Arithmetic Operators in Python

1.3. Arithmetic Operators in Python#

This section provides an overview of arithmetic operators in Python, including their usage, examples, and behavior with negative numbers.

1.3.1. Arithmetic Operators Overview#

Symbol

Operator

Example

Result

-

Negation (unary)

-5

-5

+

Addition

11 + 3.1

14.1

-

Subtraction

5 - 19

-14

*

Multiplication

8.5 * 4

34.0

/

Division

11 / 2

5.5

//

Integer division

16 // 5

3

%

Modulo/remainder

31 % 24

7

**

Exponentiation

2 ** 5

32

1.3.2. Negation#

The negation operator (-) negates the value of its operand.

1.3.2.1. Negation examples#

-5 # Result: -5 –5 # Result: 5 —5 # Result: -5

1.3.3. Addition, subtraction, multiplication, and division#

These operators perform the standard mathematical operations.

1.3.3.1. Examples#

11 + 3.1  # Result: 14.1
5 - 19    # Result: -14
8.5 * 4   # Result: 34.0  (result is float because 8.5 is float)
11 / 2    # Result: 5.5

Note: When operands are of mixed numeric types (e.g., int and float), the result is a float.

1.3.4. Integer division (//) and modulo (%)#

1.3.4.1. Integer division (//)#

The integer division operator (//) returns the floor of the division—i.e., the largest integer less than or equal to the true quotient. If both operands are integers, the result is an integer; if at least one operand is a float, the result is a float.

1.3.4.1.1. Example#

53 // 24  # Result: 2

1.3.4.2. Modulo (%)#

The modulo operator (%) returns the remainder of the division. The remainder’s sign matches the divisor’s sign.

1.3.4.2.1. Example#

53 % 24  # Result: 5

1.3.5. Working with negative numbers#

When performing integer division and modulo operations with negative numbers, Python follows these rules:

  1. Integer division rounds toward negative infinity (floor), not toward zero.

  2. The relationship between dividend, divisor, quotient, and remainder is:

    n = q * base + r

    • n: dividend (left of // or %)

    • q: quotient (result of //)

    • base: divisor (right of // or %)

    • r: remainder (result of %)

The sign of the remainder (r) always matches the sign of the divisor (base). This differs from some other languages where the remainder’s sign may match the dividend’s sign.

1.3.5.1. Case 1: Positive n and negative base#

Given n = 17 and base = -10:

17 // -10  # Result: -2
17 % -10   # Result: -3

Explanation:

  • Quotient (q) = -2 (floors from -1.7)

  • Remainder (r) = -3 (matches the divisor’s sign)

1.3.5.2. Case 2: Negative n and positive base#

Given n = -17 and base = 10:

-17 // 10  # Result: -2
-17 % 10   # Result: 3

Explanation:

  • Quotient (q) = -2 (floors from -1.7)

  • Remainder (r) = 3 (matches the divisor’s sign)

1.3.5.3. Case 3: Negative n and negative base#

Given n = -17 and base = -10:

-17 // -10  # Result: 1
-17 % -10   # Result: -7

Explanation:

  • Quotient (q) = 1 (floor of 1.7 is 1)

  • Remainder (r) = -7 (matches the divisor’s sign)

1.3.6. Exponentiation#

The exponentiation operator (**) raises a number to the power of another.

1.3.6.1. Example#

3 ** 6     # Result: 729
2 ** -3    # Result: 0.125
9 ** 0.5   # Result: 3.0

Python supports negative and fractional exponents.

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