NCERT Solutions Class 7 Maths Chapter 8: Working with Fractions (Hinglish)

Ye Ganita Prakash, yaani Class 7 Maths ki kitaab Part 1 (Reprint 2026-27), ke Chapter 8, Working with Fractions, ke har sawaal ke jawaab hain: text ke sawaal, Math Talk aur Try This, chaaron Figure it Out sets, Bhartiya ganit ke sawaal aur chess paheli. Page numbers kitaab ke hisaab se hain (pages 173–199). Chhote notes: Chapter 8 ke notes.

8.1 Fractions ka guna (pages 173–175)

Aaron 5 ghante mein: 5 × 3 = 15 km. Kachhua 3 ghante mein: 3 × 1/4 = 3/4 km. Aaron 1/5 ghante mein: 3 km ke 5 baraabar hisse, 3/5 km. Aaron 2/5 ghante mein: uska doguna, 2 × 3/5 = 6/5 km.

Figure it Out (pages 176–177)

1. Ek hafte mein: 7 × 1/2 = 7/2 = 3 1/2 glass. January (31 din) mein: 31 × 1/2 = 31/2 = 15 1/2 glass.

2. Ek din mein: 1/8 km. 5 din ke hafte mein: 5 × 1/8 = 5/8 km.

3. Har parivaar ko har hafte: 5 ÷ 3 = 5/3 = 1 2/3 litre. 4 hafte mein: 4 × 5/3 = 20/3 = 6 2/3 litre.

4. Thursday, Monday ke 3 din baad hai, isliye chaand 10 pm ke 3 × 5/6 = 5/2 = 2 1/2 ghante baad, yaani raat 12:30 baje (aadhi raat ke thoda baad) doobega.

5. (a) 7 × 3/5 = 21/5 = 4 1/5. (b) 4 × 1/3 = 4/3 = 1 1/3. (c) 9/7 × 6 = 54/7 = 7 5/7. (d) 13/11 × 6 = 78/11 = 7 1/11.

Do fractions ka guna (pages 177–179)

Kachhua aadhe ghante mein: 1/4 km ka aadha. Unit square ke rangi chauthaai ko 2 mein kaatne se poore ke 8 baraabar hisse bante hain, isliye poore ka 1/8 rangaa hai aur kachhua 1/8 km chalta hai.

Tez kachhua, 2/5 km prati ghanta, 3/4 ghante tak: 3/4 × 2/5. Square ko 5 rows aur 4 columns mein kaatne par 2/5 ka chauthaai 2/20, aur teen chauthaai 6/20 = 3/10 km.

Math Talk: 5/4 × 3/2. 3/2 ko dedh unit square ki tarah banaao, har square 2 rows aur 4 columns mein. 3/2 ka chauthaai 3 chhote hisse, 3/8, aur paanch chauthaai 15/8.

Area aur fractions ka guna (page 180)

Rangaa rectangle 1/2 unit gunaa 1/4 unit hai, aur aise aath unit square bhar dete hain, isliye uska area 1/8 square unit hai. Ye 1/2 × 1/4 ke baraabar hai: fractional sides waale rectangle ka area sides ka guna hai.

Figure it Out (pages 180–181)

1. (a) 1/3 × 1/5 = 1/15 (b) 1/4 × 1/3 = 1/12 (c) 1/5 × 1/2 = 1/10 (d) 1/6 × 1/5 = 1/30. Har ek mein square ko rows aur columns mein kaatkar ek chhota hissa rangaa jaata hai. 1/12 × 1/18 = 1/216, kyunki 18 rows aur 12 columns se 216 hisse bante hain.

2. (a) 2/3 × 4/5 = 8/15 (b) 1/4 × 2/3 = 2/12 = 1/6 (c) 3/5 × 1/2 = 3/10 (d) 4/6 × 3/5 = 12/30 = 2/5. Jaise (a) mein square ko 5 rows aur 3 columns mein kaato: 4/5 chaar rows hai, uska ek tihaai 4 hisse, aur do tihaai 15 mein se 8 hisse.

5/12 × 7/18 nikaalo (page 181). 18 rows aur 12 columns ke saath 7/18 ko 12 hisson mein baantne par 7/216 milta hai, aur aise paanch hisse 35/216. (Kitaab ki agli line mein galti se 5/12 × 7/8 chhapa hai; ye 7/18 hona chahiye.)

