Class 6 Maths Chapter 7 NCERT Solutions Hinglish mein: Fractions

Ganita Prakash (Reprint 2026-27) ke Chapter 7, Fractions, ke har “Figure it Out” sawal aur puzzle ke jawab, saath mein wo in-text sawal jo unse jude hain. Page numbers book se milte hain. Short notes: Chapter 7 notes.

Figure it Out: fractional units (pages 152–153)

1. Lagbhag ek size ke teen amrood milkar 1 kg ke hain, isliye har ek lagbhag 1/3 kg ka hai (1 ÷ 3).
2. 1 kg chawal 4 barabar packets mein: har packet 1/4 kg.
3. 3 glass juice 4 doston mein barabar: har ek ne 3 ÷ 4 = 3/4 glass piya.
4. Machhliyan 1/2 kg aur 1/4 kg ki hain. 1/2 = 2/4, isliye dono milkar 2/4 + 1/4 = 3/4 kg.
5. Chhote se bade: quarter (1/4), half (1/2), three quarters (3/4), one and a quarter (1 1/4), one and a half (1 1/2), two and a half (2 1/2).

Fraction ke shabdon wali activity ke liye: Hindi mein log paav (1/4), aadha (1/2), paune ya teen paav (3/4), sava (1 1/4), dedh (1 1/2) aur dhai (2 1/2) kehte hain. Apne parivaar ke shabd bhi likho.

Chikki ke tukde (pages 154–155)

Kya alag shape ke 1/6 tukde ek hi size ke hain? Haan. Har tukda usi chikki ke 6 barabar hisson mein se ek hai, isliye shape kuch bhi ho, har ek mein chikki utni hi hai.

Figure it Out (page 155). Poori chikki 6 × 4 = 24 chhote squares ka grid hai. Har tukde ke squares gino (triangle apne aas-paas ke rectangle ka aadha hota hai):

Tukda	Chhote squares	Chikki ka hissa
a. rectangle 1 × 2	2	2/24 = 1/12
b. triangle, 3 × 4 ka aadha	6	6/24 = 1/4
c. triangle, 3 × 2 ka aadha	3	3/24 = 1/8
d. patti 1 × 4	4	4/24 = 1/6
e. L-shape	3	3/24 = 1/8
f. triangle, 2 × 4 ka aadha	4	4/24 = 1/6
g. ek square	1	1/24
h. triangle, 1 × 2 ka aadha	1	1/24

Patti ko eighths mein modna (page 157)

2 baar 1/8 = 2/8, 4 baar 1/8 = 4/8, 6 baar 1/8 = 6/8, aur 8 baar 1/8 = 8/8 = 1. Quarter wali patti se milao: 2/8 = 1/4, 4/8 = 2/4 aur 6/8 = 3/4.

Figure it Out: fractional units se naapna (page 158)

1. 1/2 ki table ke do aur steps: 6 baar 1/2 = 6/2 = 3, aur 7 baar 1/2 = 7/2 = 3 1/2.
2. 1/4 ki table: 1/4 = ek baar quarter; 1/4 + 1/4 = 2/4; 1/4 + 1/4 + 1/4 = 3/4; chaar quarter = 4/4 = 1; paanch quarter = 5/4; aur aage aise hi.
3. Patti ko 3 barabar parton mein lapeto, mod ko tab tak khiskao jab tak parten bilkul na mil jaayein, phir dabao: har hissa 1/3 hai. Is mudi hui patti ko ek baar aur aadha modo to 6 barabar hisse milte hain, har ek 1/6.
4. a. 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4 = 1 1/4 roti (ek poori roti aur ek quarter). b. Nau quarter: 9/4 = 2 1/4 rotiyan.
5. Har circle ke barabar hisse gino: 1/3 us circle ke saath jiske 3 hisse hain, 1/5 5 hisson wale ke saath, 1/8 8 hisson wale ke saath, aur 1/6 6 hisson wale ke saath.

Number line pe lambaiyan (page 159)

1. 1 unit 3 barabar hisson mein kata hai aur neeli line unme se 2 tak jaati hai: 2/3.
2. 1 unit 5 barabar hisson mein kata hai. Chhoti neeli line 2/5 hai aur lambi 4/5.
3. 8 barabar hisson se marks hain 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 aur 8/8 = 1.

