# 6.5. Precedence of OperatorsÂ¶

Arithmetic operators take precedence over logical operators. Python will always evaluate the arithmetic operators first (** is highest, then multiplication/division, then addition/subtraction). Next comes the relational operators. Finally, the logical operators are done last. This means that the expression `x*5 >= 10 and y-6 <= 20`

will be evaluated so as to first perform the arithmetic and then check the relationships. The `and`

will be done last. Many programmers might place parentheses around the two relational expressions, `(x*5 >= 10) and (y-6 <= 20)`

. This is not necessary, but if often makes it easier for people to read and understand the code.

The following table summarizes the operator precedence from highest to lowest. A complete table for the entire language can be found in the Python Documentation.

Level |
Category |
Operators |
---|---|---|

7(high) |
exponent |
** |

6 |
multiplication |
*,/,//,% |

5 |
addition |
+,- |

4 |
relational |
==,!=,<=,>=,>,< |

3 |
logical |
not |

2 |
logical |
and |

1(low) |
logical |
or |

Note

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Common Mistake!

Students often incorrectly combine the in and or operators. For example, if they want to check
that the letter x is inside of either of two variables then they tend to write it the following
way: `'x' in y or z`

Written this way, the code would not always do what the programmer intended. This is because the
`in`

operator is only on the left side of the or statement. It doesnâ€™t get implemented on both
sides of the or statement. In order to properly check that x is inside of either variable, the in
operator must be used on both sides which looks like this:

```
'x' in y or 'x' in z
```

**Check your understanding**

- ((5*3) > 10) and ((4+6) == 11)
- Yes, * and + have higher precedence, followed by > and ==, and then the keyword "and"
- (5*(3 > 10)) and (4 + (6 == 11))
- Arithmetic operators (*, +) have higher precedence than comparison operators (>, ==)
- ((((5*3) > 10) and 4)+6) == 11
- This grouping assumes Python simply evaluates from left to right, which is incorrect. It follows the precedence listed in the table in this section.
- ((5*3) > (10 and (4+6))) == 11
- This grouping assumes that "and" has a higher precedence than ==, which is not true.

Which of the following properly expresses the precedence of operators (using parentheses) in the following expression: 5*3 > 10 and 4+6==11

Here is an animation for the above expression: