NCERT Solutions Class 7 Maths Chapter 4: Expressions using Letter-Numbers (Hinglish)

Ganita Prakash Grade 7 Part 1 (Reprint 2026-27) ke Chapter 4, Expressions using Letter-Numbers, ke har sawaal ke jawab: text ke sawaal, dono Mind the Mistake, Math Talk aur Try This sawaal, aur teeno Figure it Out. Page numbers kitaab ke hisaab se hain (pages 81–105). Har simplification do baar nikaala gaya hai. Chhote notes: Chapter 4 ke notes.

The Notion of Letter-Numbers (pages 81–84)

Aftab ki umar 18 hai. Shabnam ki kitni? 18 + 3 = 21. Shabnam ki umar 20 ho to Aftab ki kitni? a = s − 3 = 20 − 3 = 17.

a = 23 ho to Shabnam ki umar kya hai? s = 23 + 3 = 26 saal.

Maachis ke L. 5 L ke liye 10 teeliyan, 7 L ke liye 14, 45 L ke liye 90, aur n L ke liye 2n.

Ketaki ke laddu. 8 nariyal aur 9 kg gud: 8 × 35 + 9 × 60 = 280 + 540 = ₹820. c × 35 + j × 60 se 7 nariyal aur 4 kg ka daam 245 + 240 = ₹485.

7 cm bhuja waale square ki parimiti. 4q = 4 × 7 = 28 cm.

Figure it Out (pages 84–85)

1. Bhuja ke liye q lekar: (a) barabar bhujaon waala triangle: 3q; (b) niyamit pentagon: 5q; (c) niyamit hexagon: 6q.
2. Judi lambaai 20 + k metre hai.
3. Table, list ki tarah:
   3, 5, 6 note: 3 × 100 + 5 × 20 + 6 × 5 = 430
   6, 4, 3 note: 6 × 100 + 4 × 20 + 3 × 5 = 695 (udaaharan)
   8, 4, z note: 8 × 100 + 4 × 20 + z × 5 = 880 + 5z
   x, y, z note: 100x + 20y + 5z
4. (d) 10 + 8 × y: chalu hone ke 10 second, phir y kg mein se har ek ke 8 second.
5. Sankhya ke liye x lekar: (a) x + 5 (b) x − 4 (c) 13x − 2 (d) 2x − 13.
6. (a) 8 × x + 3 × y: ₹x ki 8 copiyan aur ₹y ke 3 pen khareedne ka daam 8x + 3y rupaye.
   (b) 15 × j − 2 × k: ek khel mein har goal pe 15 ank milte hain aur har foul pe 2 kat-te hain; j goal aur k foul pe score 15j − 2k.
7. Neeche ki line: w − 1, w, w + 1. Upar ki line, ek hafte pehle: w − 8, w − 7, w − 6.

Revisiting Arithmetic Expressions (pages 85–86)

1. 23 − 10 × 2 = 23 + (−20) = 3
2. 83 + 28 − 13 + 32 = (83 − 13) + (28 + 32) = 70 + 60 = 130
3. 34 − 14 + 20 = 40
4. 42 + 15 − (8 − 7) = 57 − 1 = 56
5. 68 − (18 + 13) = 68 − 31 = 37
6. 7 × 4 + 9 × 6 = 28 + 54 = 82
7. 20 + 8 × (16 − 6) = 20 + 80 = 100

Omitting the Multiplication Symbol (pages 86–87)

Kram 4, 8, 12, 16, …. Teesra term: 4 × 3 = 12; 29va term: 4 × 29 = 116; nth term: 4n.

Mind the Mistake, Mend the Mistake (page 87)

1. Galti. 10 − a = 10 − (−4) = 14, 6 nahi: −4 ghataana 4 jodna hai.
2. Galti. 3d = 3 × 6 = 18; 36, 3 aur 6 ko agal-bagal likhne se aaya.
3. Galti. 3s − 2 = 21 − 2 = 19; 15, 3 × (7 − 2) se aaya, par 3 sirf s ko guna karta hai.
4. Galti. 2r + 1 = 16 + 1 = 17; 29, 2r ko 28 padhne se aaya.
5. Sahi. 2j = 2 × 5 = 10.
6. Galti. 3(m + 1) = 3 × (−6 + 1) = 3 × (−5) = −15; 19, chinh aur bracket bhoolkar 3 × 6 + 1 se aaya.
7. Galti. 2f − 2g = 6 − 2 = 4; 2, 2f ko 23 aur 2g ko 21 padhne se aaya.
8. Galti. 2t + b = 8 + 3 = 11; 24, 2 × 4 × 3 karne se aaya.
9. Galti. h − (3 − n) = 5 − (3 − 6) = 5 − (−3) = 8; 4, bracket galat kholne se aaya.