Figure it Out: number line (page 160)

1. 0 se 1 ko 10 barabar hisson mein baanto. 1/10 pehla mark hai aur 3/10 teesra. Kyunki 4/5 = 8/10, 4/5 aathwan mark hai (ya 0 se 1 ko 5 hisson mein baant ke 4 lo).
2. Koi bhi paanch fractions chalenge, jaise 1/2, 1/4, 2/3, 5/6 aur 7/8. Har ek ke liye 0 se 1 ko denominator jitne barabar hisson mein kaato aur numerator jitne hisse gino.
3. Anginat. Kinhi do fractions ke beech hamesha ek aur hota hai, jaise unke theek beech wala, isliye ye kabhi khatam nahi hote.
4. Kaali line 3 halves tak jaati hai: 3/2 (= 1 1/2).
5. 1 se 2 ki jagah bhi fifths mein kati hai, isliye kaali lines chhoti se lambi tak 6/5, 7/5, 8/5 aur 9/5 hain.

Figure it Out: fraction mein kitne poore (page 162)

1. 7/2 = 2/2 + 2/2 + 2/2 + 1/2, isliye isme 3 poore units hain (7/2 = 3 1/2).
2. 4/3 = 3/3 + 1/3 mein 1 poora unit; 7/3 = 3/3 + 3/3 + 1/3 mein 2 poore units.

Figure it Out: mixed fractions (page 162)

1. a. 8/3 = 2 2/3: 2 poore. b. 11/5 = 2 1/5: 2 poore. c. 9/4 = 2 1/4: 2 poore.
2. Lagbhag sab. Jab numerator denominator ka multiple ho, to fraction ek poora number hota hai, jaise 8/4 = 2, aur likhne ke liye koi fractional hissa nahi bachta. Baaki har 1 se bada fraction mixed fraction mein likha ja sakta hai.
3. a. 9/2 = 4 1/2 b. 9/5 = 1 4/5 c. 21/19 = 1 2/19 d. 47/9 = 5 2/9 e. 12/11 = 1 1/11 f. 19/6 = 3 1/6

Figure it Out: mixed fractions se fractions (page 163)

Poore hisse ke fractional units gino aur baaki jodo:

• a. 3 1/4 = 12/4 + 1/4 = 13/4
• b. 7 2/3 = 21/3 + 2/3 = 23/3
• c. 9 4/9 = 81/9 + 4/9 = 85/9
• d. 3 1/6 = 18/6 + 1/6 = 19/6
• e. 2 3/11 = 22/11 + 3/11 = 25/11
• f. 3 9/10 = 30/10 + 9/10 = 39/10

Fraction wall (page 164)

1. Haan, 1/2 = 3/6: dono wall pe ek hi jagah khatam hote hain.
2. Haan. 1/3 = 2/6, isliye do thirds barabar chaar sixths: 2/3 = 4/6. Dono ki lambai same hai.
3. 1/6 ke 3 tukde 1/2 banate hain.
4. 1/6 ke 2 tukde 1/3 banate hain.

Figure it Out: equivalent fractions (page 165)

1. Haan. 3/6, 4/8 aur 5/10 mein numerator theek denominator ka aadha hai, isliye har ek 1/2 ke barabar hai. Fraction wall pe teeno 1/2 wali line pe khatam hote hain.
2. Jaise 1/3 (dono ko 2 se bhaag) aur 4/12 (dono ko 2 se guna). 3/9 bhi sahi hai.
3. 4/6 = 2/3 = 6/9 = 8/12 = 10/15 = 12/18 = …

Figure it Out: rotiyan aur cake baantna (page 166)

1. Har roti ko 4 quarters mein kaato. 12 quarters mein se har bachche ko 3 milte hain: 3/4 roti. Division fact: 3 ÷ 4 = 3/4. Addition fact: 3 = 3/4 + 3/4 + 3/4 + 3/4. Multiplication fact: 3 = 4 × 3/4.
2. Har bachche ko 2/4 = 1/2 roti. Division fact: 2 ÷ 4 = 1/2. Addition fact: 2 = 1/2 + 1/2 + 1/2 + 1/2. Multiplication fact: 2 = 4 × 1/2.
3. Anil ko 2 ÷ 5 = 2/5 cake milta hai. 10 bachchon ko utna hi hissa dene ke liye 4 cake chahiye, kyunki 4/10 = 2/5. Dono groups ko milao to 6 cake 15 bachchon mein bate: 6/15 = 2/5, phir wahi hissa.

