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4.4: Operator Precedence

Last updated

Mar 30, 2025
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- 4.3: Boolean Operations
- 4.5: Chained Decisions

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Learning Objectives

By the end of this section you should be able to

Describe how precedence impacts order of operations.
Describe how associativity impacts order of operations.
Explain the purpose of using parentheses in expressions with multiple operators.

Precedence

When an expression has multiple operators, which operator is evaluated first? Precedence rules provide the priority level of operators. Operators with the highest precedence execute first. Ex: 1 + 2 * 3 is 7 because multiplication takes precedence over addition. However, (1 + 2) * 3 is 9 because parentheses take precedence over multiplication.

Operator	Meaning
()	Parentheses
**	Exponentiation (right associative)
*, /, //, %	Multiplication, division, floor division, modulo
+, -	Addition, subtraction
<, <=, >, >=, ==, !=	Comparison operators
not	Logical `not` operator
and	Logical `and` operator
or	Logical `or` operator

Table 4.4 Operator precedence from highest to lowest.

Checkpoint: Operator precedence

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Concepts in Practice: Precedence rules

Which part of each expression is evaluated first?

x ** 2 + 6 / 3

6 / 3

x ** 2

2 + 6

not 3 * 5 > 10

3 * 5
not 3
5 > 10

z == 5 and x / 8 < 100

5 and x
x / 8
8 < 100

Associativity

What if operators beside each other have the same level of precedence? Associativity determines the order of operations when precedence is the same. Ex: 8 / 4 * 3 is evaluated as (8/4) * 3 rather than 8 / (4*3) because multiplication and division are left associative. Most operators are left associative and are evaluated from left to right. Exponentiation is the main exception (noted above) and is right associative: that is, evaluated from right to left. Ex: 2 ** 3 ** 4 is evaluated as 2 ** (3**4).

When comparison operators are chained, the expression is converted into the equivalent combination of comparisons and evaluated from left to right. Ex. 10 < x <= 20 is evaluated as 10 < x and x <= 20.

Checkpoint: Operation precedence

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Concepts in Practice: Associativity

How is each expression evaluated?

10 + 3 * 2 / 4

10 + (3 * (2 / 4))

10 + ((3 * 2) / 4)

(10 + 3) * (2 / 4)

2 * 2 ** 2 ** 3

2 * ((2 ** 2) ** 3)
2 * (2 ** (2 ** 3))
((2*2) ** 2) ** 3

100 < x > 150

100 < x and x < 150
100 < x or x > 150
100 < x and x > 150

Enforcing order and clarity with parentheses

Operator precedence rules can be hard to remember. Parentheses not only assert a different order of operations but also reduce confusion.

Checkpoint: Using parentheses

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Concepts in Practice: Using parentheses

Consider the example above. Why was the evaluation order different from what the programmer wanted?

Equality has precedence over and.

All operators are evaluated right to left.

Order is random when parentheses aren't used.

Given x = 8 and y = 9, what is the result of the following?
x + 3 * y - 5

30
44
94

Given x = 8 and y = 9, what is the result of the following?
(x+3) * (y-5)

30
44
94

PEP 8 recommendations: spacing around operators

The PEP 8 style guide recommends consistent spacing around operators to avoid extraneous and confusing whitespace.

Avoid multiple spaces and an unequal amount of whitespace around operators with two operands.
Avoid: x= y * 44
Better: x = y * 44
Avoid spaces immediately inside parentheses.
Avoid: x = ( 4 * y )
Better: x = (4 * y)
Surround the following operators with one space: assignment, augment assignment, comparison, Boolean.
Avoid: x= y<44
Better: x = y < 44
Consider adding whitespace around operators with lower priority.
Avoid: x = 5 * z+20
Better: x = 5*z + 20

Learning Objectives

Precedence

Checkpoint: Operator precedence

Concepts in Practice: Precedence rules

Associativity

Checkpoint: Operation precedence

Concepts in Practice: Associativity

Enforcing order and clarity with parentheses

Checkpoint: Using parentheses

Concepts in Practice: Using parentheses

PEP 8 recommendations: spacing around operators

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