Parity: odd aur even

Parity kya hai?

Kisi number ko dots ka ek samooh socho. Agar saare dots jodon mein lag jaayein aur koi akela na bache, to number even hai: 6 se 3 jodiyan banti hain aur 10 se 5. Agar hamesha ek dot bina saathi ke bachta hai, to number odd hai, jaise 7 ya 11. To odd number jodiyon ka samooh aur ek extra dot hai, ya ulti taraf se dekho to aisi jodiyan jinmein ek dot kam ho. Koi number odd hai ya even, ise uski parity kehte hain.

Even aur odd numbers jodna

Dots ke chitra proof ka kaam karte hain. Do even numbers milaao to har dot ka saathi phir bhi hai, isliye even + even = even, chaahe kitne bhi even numbers jodo. Do odd numbers milaao to dono ke bache hue dots aapas mein jodi bana lete hain, isliye odd + odd = even. Ek even aur ek odd number milkar theek ek dot bachaate hain, isliye even + odd = odd. Lambe jodon mein sirf odd numbers maayne rakhte hain: 4 ya 6 odd numbers ke bache dots saare jodiyan bana lete hain aur jod even hota hai, jabki 3 ya 5 odd numbers mein ek dot bach jaata hai aur jod odd hota hai.

Parity se hal hone waali paheliyan

Kishor ko paanch number cards chunkar 30 banaana hai, par uske saare cards odd hain: 13, 9, 1, 7, 11, 5 ya 3. Har tareeka aazmaane mein bahut samay lagega, par parity turant faisla kar deti hai. Paanch odd numbers ka jod odd hota hai, aur 30 even hai, isliye is paheli ka koi hal nahi.

Martin aur Maria ke janmdin mein theek ek saal ka fark hai. Kya unki umar ka jod 112 ho sakta hai? Ginti ke numbers baari-baari aate hain, odd, even, odd, even, isliye do lagaataar numbers hamesha ek odd aur ek even hote hain, aur unka jod odd hota hai: 51 + 52 = 103. 112 even hai, isliye ye namumkin hai.

Ghataav aur guna

Ghataav jod jaisa hi pattern maanta hai: even − even aur odd − odd even hote hain, jabki even − odd aur odd − even odd. Guna alag tarah chalta hai. Kuch rows aur columns waale chhote squares ke grid ko socho. 3 × 3 grid mein 9 squares hain, odd, par 3 × 4 grid mein 12, even. Agar koi bhi taraf even ho, to grid squares ki jodiyon mein kat jaata hai, isliye guna even hai. Guna tabhi odd hai jab dono taraf odd hon. Isliye 27 × 13 odd hai, jabki 42 × 78 aur 135 × 654 even, bina guna kiye.

Expressions ki parity

Kisi algebraic expression ki parity tay bhi ho sakti hai aur badalti bhi. 3n + 4, n = 3 par odd (13) hai, par n = 8 par even (28). 100p, 2n ya 48w − 2 jaise expressions hamesha even hain, kyunki har value 2 se poori bant jaati hai; 2n + 1 aur 4n + 3 hamesha odd hain. Saare even numbers ki list ke liye 2n lete hain, n = 1, 2, 3, … ke liye, aur saare odd numbers ki list ke liye 2n − 1. 100th even number 200 hai, aur har odd number usi jagah ke even number se ek kam hota hai, isliye 100th odd number 199 hai.

Ye kyun zaroori hai

Parity maths ke sabse tez auzaaron mein se hai, ye saabit karne ke liye ki koi cheez namumkin hai. Ye magic square kya hai mein bhi madad karti hai, aur Virahanka numbers kya hain mein odd aur even ke pattern mein bhi. Har sawaal ka jawaab Chapter 6 ke NCERT solutions mein hai; poore Chapter 6 ke notes bhi dekho.