Barabar hisse (page 168)

2 rotiyan 3 bachchon mein, 4 rotiyan 6 mein, 6 rotiyan 9 mein: har bachche ko barabar, 2/3, milta hai, kyunki 4/6 aur 6/9 dono simplify hoke 2/3 bante hain. Har jode mein 2/3 ke numerator aur denominator ko ek hi number (2 ya 3) se guna kiya gaya hai.

Figure it Out (page 168).

• a. 5/4 = 10/8: 10 glass 8 doston mein.
• b. 4/3 = 12/9: 12 kg 9 thailon mein.
• c. 7/5 = 14/10: 14 rotiyan 10 bachchon mein (21 rotiyan 15 bachchon mein bhi sahi hai).

Kis group ko zyada milega? (pages 169–170)

Bachche utne hi, par units zyada: har bachche ka hissa badhta hai. Isi liye 1/5 < 2/5 aur 3/7 < 4/7, aur kyunki 1/2 = 4/8, isliye 1/2 < 5/8 bhi.

1. Group 1 mein har ek ko 3/4 glass aur Group 2 mein 7/10 milta hai. Denominator 20 se: 3/4 = 15/20 aur 7/10 = 14/20, isliye Group 1 ke har bachche ko zyada milta hai.
2. 4/7 aur 5/7: Group 2 ke har bachche ko zyada milta hai.

Doosra jodha compare karna aasaan tha, kyunki bachchon ki ginti, yaani denominator, same hai.

Jodon ko same fractional units (page 172)

Sabse chhote common denominator se:

• a. 7/2 aur 3/5 → 35/10 aur 6/10
• b. 8/3 aur 5/6 → 16/6 aur 5/6
• c. 3/4 aur 3/5 → 15/20 aur 12/20
• d. 6/7 aur 8/5 → 30/35 aur 56/35
• e. 9/4 aur 5/2 → 9/4 aur 10/4
• f. 1/10 aur 2/9 → 9/90 aur 20/90
• g. 8/3 aur 11/4 → 32/12 aur 33/12
• h. 13/6 aur 1/9 → 39/18 aur 2/18

Koi bhi common multiple chalta hai; a. ke liye 70/20 aur 12/20 bhi sahi hai.

Figure it Out: lowest terms (page 173)

• a. 17/51: 51 = 3 × 17, isliye dono ko 17 se bhaag do: 1/3.
• b. 64/144: HCF 16 hai: 4/9.
• c. 126/147: 126 = 6 × 21 aur 147 = 7 × 21, isliye 21 se bhaag do: 6/7.
• d. 525/112: dono 7 ke multiples hain (525 = 7 × 75, 112 = 7 × 16): 75/16.

Figure it Out: fractions compare karna (page 174)

1. a. 8/3 = 16/6 aur 5/2 = 15/6, isliye 8/3 > 5/2. b. 4/9 = 28/63 aur 3/7 = 27/63, isliye 4/9 > 3/7. c. 7/10 = 49/70 aur 9/14 = 45/70, isliye 7/10 > 9/14. d. Denominator same: 12/5 > 8/5. e. 5/2 = 10/4, isliye 9/4 < 5/2.
2. a. Denominator 30 se: 7/10 = 21/30, 11/15 = 22/30, 2/5 = 12/30. Ascending: 2/5 < 7/10 < 11/15. b. Denominator 24 se: 19/24, 5/6 = 20/24, 7/12 = 14/24. Ascending: 7/12 < 19/24 < 5/6.
3. a. Denominator 32 se: 25/16 = 50/32, 7/8 = 28/32, 13/4 = 104/32, 17/32. Descending: 13/4 > 25/16 > 7/8 > 17/32. b. Denominator 60 se: 3/4 = 45/60, 12/5 = 144/60, 7/12 = 35/60, 5/4 = 75/60. Descending: 12/5 > 5/4 > 3/4 > 7/12.

Number line pe jodna (pages 175–177)

Meena aur uske bhai ne chikki ka 3/4 khaya, isliye 1/4 bachi. Number line pe 4/7 + 6/7 matlab 1/7 ki 4 chhalaangein aur phir 6 aur: 10 chhalaangein 10/7 = 1 3/7 pe khatam hoti hain, wahi jo numerators jodne se aata hai.

