Class 7 Maths Chapter 8: Working with Fractions (Hinglish Notes)
Ye chapter 5 lines mein
Working with Fractions batata hai ki fractions ka guna aur bhaag kaise karein. Fraction aur poore number ke guna mein pehle bhaag aur phir guna karte hain; do fractions ka guna unit square mein ek rectangle ka area hai, jisse Brahmagupta ka niyam a/b × c/d = (a × c)/(b × d) milta hai. Fraction se bhaag dena uske reciprocal se guna karna hai. Purane Bhartiya sawaal in niyamon ko kaam mein laate hain.
Ye chapter kis baare mein hai?
Aaron ek ghante mein 3 km chalta hai, to 5 ghante mein 5 × 3 = 15 km. Uska paaltu kachhua dheema hai, ek ghante mein sirf 1/4 km. Kachhua kitna chalega, ya Aaron ghante ke ek hisse mein kitna chalega, aise sawaalon ke liye fractions ka guna chahiye. Chapter fractions ke guna aur bhaag ke niyam kadam ba kadam banaata hai, unhe chitron se jaanchta hai, aur un Bhartiya ganitagyon ke sawaalon par khatam hota hai jinhone ye niyam sabse pehle likhe.
Fraction aur poore number ka guna
3 ghante mein kachhua 3 × 1/4 = 1/4 + 1/4 + 1/4 = 3/4 km chalta hai. Ghante ke 2/5 hisse mein Aaron 2/5 × 3 km chalta hai. 3 km ko 5 baraabar hisson mein kaato to 3/5 km milta hai, jo 1/5 ghante ki doori hai, aur iska doguna 2 × 3/5 = 6/5 km. Yaani 2/5 × 3 ke liye multiplicand ko multiplier ke denominator se bhaag do, phir uske numerator se guna karo. Isi tarah ₹8 prati ghante par 1 1/4 ghante ka internet 5/4 × 8 = ₹10 ka hai. Padho fractions ka guna.
Do fractions ka guna
Aadhe ghante mein kachhua kitna chalega? 1/4 km ka aadha. Unit square ko poora maano, uska 1/4 rang do, aur us chauthaai ko 2 mein kaato: tukda square ka 1/8 hai, isliye 1/2 × 1/4 = 1/8. 3/4 × 2/5 ke liye square ko 5 rows aur 4 columns mein kaato; 2/5 do rows hain, uska chauthaai 20 mein se 2 hisse hai, aur teen chauthaai 6 hisse, isliye product 6/20 = 3/10 hai. Ye chhote rectangle ek kaam ki baat dikhaate hain: fractional sides waale rectangle ka area uski sides ka guna hai.
Brahmagupta ka niyam aur cancel karna
Chitron se ek chhota raasta dikhta hai. 1/18 × 1/12 mein square ke 18 × 12 = 216 hisse hain, isliye product 1/216 hai; 5/12 × 7/18 ke liye 35/216. Aam taur par a/b × c/d = (a × c)/(b × d), ek niyam jo Brahmagupta ne apne Brahmasphutasiddhanta (628 CE) mein pehli baar aam roop mein diya. Poore number ko 1 ke upar likh sakte hain, isliye 3 × 3/4 = 9/4. Guna se pehle common factors cancel kar sakte hain: 12/7 × 5/24 mein 12 aur 24 mein 12 saajha hai, isliye jawaab 5/14. Guna ka kram fark nahi daalta, jaise rectangle ghumaane par uska area nahi badalta.
Kya product hamesha bada hota hai?
Ginti ke numbers mein 3 × 5 = 15 dono se bada hai. Fractions mein ye numbers par nirbhar hai. Dono numbers 1 se bade hon to product dono se bada, jaise 4/3 × 4 = 16/3. Dono 0 aur 1 ke beech hon to product dono se chhota, jaise 3/4 × 2/5 = 3/10. Ek 0 aur 1 ke beech aur doosra 1 se bada ho to product dono ke beech, jaise 3/4 × 5 = 15/4. Saar ye ki 0 aur 1 ke beech ke number se guna doosre number ko chhota karta hai, aur 1 se bade number se guna use bada.
Fractions ka bhaag
Har bhaag ko guna ki tarah padh sakte hain: 12 ÷ 4 poochhta hai ki 4 ko kis se guna karein to 12 mile. To 1 ÷ 2/3 poochhta hai ki 2/3 ko kis se guna karein to 1 mile, aur jawaab 3/2 hai, kyunki 2/3 × 3/2 = 1. Fraction 3/2, 2/3 ka reciprocal hai. Kisi bhi fraction se bhaag dene ke liye uske reciprocal se guna karo: 2/3 ÷ 3/5 = 2/3 × 5/3 = 10/9. Niyam ke roop mein a/b ÷ c/d = (a × d)/(b × c), jise bhi Brahmagupta ne pehli baar aam roop mein diya. 0 aur 1 ke beech ke number se bhaag dene par jawaab dividend se bada aata hai (6 ÷ 1/4 = 24), aur 1 se bade number se bhaag dene par chhota. Padho fractions ka bhaag.
Bhartiya ganit ke sawaal
Bharat mein fractions ka lamba itihaas hai. Lagbhag 800 BCE ke geometry granth Shulbasutra mein fractions ka bhaag pehle se hai: Baudhayana poochhte hain ki 1/5 unit side waali kitni square eentein 7 1/2 square units dhakengi (375/2). Prithudakasvami ke chaar fawwaare milkar ek kund ko din ke 1/12 hisse mein bharte hain, aur Bhaskara II ki Lilavati mein ek kanjoos ka fractions ke fractions waala daan sirf ek kauri nikalta hai. Ye tareeke North Africa aur Arab duniya tak gaye aur Europe mein lagbhag 17th century mein hi aam hue. Padho Bhartiya ganit ke fraction sawaal.
