Arithmetic operators — +, −, - , - , - , %, - (floor div, modulo, power)

1.2.6 · Coding › Introduction to Programming (Python)

YEH HAIN KYA?

Definition Saat arithmetic operators

Op	Name	Example	Result
`+`	addition	`7 + 2`	`9`
`-`	subtraction	`7 - 2`	`5`
`*`	multiplication	`7 * 2`	`14`
`/`	true division	`7 / 2`	`3.5` (hamesha ek `float`)
`//`	floor division	`7 // 2`	`3` (remainder drop kar deta hai, neeche round karta hai)
`%`	modulo	`7 % 2`	`1` (remainder)
`**`	exponentiation	`7 ** 2`	`49`

Sabse important baat jo andar tak utarni chahiye: ==/ hamesha ek float deta hai==, chahe 4 / 2 hi kyun na ho — yeh 2.0 deta hai, jabki ==// woh sabse bada integer deta hai jo true quotient se zyada nahi hota==.

`//` aur `%` exist kyun karte hain? (long division se derive karo)

Jab tum $a \div b$ haath se calculate karte ho toh do numbers milti hain: ek whole-number quotient $q$ aur ek bacha hua remainder $r$ . Python dono ko tumhare liye rakhta hai:

$a = b \cdot q + r$

Yeh division algorithm hai. Solve karo:

$q = a / / b$ (floor division — kitne poore $b$ fit hote hain $a$ mein)
$r = a % b$ (modulo — kya bacha hua hai)

Figure — Arithmetic operators — +, −, - , - , - , %, - (floor div, modulo, power)

Operator precedence (Python order kaise decide karta hai)

Worked examples

Common mistakes (steel-manned)

Flashcards

Python 3 mein / hamesha kya return karta hai, chahe 4/2 hi ho?

Ek float (2.0) — / true division hai.

/ aur // mein kya fark hai?

/ true (float) division; // floor division → sabse bada integer ≤ true quotient.

// aur % ko link karne wali division-algorithm identity batao.

a == (a // b) * b + (a % b).

17 // 5 aur 17 % 5?

3 aur 2.

-17 // 5 =? Kyun?

-4, kyunki floor division −∞ ki taraf round karta hai (true quotient −3.4 → −4).

-17 % 5 =?

3 — result divisor b ka sign leta hai; check karo (-4)*5+3=-17.

Python ka % kiska sign follow karta hai?

Divisor b ka sign (C/Java se alag).

n ka last decimal digit kaise nikaalte hain?

n % 10.

n ka last decimal digit kaise hatate hain?

n // 10.

** left- ya right-associative hai? 2 ** 3 ** 2?

Right-associative → 2 ** (3 ** 2) = 512.

Sabse zyada precedence wala arithmetic operator?

** (exponentiation).

n even hai test kaise karo?

n % 2 == 0.

9 ** 0.5 =? Kyun?

3.0; fractional exponent 1/2 square root hai, ek float return karta hai.

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho tumhare paas 17 candies hain aur 5 dost hain. Floor division 17 // 5 = 3 kehta hai "har dost ko 3 poori candies milti hain." Modulo 17 % 5 = 2 kehta hai "2 candies tumhare haath mein bachi hain." Wapas jodte hain: 3 candies × 5 dost + 2 bachi = 17. Yeh exactly wahi candies hain jo tumne shuru mein li theen! / woh jhanjhat wala dost hai jo kehta hai "actually har ek ko 3.4 candies milti hain" kuch kaat ke. Aur ** bas "ek number ko baar baar khud se multiply karna" hai.

Connections

Variables and Assignment — operators un values ko combine karte hain jo tum store karte ho.
Data Types — int float complex — / float mein promote karta hai; ** fractions ke saath bhi.
Operator Precedence and Parentheses — poore PEMDAS-style rules.
Boolean and Comparison Operators — % even/odd aur divisibility tests chalata hai.
Augmented Assignment — += -= //= %= **= — inhi se bana shorthand.
Loops and Iteration — % "har Nth" ke liye, // index math ke liye.