Figure it Out: fractions jodna (page 179)

1. Brahmagupta ke tareeke se:
   • a. 2/7 + 5/7 + 6/7 = 13/7 = 1 6/7
   • b. 3/4 + 1/3 = 9/12 + 4/12 = 13/12 = 1 1/12
   • c. 2/3 + 5/6 = 4/6 + 5/6 = 9/6 = 3/2 = 1 1/2
   • d. 2/3 + 2/7 = 14/21 + 6/21 = 20/21
   • e. 3/4 + 1/3 + 1/5 = 45/60 + 20/60 + 12/60 = 77/60 = 1 17/60
   • f. 2/3 + 4/5 = 10/15 + 12/15 = 22/15 = 1 7/15
   • g. 4/5 + 2/3 = 12/15 + 10/15 = 22/15 (f. jaisa hi, ulte order mein)
   • h. 3/5 + 5/8 = 24/40 + 25/40 = 49/40 = 1 9/40
   • i. 9/2 + 5/4 = 18/4 + 5/4 = 23/4 = 5 3/4
   • j. 8/3 + 2/7 = 56/21 + 6/21 = 62/21 = 2 20/21
   • k. 3/4 + 1/3 + 1/5 = 77/60 (e. jaisa hi jod)
   • l. 2/3 + 4/5 + 3/7 = 70/105 + 84/105 + 45/105 = 199/105 = 1 94/105
   • m. 9/2 + 5/4 + 7/6 = 54/12 + 15/12 + 14/12 = 83/12 = 6 11/12
2. 2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12 litre hara paint.
3. 2/5 + 3/4 = 8/20 + 15/20 = 23/20 = 1 3/20 m. Ye 1 m se zyada hai, isliye haan, lace kaafi hai, aur 3/20 m bachegi bhi.

Figure it Out: same denominator mein ghatana (page 181)

1. 5/8 − 3/8 = 2/8 = 1/4
2. 7/9 − 5/9 = 2/9
3. 10/27 − 1/27 = 9/27 = 1/3

Number line pe 6/7 − 4/7 matlab 6/7 se shuru karke 1/7 ki 4 chhalaangein peeche, jo 2/7 pe khatam hoti hain. Example 3/4 − 2/3 mein 3/4 ko 3/3 se aur 2/3 ko 4/4 se guna karte hain taaki dono ka denominator 12 ho jaaye, jo 4 aur 3 ka common multiple hai.

Figure it Out: alag denominators mein ghatana (page 182)

1. a. 8/15 − 3/15 = 5/15 = 1/3 b. 2/5 − 4/15 = 6/15 − 4/15 = 2/15 c. 5/6 − 4/9 = 15/18 − 8/18 = 7/18 d. 2/3 − 1/2 = 4/6 − 3/6 = 1/6
2. a. 10/3 − 13/4 = 40/12 − 39/12 = 1/12 b. 23/3 − 18/5 = 115/15 − 54/15 = 61/15 = 4 1/15 c. 45/7 − 29/7 = 16/7 = 2 2/7
3. a. Jaya 7/10 − 1/2 = 7/10 − 5/10 = 2/10 = 1/5 km paidal chalti hai. b. 10/3 = 40/12 aur 13/4 = 39/12, isliye Namit kam time leta hai, 1/12 minute kam.

Puzzle: alag fractional units jinka jod 1 ho (pages 184–185)

1. Teen alag fractional units: 1/2 + 1/3 + 1/6 = 1. Bas yahi ek tareeka hai (order badalna alag nahi ginte).
2. Chaar alag fractional units: theek chhe tareeke hain.
   • 1/2 + 1/3 + 1/7 + 1/42
   • 1/2 + 1/3 + 1/8 + 1/24
   • 1/2 + 1/3 + 1/9 + 1/18
   • 1/2 + 1/3 + 1/10 + 1/15
   • 1/2 + 1/4 + 1/5 + 1/20
   • 1/2 + 1/4 + 1/6 + 1/12

Sirf yahi kyun? Sabse bada fraction 1/2 hi hona chahiye, kyunki 1/3 + 1/4 + 1/5 + 1/6 bhi 1 se kam hai. Phir baaki teen ko milkar 1/2 banana hai, jisse doosra 1/3 ya 1/4 hi ho sakta hai, aur aakhri do ka jod 1/6 ya 1/4. Ek check karo: 1/2 + 1/4 + 1/6 + 1/12 = 6/12 + 3/12 + 2/12 + 1/12 = 12/12 = 1.