Simplification of Algebraic Expressions (pages 87–93)

Din 2 aur 3 ki pencils. 3c aur 10c, isliye pencils se 5c + 3c + 10c = 18c; c = ₹50 pe ₹900. Erasers se 4d + 6d + d = 11d. Jaanch: c = 2 pe 5c + 3c + 10c = 10 + 6 + 20 = 36 aur 18c = 36.

Kursi aur mez kiraye pe: tareeka. Kursiyon ki ginti ko ₹40 se aur mezon ki ko ₹75 se guna karke jodo, to diya gaya paisa: 40x + 75y. ₹6 aur ₹10 se guna karke jodo, to waapas mila: 6x + 10y. Kul kharch (40x + 75y) − (6x + 10y) = 34x + 65y. Kya ise (40x + 75y) + (−6x − 10y) likh sakte the? Haan: bracket ghataana uske inverse ko jodne jaisa hai.

Charu ka quiz. 7p − 3q matlab round 1 mein 7 sahi aur 3 galat jawab, aur aise hi aage. p = 4 aur q = 1 pe round 2: 32 − 4 = 28, aur round 3: 24 − 2 = 22. Penalty na ho to q = 0. Charu ka antim score 21p − 9q = 84 − 9 = 75.

23p − 7q dene waale Krishita ke rounds. Jaise 8p − 2q, 7p − 3q aur 8p − 2q, ya 9p − 3q, 7p − 2q aur 7p − 2q. Kiska score zyaada? Krishita ka: 23p − 7q − (21p − 9q) = 23p − 7q − 21p + 9q = 2p + 2q, jo 0 se zyaada hai kyunki p aur q positive hain.

5u aur 5 + u. u = 2: 10 aur 7; u = 5: 25 aur 10; u = 8: 40 aur 13; u = 11: 55 aur 16. Barabar nahi.

10y − 3 aur 10(y − 3). y = 0: −3 aur −30; y = 2: 17 aur −10; y = 7: 67 aur 40; y = 10: 97 aur 70. Ye barabar nahi; pehla hamesha 27 zyaada hai.

Figure it Out (pages 93–94)

1. Har chitra ki sankhyaon ka jod:
   (i) 5y, −6, x, x, 2, 5y: like terms se (5y + 5y) + (x + x) + (−6 + 2) = 10y + 2x − 4; lines se (5y − 6 + x) + (x + 2 + 5y) bhi yahi deta hai.
   (ii) chaar 2p, chaar 3q aur 3, −2, 3, −2: 8p + 12q + 2; column dar column jodne se bhi yahi.
   (iii) chaar −5g aur baarah 5k: 60k − 20g; bahari columns 10k − 10g aur beech ke columns 40k dete hain.
2. Simplest forms:
   (a) p + p + p + p = 4p; p + p + p + q = 3p + q
   (b) p + q + p − q = 2p
   (c) p − q + p − q = 2p − 2q
   (d) p + q − p + q = 2q
   (e) p + q − (p + q) = 0
   (f) p − q − p − q = −2q
   (g) 2d − d − d − d = −d
   (h) 2d − d − d − c = −c
   (i) 2d − d − (d − c) = c
   (j) 2d − (d − d) − c = 2d − c
   (k) 2d − d − c − c = d − 2c

Mind the Mistake, Mend the Mistake (pages 94–95)

1. 3a + 2b ko 5 diya: galti; unlike terms nahi judte. Sahi: 3a + 2b.
2. 3b − 2b − b ko 0 diya: sahi.
3. 6(p + 2) ko 6p + 8 diya: galti; 6 × 2 = 12. Sahi: 6p + 12.
4. (4x + 3y) − (3x + 4y) ko x + y diya: galti; minus +4y ko −4y banata hai. Sahi: x − y.
5. 5 − (2 − 6z) ko 3 − 6z diya: galti; −(−6z) = +6z. Sahi: 3 + 6z.
6. 2 + (x + 3) ko 2x − 6 diya: galti; bracket se pehle plus kuch nahi badalta. Sahi: x + 5.
7. 2y + (3y − 6) ko −y + 6 diya: galti; bracket se pehle plus hone pe bhi andar ke chinh badal diye. Sahi: 5y − 6.
8. 7p − p + 5q − 2q ko 7p + 3q diya: galti; −p chhoot gaya. Sahi: 6p + 3q.
9. 5(2w + 3x + 4w) ko 10w + 15x + 20w diya: simplest nahi; like terms judte hain. Sahi: 30w + 15x.
10. 3j + 6k + 9h + 12 ko 3(j + 2k + 3h + 4) diya: barabar hai, par bracket simplest form nahi. Sahi: 3j + 6k + 9h + 12.
11. 4(2r + 3s + 5) ko −20 − 8r − 12s diya: galti; saare chinh ulat diye. Sahi: 8r + 12s + 20.