Saar mein
Fractions ka guna numerators aur denominators ka guna karke karo, jahan ho sake pehle cancel karke; bhaag reciprocal se guna karke karo; aur numbers ke size se jaancho ki jawaab bada hona chahiye ya chhota. Chapter ek chess paheli par khatam hota hai, jisme rani (queens) aise rakhni hain ki koi kisi par hamla na kar sake. Har sawaal ke jawaab Chapter 8 ke NCERT solutions mein hain.
Key terms (zaroori shabd)
| Term | Matlab |
|---|---|
| Multiplier aur multiplicand | 2/5 × 3 mein pehla number, 2/5, multiplier hai aur doosra, 3, multiplicand: hum 3 ka 2/5 nikaalte hain. |
| Unit square | 1 unit side ka square jise ‘poora’ maana jaata hai; ise rows aur columns mein kaatne se do fractions ka guna area ke roop mein dikhta hai. |
| Product (guna-phal) | Guna ka nateeja; fractions mein ye guna kiye numbers se bada, chhota ya unke beech ho sakta hai. |
| Brahmagupta ka niyam | a/b × c/d = (a × c)/(b × d): numerators ka guna aur denominators ka guna, jise 628 CE mein aam roop mein likha gaya. |
| Common factors cancel karna | Guna se pehle numerator aur denominator ko kisi saajhe factor se bhaag dena, taaki jawaab lowest form mein aaye. |
| Apavartana | Fraction ko lowest terms mein laane ka purana Bhartiya naam, jiska zikr Jaina vidwaan Umasvati ne bhi kiya. |
| Reciprocal | a/b ka numerator aur denominator badalne se bana fraction b/a; kisi fraction ka uske reciprocal se guna hamesha 1 hota hai. |
| Dividend, divisor aur quotient | 12 ÷ 4 = 3 mein 12 dividend, 4 divisor aur 3 quotient hai; bhaag poochhta hai ki divisor ko kis number se guna karein to dividend mile. |
| Mixed fraction | Poora number aur ek proper fraction saath mein, jaise 1 1/4, jo improper fraction 5/4 ke baraabar hai. |
| Shulbasutra | Lagbhag 800 BCE tak purane Bhartiya geometry granth, jo yagya vediyan banaane ke baare mein hain; inme non-unit fractions ka istemaal hai. |
| Lowest form | Aisa fraction jiske numerator aur denominator mein 1 ke alaawa koi saajha factor na ho, jaise 5/14. |
| Dramma | Madhyakaalin Bharat ka chaandi ka sikka; Bhaskara II ki paheli mein ek dramma 1280 kauriyon ke baraabar tha. |
Is chapter ke topics
Practice karo
-
2/5 × 3 kitna hai?
Jawab dekho
Jawab: (b) 6/5
-
3/4 × 2/5 kitna hai?
Jawab dekho
Jawab: (c) 3/10
-
3/5 ka reciprocal kya hai?
Jawab dekho
Jawab: (b) 5/3
-
2/3 ÷ 3/5 kitna hai?
Jawab dekho
Jawab: (b) 10/9
-
Kaunsa product dono guna kiye numbers se chhota hai?
Jawab dekho
Jawab: (c) 3/4 × 2/5
-
6 ÷ 1/4 kitna hai?
Jawab dekho
Jawab: (b) 24
Students ke sawal
Class 7 Maths Chapter 8 ke mukhya topics kya hain?
Fraction aur poore number ka guna; unit square aur rectangle ke area se do fractions ka guna; Brahmagupta ka niyam aur common factors cancel karna; product guna kiye numbers se bada hai ya chhota; reciprocal se fractions ka bhaag; word problems; aur Shulbasutra se Bhaskara II tak Bhartiya ganit ke fraction sawaal.
Kya Working with Fractions nayi NCERT Class 7 Maths ki kitaab mein hai?
Haan. Ye Ganita Prakash, yaani Class 7 Maths ki kitaab Part 1 (Reprint 2026-27), ka Chapter 8 hai, pages 173 se 199 tak. Ye A Tale of Three Intersecting Lines ke baad aata hai aur Part 1 ka aakhri chapter hai.
Do fractions ka guna kaise karte hain?
Numerators ka aapas mein guna karo aur denominators ka aapas mein: a/b × c/d = (a × c)/(b × d). Jaise 3/4 × 2/5 = 6/20 = 3/10. Pehle common factors cancel karne se numbers chhote rehte hain. Ye niyam Brahmagupta ne 628 CE mein aam roop mein diya.
Ek fraction ko doosre se bhaag kaise dete hain?
Divisor ka numerator aur denominator badalkar uska reciprocal banaao, phir dividend ko usse guna karo. Jaise 2/3 ÷ 3/5 = 2/3 × 5/3 = 10/9. Ye isliye sahi hai kyunki 3/5 × 10/9 se waapas 2/3 milta hai.
Koi sawal atak gaya?
Photo lo, Lagnever AI step-by-step samjhayega. 7 din ka trial sirf ₹2.
Google Play se app lo Browser mein kholo
Parents ke liye: trial ke baad plan har mahine UPI ya card autopay se renew hota hai. App mein kabhi bhi cancel kar sakte hain.