Arithmetic operators — +, −, - , - , - , %, - (floor div, modulo, power)
WHAT are they?
The key one to internalise: ==/ always gives a float==, even 4 / 2 gives 2.0,
while ==// gives the largest integer not greater than the true quotient==.
WHY do // and % exist? (derive from long division)
When you compute by hand you produce two numbers: a whole-number quotient and a leftover remainder . Python keeps both for you:
This is the division algorithm. Solve it:
- (the floor division — how many whole 's fit in )
- (modulo — what is left over)
Operator precedence (HOW Python decides order)
Worked examples
Common mistakes (steel-manned)
Flashcards
What does / always return in Python 3, even for 4/2?
float (2.0) — / is true division.What is the difference between / and //?
/ true (float) division; // floor division → largest integer ≤ the true quotient.State the division-algorithm identity linking // and %.
a == (a // b) * b + (a % b).17 // 5 and 17 % 5?
3 and 2.-17 // 5 =? Why?
-4, because floor division rounds toward −∞ (true quotient −3.4 → −4).-17 % 5 =?
3 — result takes sign of divisor b; check (-4)*5+3=-17.Which sign does Python's % follow?
b (unlike C/Java).How do you get the last decimal digit of n?
n % 10.How do you remove the last decimal digit of n?
n // 10.Is ** left- or right-associative? 2 ** 3 ** 2?
2 ** (3 ** 2) = 512.Highest-precedence arithmetic operator?
** (exponentiation).Test that n is even?
n % 2 == 0.9 ** 0.5 =? Why?
3.0; fractional exponent 1/2 is the square root, returns a float.Recall Feynman: explain it to a 12-year-old
Imagine you have 17 candies and 5 friends. Floor division 17 // 5 = 3 says
"each friend gets 3 whole candies." Modulo 17 % 5 = 2 says "2 candies are left
over in your hand." Put them back together: 3 candies × 5 friends + 2 leftover = 17. That's
exactly the candies you started with! / is the fussy friend who says "actually each gets
3.4 candies" by chopping some up. And ** is just "multiply a number by itself again and
again."
Connections
- Variables and Assignment — operators combine the values you store.
- Data Types — int float complex —
/promotes to float;**with fractions too. - Operator Precedence and Parentheses — the full PEMDAS-style rules.
- Boolean and Comparison Operators —
%powers even/odd and divisibility tests. - Augmented Assignment — += -= //= %= **= — shorthand built from these.
- Loops and Iteration —
%for "every Nth",//for index math.
Concept Map
Hinglish (regional understanding)
Intuition Hinglish mein samjho
Dekho, Python ke saat arithmetic operators hain: + - * / // % **. In mein se + - *
aur ** (power) toh school wale hi hain. Asli kaam ke do naye dost hain — // (floor
division) aur % (modulo). Yeh dono actually wahi purani long division hmain jo
bachpan mein karte the: // batata hai kitne poore groups bante hain (quotient), aur
% batata hai bacha kitna (remainder). Jaise 17 candies, 5 dost: har ek ko 3 milti hain
(17 // 5 = 3) aur 2 bach jaati hain (17 % 5 = 2). Ek golden identity yaad rakho:
a = (a // b)*b + (a % b) — yeh hamesha sach hoti hai.
Sabse bada confusion: Python 3 mein / hamesha float deta hai, matlab 4 / 2 bhi
2.0 dega, aur 5 / 2 2.5. Agar tumhe integer chahiye toh // use karo. C/Java se
aaye ho toh dimaag mein yeh fix kar lo.
Negative numbers mein thoda dhyaan. // "floor" karta hai matlab -∞ ki taraf round,
truncate nahi. Isliye -17 // 5 = -4 (na ki -3), aur -17 % 5 = 3 (positive!), kyunki
Python ka % divisor ka sign leta hai. Confuse ho jao toh seedha formula laga do:
r = a - (a // b) * b. Aur ** right-associative hai: 2 ** 3 ** 2 = 2 ** 9 = 512,
not 64. Jab bhi doubt ho, bracket laga do — clean aur safe. Bas itna samajh lo toh
yeh poora topic 20% effort mein 80% clear ho jaata hai.