2.6. Arithmetic Operators in Python

Arithmetic operators are symbols that perform mathematical operations on values (numbers). They are essential for any type of calculation, from simple sums to more complex operations.

2.6.1. The Main Arithmetic Operators

Python supports the most common arithmetic operators. Here’s a list and an explanation of each:

Operator	Name	Description	Example
+	Addition	Adds two values.	a + b
-	Subtraction	Subtracts the right operand from the left operand.	a - b
*	Multiplication	Multiplies two values.	a * b
/	Division	Divides the left operand by the right operand. Always returns a float in Python 3.	a / b
//	Floor Division	Divides and returns the integer part of the quotient (rounds down).	a // b
%	Modulo (Remainder)	Returns the remainder of the division of the left operand by the right operand.	a % b
**	Exponentiation	Raises the left operand to the power of the right operand.	a ** b

2.6.2. Detailed Examples

Let’s see each operator in action:

# Defining some variables for the examples
num1 = 20
num2 = 7
num3 = 2.5

2.6.2.1. Addition (+)

result_addition = num1 + num2
print(f"Addition: {num1} + {num2} = {result_addition}") # 20 + 7 = 27

# Addition also works with floats
result_addition_float = num1 + num3
print(f"Addition with float: {num1} + {num3} = {result_addition_float}") # 20 + 2.5 = 22.5

2.6.2.2. Subtraction (-)

result_subtraction = num1 - num2
print(f"Subtraction: {num1} - {num2} = {result_subtraction}") # 20 - 7 = 13

result_subtraction_float = num2 - num3
print(f"Subtraction with float: {num2} - {num3} = {result_subtraction_float}") # 7 - 2.5 = 4.5

2.6.2.3. Multiplication (*)

result_multiplication = num1 * num2
print(f"Multiplication: {num1} * {num2} = {result_multiplication}") # 20 * 7 = 140

result_multiplication_float = num1 * num3
print(f"Multiplication with float: {num1} * {num3} = {result_multiplication_float}") # 20 * 2.5 = 50.0

2.6.2.4. Division (/)

Remember: Always returns a float!

result_division = num1 / num2
print(f"Division: {num1} / {num2} = {result_division}") # 20 / 7 = 2.8571...

result_exact_division = 10 / 2
print(f"Exact Division: 10 / 2 = {result_exact_division}") # 10 / 2 = 5.0 (still a float)

2.6.2.5. Integer Division (//) - Floor Division

This operator truncates the result, discarding the decimal part. The result is always an int if both operands are int, or a float if one of the operands is float.

result_integer_division = num1 // num2
print(f"Integer Division: {num1} // {num2} = {result_integer_division}") # 20 // 7 = 2

# With negative numbers, integer division rounds down to the nearest whole number (towards negative infinity)
print(f"Integer Division (negative): -10 // 3 = {-10 // 3}") # Output: -4
print(f"Integer Division (negative): 10 // -3 = {10 // -3}") # Output: -4

# With float, the result will also be float, but with the decimal part truncated
result_integer_division_float = num1 // num3
print(f"Integer Division with float: {num1} // {num3} = {result_integer_division_float}") # 20 // 2.5 = 8.0

2.6.2.6. Modulo (%) - Remainder of Division

Useful for checking parity, cycles, and other logic that depends on the remainder of a division.

result_modulo = num1 % num2
print(f"Modulo: {num1} % {num2} = {result_modulo}") # 20 % 7 = 6 (because 20 = 2*7 + 6)

# Checking if a number is even or odd
even_number = 12
odd_number = 13
print(f"{even_number} is even? {even_number % 2 == 0}")   # True
print(f"{odd_number} is odd? {odd_number % 2 != 0}") # True

2.6.2.7. Exponentiation (**)

result_exp = num2 ** 2 # 7 raised to the power of 2 (7 squared)
print(f"Exponentiation: {num2} ** 2 = {result_exp}") # 7 ** 2 = 49

result_exp_cubed = 3 ** 3 # 3 raised to the power of 3 (3 cubed)
print(f"Exponentiation: 3 ** 3 = {result_exp_cubed}") # 3 ** 3 = 27

# With floats
result_exp_float = 2 ** num3 # 2 raised to the power of 2.5
print(f"Exponentiation with float: 2 ** {num3} = {result_exp_float}") # 2 ** 2.5 = 5.65685...

2.6.3. Order of Precedence for Arithmetic Operators

Just like in mathematics, operators in Python follow an order of precedence to determine which operation is performed first in a complex expression.

1. Parentheses (): Force a specific order of operations.

2. Exponentiation **

3. Multiplication *, Division /, Floor Division //, Modulo %: Evaluated from left to right.

4. Addition +, Subtraction -: Evaluated from left to right.

Tip: When in doubt, or to ensure code clarity, use parentheses to group operations, even if the default precedence would already resolve them in the desired order.

2.6.3.1. Precedence Example:

calculation1 = 5 + 3 * 2 # 3 * 2 is done first (6), then 5 + 6
print(f"5 + 3 * 2 = {calculation1}") # Output: 11

calculation2 = (5 + 3) * 2 # Parentheses force 5 + 3 first (8), then 8 * 2
print(f"(5 + 3) * 2 = {calculation2}") # Output: 16

calculation3 = 20 / 2 ** 2 # 2 ** 2 is done first (4), then 20 / 4
print(f"20 / 2 ** 2 = {calculation3}") # Output: 5.0

Mastering arithmetic operators is fundamental, as they are the basis for any program involving calculations, from a simple currency converter to complex scientific algorithms.