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4.4: Operator Precedence

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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.

    Table 4.4 Operator precedence from highest to lowest.
    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
    Checkpoint: Operator precedence
    Concepts in Practice \(\PageIndex{1}\): Precedence rules

    Which part of each expression is evaluated first?x ** 2 + 6 / 3

    1. 6 / 3
    2. x ** 2
    3. 2 + 6
    Answer

    b. Exponentiation has the highest precedence, then division, then addition.

    Concepts in Practice \(\PageIndex{2}\): Precedence rules

    Which part of each expression is evaluated first?

    not 3 * 5 > 10

    1. 3 * 5
    2. not 3
    3. 5 > 10
    Answer

    a. Multiplication has the highest precedence, then greater than, then not.

    Concepts in Practice \(\PageIndex{3}\): Precedence rules

    Which part of each expression is evaluated first?

    z == 5 and x / 8 < 100

    1. 5 and x
    2. x / 8
    3. 8 < 100
    Answer

    b. Division has the highest precedence, then equality and less than, then and .

    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
    Concepts in Practice \(\PageIndex{4}\): Precedence rules

    How is each expression evaluated?10 + 3 * 2 / 4

    1. 10 + (3 * (2 / 4))
    2. 10 + ((3 * 2) / 4)
    3. (10 + 3) * (2 / 4)
    Answer

    b. Multiplication and division have the highest precedence, are left associative, and have higher precedence than addition.

    Concepts in Practice \(\PageIndex{5}\): Precedence rules

    How is each expression evaluated?

    2 * 2 ** 2 ** 3

    1. 2 * ((2 ** 2) ** 3)
    2. 2 * (2 ** (2 ** 3))
    3. ((2*2) ** 2) ** 3
    Answer

    b. Exponentiation is right associative and has higher precedence than multiplication.

    Concepts in Practice \(\PageIndex{6}\): Precedence rules

    How is each expression evaluated?

    100 < x > 150

    1. 100 < x and x < 150
    2. 100 < x or x > 150
    3. 100 < x and x > 150
    Answer

    c. The expression is valid and is separated into comparisons connected with and .

    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
    Concepts in Practice \(\PageIndex{7}\): Precedence rules

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

    1. Equality has precedence over and.
    2. All operators are evaluated right to left.
    3. Order is random when parentheses aren't used.
    Answer

    a. The equality operator, ==, has higher precedence than the logical and .

    Concepts in Practice \(\PageIndex{8}\): Precedence rules

    Given x = 8 and y = 9, what is the result of the following?

    x + 3 * y - 5

    1. 30
    2. 44
    3. 94
    Answer

    a. The expression is evaluated as x + (3*y) - 5. 8 + (3*9) - 5 = 30.

    Concepts in Practice \(\PageIndex{9}\): Precedence rules

    Given x = 8 and y = 9, what is the result of the following?

    (x+3) * (y-5)

    1. 30
    2. 44
    3. 94
    Answer

    b. The expressions in parentheses are evaluated first. (8+3) * (9-5) = 11 * 4 = 44.

    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

    This page titled 4.4: Operator Precedence is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.