Lowest form (pages 182–183)

12/7 × 5/24: 12 ko 24 ke saath cancel karo, (1 × 5)/(7 × 2) = 5/14. 14/15 × 25/42: 14 ko 42 ke saath (1 aur 3 bachte hain) aur 25 ko 15 ke saath (5 aur 3 bachte hain) cancel karo, 5/9.

Figure it Out (pages 183–184)

1. (a) 1/3 × 7/10 = 7/30 (b) 2/3 × 7/10 = 14/30 = 7/15 (c) 3/4 × 7/10 = 21/40 (d) 7/10 × 7/10 = 49/100. (e) Try This: humein (samay) × 7/10 = 1 chahiye, isliye tap 1 ÷ 7/10 = 10/7 = 1 3/7 ghante chalna chahiye.

2. Sadak ke baad Somu ke paas 1 − 1/6 = 5/6 bachti hai. (a) Krishna: 1/2 × 5/6 = 5/12. (b) Bora: 1/3 × 5/6 = 5/18. (c) Somu: 5/6 − 5/12 − 5/18 = 30/36 − 15/36 − 10/36 = 5/36.

3. 3 3/4 × 9 3/5 = 15/4 × 48/5 = cancel karne ke baad 3 × 12 = 36 square feet.

4. Ek line mein chaar paudhon ke beech 3 gap hain, isliye doori 3 × 3/4 = 9/4 = 2 1/4 m.

5. 500 g ka 12/15 = 4/5 × 500 = 400 g; 4 kg ka 3/20 = 3/20 × 4000 = 600 g. 4 kg ka 3/20 bhaari hai.

Kya product hamesha bada hota hai? (pages 184–185)

Dono numbers 1 se bade hon to product dono se bada (4/3 × 4 = 16/3), dono 0 aur 1 ke beech hon to dono se chhota (3/4 × 2/5 = 3/10), aur ek 0 aur 1 ke beech aur doosra 1 se bada ho to dono ke beech (3/4 × 5 = 15/4). Aur udaaharan: 5/2 × 3 = 15/2; 1/2 × 1/3 = 1/6; 2/3 × 6 = 4.

Khaali jagah: ek number 0 aur 1 ke beech ho to product doosre se chhota (less); ek number 1 se bada ho to product doosre se bada (greater).

8.2 Fractions ka bhaag (pages 186–189)

12 ÷ 4 = 3 kyunki 4 × 3 = 12. 1 ÷ 2/3 = 3/2, kyunki 2/3 × 3/2 = 1. 3 ÷ 2/3 = 9/2, kyunki 2/3 × 9/2 = 3. 1/5 ÷ 1/2 = 2/5, kyunki 1/2 × 2/5 = 1/5. 2/3 ÷ 3/5 = 10/9, kyunki 3/5 × 10/9 = 2/3. Niyam: dividend ko divisor ke reciprocal se guna karo, a/b ÷ c/d = (a × d)/(b × c).

Quotient kab dividend se chhota ya bada hota hai? Dividend = divisor × quotient, isliye 0 aur 1 ke beech ka divisor quotient ko dividend se bada banaata hai (6 ÷ 1/4 = 24, 1/8 ÷ 1/4 = 1/2), aur 1 se bada divisor use chhota (6 ÷ 3 = 2). Divisor aur quotient: divisor × quotient = dividend ko isi tarah padhne se, quotient 1 se tab bada hota hai jab dividend divisor se bada ho, aur 0 aur 1 ke beech tab jab dividend divisor se chhota ho.

8.3 Fractions waale kuch sawaal (pages 190–191)

Example 3: 1/4 ÷ 5 = 1/4 × 1/5 = har cup mein 1/20 litre doodh. Example 4: 15/2 ÷ 1/25 = 375/2 eentein. Example 5 (fawwaare): 1 ÷ 1/2 = 2, 1 ÷ 1/4 = 4, 1 ÷ 1/5 = 5; 1 + 2 + 4 + 5 = din mein 12 baar, isliye saath mein din ka 1/12 lagta hai.

Fractional relations (pages 192–193)

Math Talk: hal kiya square. Laal square poore ka 1/4 hai, peela triangle uska aadha, 1/8, aur rangaa hissa triangle ke 4 baraabar tukdon mein se 3 hai, isliye 3/4 × 1/8 = 3/32.

Do figures: (a) rangi patti diagonal aur baayein aur neeche ki sides ke midpoints ko jodne waali line ke beech hai: aadha square, kone ke 1/8 triangle ko ghataakar, yaani 3/8. (b) Upar baayein chauthaai mein ek tircha square uski sides ke midpoints ko jodta hai; do rangi kone ki triangles har ek chauthaai ka 1/8 hain, isliye 2 × 1/8 × 1/4 = 1/16.

