 - ((7 // 2) * 3) + 1

So 7 // 2 is executed first, followed by the multiplication by 3. You then get the subtraction from ten and adding one at the end.

We've glossed over an issue that doesn't affect your particular case, but is very important for writing real Python programs. PEMDAS isn't really about order of operations; it doesn't decide what order things are evaluated in. It's really about argument grouping. PEMDAS says that a + b + c * d is evaluated as (a + b) + (c * d), but it doesn't say whether a + b or c * d is evaluated first.

In math, it doesn't matter what you evaluate first, as long as you respect the argument grouping. In Python, if you evaluted b() and c() first in a() + (b() + c()) just because they're in parentheses, you could get a completely different result, because Python functions can have side effects.

Python expression evaluation mostly works from left to right. For example, in a() + b() + (c() * d()), evaluation order goes as follows:

• a()
• b()
• the first +, now that its arguments are ready
• c()
• d()
• the *, now that its arguments are ready
• the second +, now that its arguments are ready

This is despite the high precedence of * and the parentheses around the multiplication.

PEMDAS is better expressed as

P   Parentheses, then
E   Exponents, then
MD  Multiplication and division, left to right, then
AS  Addition and subtraction, left to right

So in your expression, the division should be done before the multiplication, since it is to the left of the multiplication. After those are done, then do the subtraction then the addition.

This is documented here (Python Documentation / Expressions / Operator-Precedence):

• Multiplication and division, including integer division, happen on the same precedence level, so the order is determined by the direction in which operands are grouped:
• Evaluation order of all the multiplications and divisions is left to right (like for most binary operations, except exponentiation).