Arithmetic Operators

1.3. Arithmetic Operators#

Table 1.1 lists the arithmetic operators.

Table 1.1 Arithmetic operators#

Symbol

Operator

Example

Result

-

Negation

-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

%

Modulus/Remainder

31 % 24

7

**

Exponentiation

2 ** 5

32

Operators that have two operands are called binary operators. Negation is a unary operator because it applies to one operand.

1.3.1. Negation#

The negation operator simply negates the value.

-5

-5

--5

5

1.3.2. Addition, Subtraction, Multiplication, and Division#

  • The addition, subtraction, multiplication, and division operators are the familiar mathematical operators.

Warning

When the operands are of mixed data type, meaning int and float, the resulting value will be type float.

1.3.3. Integer Division, Modulo#

To know the integer part of a division result, use the integer division operator. For example, to know how many 24-hour days there are in 53 hours.

53 // 24

2

To find out how many hours are left over, you can use the modulo operator, which gives the remainder of the division:

53 % 24 

5

1.3.3.1. Working with Negative Numbers#

To correctly compute the result with negative numbers in integer division and the modulo operation, remember two rules:

  • Rule 1: Python’s integer division rounds towards negative infinity, which differs from truncation. Truncation simply discards digits after the decimal point. Therefore, exercise caution when dealing with negative operands.

  • Rule 2: n = q * base + r, where:

    • n represents the dividend, the number to the left of // and %.

    • q stands for the quotient, obtained through integer division.

    • base denotes the divisor, the number to the right of // and %

    • r signifies the remainder, the outcome of the modulo operator.

By considering the equation in rule Rule 2, it will follow that for the modulo operator, the sign of the remainder matches the sign of the divisor.

1.3.3.2. Case 1: Positive n and Negative base#

Consider:

  • n = 17

  • base = -10

When dividing 17 by -10, the result is -1.7, which rounds down to -2 due to Rule 1 and is the quotient (q). To calculate the modulo operator result, solve for r in the equation 17 = -2 * -10 + r, yielding r = -3. Observe that the sign of the remainder matches that of the divisor.

17 // -10

-2

17 % -10

-3

1.3.3.3. Case 2: Negative n and Positive base#

Consider:

  • n = -17

  • base = 10

When dividing -17 by 10, the result is -1.7, which rounds down to -2 due to Rule 1 and is the quotient (q). To determine the modulo result, solve for r in the equation -17 = -2 * 10 + r, yielding r = 3. Observe that the sign of the remainder matches that of the divisor.

-17 // 10

-2

-17 % 10

3

1.3.3.4. Case 3: Negative n and Negative base#

Consider:

  • n = -17

  • base = -10

When dividing 17 by 10, the result is 1.7, which rounds down to 1 due to Rule 1 and is the quotient (q). To determine the modulo result, solve for r in the equation -17 = 1 * -10 + r, yielding r = -7. Observe that the sign of the remainder matches that of the divisor.

-17 // -10

1

-17 % -10

-7

1.3.4. Exponentiation#

The following expression calculates 3 raised to the 6th power:

3 ** 6

729
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