Dramma waala daan (pages 193–194)

1/2 × 2/3 × 3/4 × 1/5 × 1/16 × 1/4 = 6/7680 = 1/1280 dramma, yaani ek kauri. Khaali jagah: 1 kauri = 1/30 taambe ka pana, aur 1 kauri = 1/30 × 1/48 = 1/1440 gold dinar.

Figure it Out (pages 196–198)

1.

• 3 ÷ 7/9 = 3 × 9/7 = 27/7
• 14/4 ÷ 2 = 14/8 = 7/4
• 2/3 ÷ 2/3 = 1
• 14/6 ÷ 7/3 = 14/6 × 3/7 = 1
• 4/3 ÷ 3/4 = 16/9
• 7/4 ÷ 1/7 = 49/4
• 8/2 ÷ 4/15 = 4 × 15/4 = 15
• 1/5 ÷ 1/9 = 9/5
• 1/6 ÷ 11/12 = 12/66 = 2/11
• 3 2/3 ÷ 1 3/8 = 11/3 × 8/11 = 8/3 = 2 2/3

2. (a) (iii) 8 ÷ 1/4 = 32 bag. (b) (iv) 1/2 ÷ 8 = har badge ke liye 1/16 m. (c) (iii) 5 ÷ 1/6 = 30 loaf; option (iv), 5 × 6, bhi wahi number deta hai kyunki 1/6 se bhaag uske reciprocal 6 se guna hai, par baantne ko (iii) hi dikhata hai.

3. 6 roti 12 ka aadha hai, isliye 1/2 × 1/4 = 1/8 kg aata.

4. Har 1 ÷ 1/n, n hai, isliye jod 6 + 10 + 13 + 9 + 2 = 40.

5. Padhe gaye: 1/5 × 400 = 80 page aur 3/10 × 400 = 120 page, kul 200. Baaki: 200 page.

6. 2 3/4 × 16 = 11/4 × 16 = 44 km.

7. 5 1/6 − 1/2 = 31/6 − 3/6 = 28/6 = 4 2/3 ghante bachte hain.

8. Bacha hua cake, 1 − 4/5 = 1/5, teen doston mein baraabar baanta gaya, isliye har ek ko 1/5 ÷ 3 = 1/15 cake mila.

9. 565/465 aur 707/676 dono 1 se bade hain, isliye product dono se bada aur 1 se bhi bada hai: (a), (c) aur (e).

10. Neeche daayein chauthaai mein rangaa hissa uska baayan aadha (chauthaai ka 1/2) hai, tirchi line ke upar ke triangle (chauthaai ka 1/8) ko ghataakar, yaani chauthaai ka 3/8: 3/8 × 1/4 = poore square ka 3/32.

11. Pehle point par aadhi cheentiyan aam ke ped ki taraf jaati hain; doosre par baaki ka aadha; teesre par group chaar raaston mein bat jaata hai (do aam ki taraf, ek ganne ke khet ki taraf, ek aage); chauthe par do mein. Aam ka ped: 1/2 + 1/4 + 1/16 + 1/16 + 1/32 = 29/32. Ganne ka khet: 1/16 + 1/32 = 3/32. Dono milkar 1 hote hain.

12. 1 − 1/2 = 1/2; (1 − 1/2) × (1 − 1/3) = 1/2 × 2/3 = 1/3; (1 − 1/5) tak: 1/5; (1 − 1/10) tak: 1/10. Aam baat: (1 − 1/2) × (1 − 1/3) × … × (1 − 1/n) = 1/n, kyunki product 1/2 × 2/3 × 3/4 × … × (n − 1)/n hai aur har numerator apne pichhle denominator ko cancel kar deta hai.

Chess paheli: hamla na karne waali raaniyan (page 199)

4 × 4 board par 4 raaniyan: rows 1 se 4 mein columns 2, 4, 1 aur 3 par rakho. 8 × 8 board par 8 raaniyan: ek jawaab rows 1 se 8 mein columns 1, 5, 8, 6, 3, 7, 2 aur 4 hai. Dono mein koi do raaniyan ek row, column ya diagonal mein nahi hain; 8 raaniyon ki paheli ke aur jawaab bhi hain.

Chhote notes aur zyaada practice topic pages par hain: fractions ka guna, fractions ka bhaag aur Bhartiya ganit ke fraction sawaal.