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Python Basics

Python Arithmetic Operators

1. Key Terminology

Term Meaning Example
Operator The operation being applied +, -, *, /
Operand The values the operator acts on x and y in x + y
Expression Operator + operands combined x + y
Evaluate Computing an expression to get a result x + y → 5 
x = 2
y = 3
result = x + y    # x and y are operands, + is operator, x+y is expression

2. The 7 Arithmetic Operators

① Addition +

2 + 3      # 5   (int)
3.4 + 2    # 5.4 (float)
1.0 + 2    # 3.0 (float — not int!)

② Subtraction -

5 - 3       # 2
-2 - (-3)   # 1   — wrap negatives in parentheses for clarity
4 - (-8)    # 12  ← cleaner to write as 4 - (-8)

③ Multiplication *

4 * 3      # 12  (int)
4 * 2.0    # 8.0 (float)

④ Division /

10 / 2     # 5.0  ← always returns float, even if result is whole
10 / 2.5   # 4.0
10 / 0     # ❌ ZeroDivisionError

Division always returns a float, regardless of operand types

⑤ Exponentiation **

10 ** 2    # 100
2 ** 0     # 1
2 ** -1    # 0.5

⑥ Integer Division //

10 // 3    # 3   (chops off decimals, no rounding)
11 // 3    # 3   (not 4 — always floors, never rounds up)
3.5 // 4   # 0.0 (float operand → float result)
10 // 0    # ❌ ZeroDivisionError

Gives how many times the right operand fits evenly into the left

⑦ Modulus %

11 % 3     # 2   (remainder: 3×3=9, 11-9=2)
11 % 2     # 1
11 % 1     # 0   (no remainder)
10 % 0     # ❌ ZeroDivisionError

Returns the remainder after division

3. Float Contagion Rule

Whenever any operand is a float, the result is always a float

1.0 + 2     # 3.0  (not 3)
10 / 2      # 5.0  (division always float)
3.5 // 4    # 0.0  (float operand → float result)

4. Order of Operations (Operator Precedence)

From highest to lowest priority:

Priority Operator(s) Symbol
1 Parentheses / Brackets ()
2 Exponentiation **
3 Multiplication, Division, Modulus *, /, //, %
4 Addition, Subtraction +, -
  • Operators at the same priority level execute left to right
  • Use parentheses liberally to make complex expressions easier to read

Worked Example

x, y, z = 11, 2, 4

result = (x + y - z) ** (x % z) - 7 / 2 // 4
#         (11+2-4)  ** (11%4)   - 3.5  // 4
#             9     **   3      -  0.0
#                   729         -  0.0
#                          = 729.0

5. Using Operators with Wrong Types

Combination Result
int + int ✅ works
float + int ✅ works (returns float)
str + str ✅ concatenation (e.g. "a" + "b" → "ab")
str + int ❌ TypeError
str / int ❌ TypeError

Special Case — Booleans

  • True is treated as 1, False as 0
4.5 / True    # 4.5  (True == 1)
4.5 / False   # ❌ ZeroDivisionError (False == 0)

6. Key Takeaways & Recap

  1. 7 operators: +, -, *, /, **, //, %
  2. Division / always returns a float — even 10 / 2 gives 5.0
  3. Any float operand makes the whole result a float
  4. // floors the result (never rounds up); % gives the remainder
  5. Never divide by zero — any division-based operator will crash
  6. Precedence: () → ** → * / // % → + - (left to right within same level)
  7. Mixing str with numeric operators causes a TypeError