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Fractions ka bhaag

Short mein jawab

Fraction se bhaag dene ke liye uske reciprocal se guna karo: a/b ÷ c/d = a/b × d/c = (a × d)/(b × c). Bhaag poochhta hai ki divisor ko kis number se guna karein to dividend mile. 0 aur 1 ke beech ke divisor se quotient dividend se bada aata hai.

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Bhaag ko guna ki tarah padhna

Hum jaante hain ki 12 ÷ 4 = 3. Yahi baat ulti taraf se bhi poochhi ja sakti hai: 4 ko kis number se guna karein to 12 mile? Har bhaag ko ek khaali jagah waale guna ki tarah likhna hi fractions ke bhaag ko aasaan banaata hai. 12 ÷ 4 = 3 mein 12 dividend, 4 divisor aur 3 quotient hai.

Reciprocal

1 ÷ 2/3 kitna hai? Ise 2/3 × ? = 1 likho. Agar 2 aur 3 ek doosre ko cancel kar dein to 1 bachega, aur 2/3 × 3/2 theek yahi karta hai. Isliye 1 ÷ 2/3 = 3/2. Fraction 3/2, jisme numerator aur denominator ki jagah badli gayi hai, 2/3 ka reciprocal hai, aur kisi bhi fraction ka uske reciprocal se guna 1 hota hai. Ab 3 ÷ 2/3 teen guna maangta hai: 2/3 × 3/2 × 3 = 3, isliye 3 ÷ 2/3 = 9/2. Isi tarah 1/5 ÷ 1/2 = 2 × 1/5 = 2/5.

Niyam

2/3 ÷ 3/5 ko dekho, yaani 3/5 × ? = 2/3. Divisor ka reciprocal 5/3, 3/5 ko 1 bana deta hai, aur phir 2/3 se guna karne par 2/3 milta hai, isliye quotient 5/3 × 2/3 = 10/9 hai. Har bhaag inhi do kadmon se hota hai: divisor ka reciprocal nikaalo, phir use dividend se guna karo.

a/b ÷ c/d = a/b × d/c = (a × d)/(b × c).

Brahmagupta ne ye niyam pehli baar aam roop mein apne Brahmasphutasiddhanta (628 CE) mein diya, aur Bhaskara II ne baad mein ise reciprocal se guna karna bataaya.

Fraction se bhaag: 2/3 ÷ 3/5 ko guna mein badlo, reciprocal 5/3 nikaalo, aur guna karke 10/9 pao
Fraction se bhaag

Kya quotient bada hai?

6 ÷ 3 = 2, jo 6 se chhota hai, par 6 ÷ 1/4 = 24 kahin bada hai: chhah poore mein 24 chauthaai hain. Isi tarah 1/8 ÷ 1/4 = 1/2, jo 1/8 se bada hai. Dividend = divisor × quotient, isliye guna ke niyam baat saaf kar dete hain: 0 aur 1 ke beech ka divisor quotient ko dividend se bada banaata hai, aur 1 se bada divisor use chhota. Dividend aur divisor ki tulna quotient ke baare mein bhi batati hai: quotient 1 se tabhi bada hota hai jab dividend divisor se bada ho.

Kya quotient bada hai? 3 se bhaag 6 ko chhota karta hai, par 1/4 se bhaag use 24 bana deta hai, kyunki chhah poore mein 24 chauthaai hain
Quotient bada ya chhota?

Sawaalon mein bhaag

Leena 1/4 litre doodh se 5 cup chai banaati hai. Har cup mein 1/4 ÷ 5 litre hai: 5 ka reciprocal 1/5 hai, isliye har cup ko 1/4 × 1/5 = 1/20 litre milta hai. Doosre sawaal bhi isi tarah chalte hain: 8 m lace, har baar 1/4 m, 8 ÷ 1/4 = 32 bag sajaati hai; 1/2 m ribbon 8 badges mein baantne par har ek ko 1/2 ÷ 8 = 1/16 m; aur 1/6 kg prati loaf ke hisaab se 5 kg aate se 5 ÷ 1/6 = 30 loaf bante hain. Asal kadam ye tay karna hai ki kaunsi maatra baanti ya naapi ja rahi hai, aur kaunsi bhaag de rahi hai.

Har cup mein doodh: 1/4 litre 5 cup mein baantne par har cup mein 1/20 litre
Har cup mein doodh

Ye kyun zaroori hai

Fractions ka bhaag ‘kitne fit honge?’ aur ‘har ek ko kitna?’ jaise sawaalon ka jawaab deta hai, khaana banaane, baantne, naapne aur banaane mein. Guna kaise hota hai, ye fractions ka guna mein hai, aur bhaag waale purane Bhartiya sawaal, jaise Baudhayana ki eentein aur chaar fawwaare, Bhartiya ganit ke fraction sawaal mein. Har sawaal ke jawaab Chapter 8 ke NCERT solutions mein hain; poore Chapter 8 ke notes bhi dekho.

Practice karo

  1. 7/4 ka reciprocal kya hai?

    1. (a) 7/4
    2. (b) 4/7
    3. (c) 1/7
    4. (d) 28
    Jawab dekho

    Jawab: (b) 4/7

  2. 3 ÷ 2/3 kitna hai?

    1. (a) 2
    2. (b) 9/2
    3. (c) 2/9
    4. (d) 6/3
    Jawab dekho

    Jawab: (b) 9/2

  3. 1/4 litre doodh 5 cup mein baraabar baanta gaya. Har cup mein kitna doodh hai?

    1. (a) 5/4 litre
    2. (b) 1/9 litre
    3. (c) 1/20 litre
    4. (d) 4/5 litre
    Jawab dekho

    Jawab: (c) 1/20 litre

  4. Maria ke paas 8 m lace hai aur har bag par 1/4 m lagti hai. Kitne bag saj sakte hain?

    Jawab dekho

    Jawab: 8 ÷ 1/4 = 8 × 4 = 32 bag.

  5. Bina hisaab ke batao, 5 ÷ 3/7 kya 5 se zyaada hai ya kam?

    Jawab dekho

    Jawab: Zyaada, kyunki divisor 3/7 0 aur 1 ke beech hai, aur aise number se bhaag dene par quotient dividend se bada aata hai. Asal mein 5 ÷ 3/7 = 35/3.

Students ke sawal

Fraction ka reciprocal kya hota hai?

Numerator aur denominator ki jagah badalne se jo fraction banta hai: 3/5 ka reciprocal 5/3 hai, aur 5 (yaani 5/1) ka 1/5. Kisi number ka uske reciprocal se guna hamesha 1 hota hai, isiliye bhaag mein reciprocal sabse kaam ki cheez hai.

Fractions ke bhaag mein reciprocal se guna kyun karte hain?

Bhaag poochhta hai ki divisor ko kis se guna karein to dividend mile. 2/3 ÷ 3/5 mein humein 3/5 × ? = 2/3 chahiye. 3/5 ko uske reciprocal 5/3 se guna karne par 1 milta hai, aur phir 2/3 se guna karne par 2/3, isliye jawaab 5/3 × 2/3 = 10/9 hai.

Fractions ke bhaag ka niyam sabse pehle kisne diya?

Brahmagupta ne 628 CE mein apne Brahmasphutasiddhanta mein aam niyam diya: divisor ka numerator aur denominator badlo, phir guna karo. Bhaskara II ne Lilavati (1150 CE) mein ise ulte kiye divisor, yaani uske reciprocal, se guna karna bataaya.

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