Terms ki ginti aur letter-numbers ki ginti. Har simplest form mein har letter-number sirf ek term mein aata hai, aur zyaada se zyaada ek term sirf sankhya hota hai. Isliye terms ki ginti letter-numbers ki ginti ke barabar hai, ya number term ho to ek zyaada (aur 0 mein koi term nahi).

Pick Patterns and Reveal Relationships (pages 95–101)

Formula Detective (page 95). Formula 2a − b hai, isliye aakhri machine 2 × 6 − 4 = 8 deti hai. Baaki outputs bhi milte hain: 2 × 8 − 1 = 15, 2 × 9 − 11 = 7, 2 × 10 − 10 = 10.

Page 96 ki do machines.
Pehli machine: a + b − 2: 5 + 2 − 2 = 5, 8 + 1 − 2 = 7, 9 + 11 − 2 = 18, 10 + 10 − 2 = 18, aur a aur b ke liye a + b − 2.
Doosri machine: ab + 1: 4 × 1 + 1 = 5, 6 × 0 + 1 = 1, 3 × 2 + 1 = 7, 10 × 3 + 1 = 31, aur a aur b ke liye ab + 1.

Apna formula banao. Jaise 3a − b: 4 aur 2 se 10, 5 aur 5 se 10, aur 2 aur 6 se 0. Sahpaathiyon ko niyam dhoondhne ki chunauti do.

Saree ke designs (page 97). nth A 3n − 2 pe aur nth B 3n − 1 pe hai. Position 99 (shesh 0) pe C, 122 (shesh 2) pe B, aur 148 (shesh 1) pe A.

Vikarn jod jaancho (page 99). 5, 6, 12, 13 waale square mein: 5 + 13 = 18 = 6 + 12, aur 2a + 8 = 2 × 5 + 8 = 18.

Plus aakaar: hamesha kendra ka 5 guna? Haan. Kendra a ho to sankhyaayein a − 7, a − 1, a, a + 1 aur a + 7 hain, aur jod 5a hai. 8, 14, 15, 16 aur 22 ka jod 75 = 5 × 15 hai.

Doosre aakaar. Teen taareekhon ki khadi ya leti line ka jod beech waali ka 3 guna; paanch taareekhon ke X (a − 8, a − 6, a, a + 6, a + 8) ka jod 5a; aur 3 × 3 square ka jod uske kendra ka 9 guna.

Maachis ke triangles (pages 100–101). Step 33: 3 + 2 × 32 = 67; Step 84: 169; Step 108: 217. 3 + 2(y − 1) aur 2y + 1 dono sahi ginti dete hain, aur dono ek hi expression hain. Step 3 mein 3 leti aur 4 tirchhi teeliyan, aur Step 4 mein 4 aur 5. Step y pe y leti aur y + 1 tirchhi teeliyan, jo milkar 2y + 1 banti hain.

Figure it Out (pages 102–105)

1. (a) 30x + 20y. Baaki ya to daam ulat dete hain, ya kulon ko guna karte hain, ya ghataate hain.
2. (a) p + q + r. Har graahak ko ek jhanda mila, aur graahak p + q + r the.
3. (a) Har din-raat ghonga u − d cm badhta hai, isliye 10 din-raat baad wo shuruaat se 10(u − d) cm, yaani 10u − 10d, upar hai.
   (b) d > u ho to wo chadhne se zyaada phisalta hai, isliye har din neeche jaata hai aur shuruaat se 10(d − u) cm neeche khatm hota hai; wo kabhi bahar nahi nikal sakta.
4. Hafta 1: 5 × 7 = 35 km; hafta 2: (5 + z) × 7 = 35 + 7z; hafta 3: (5 + 2z) × 7 = 35 + 14z. Kul: 105 + 21z km.
5. w + 2 se: −5 se w − 3, phir ×3 se 3w − 9; −8 se w − 6, phir −4 se w − 10; −4 se w − 2, phir ×3 se 3w − 6.

6. Yahapur, teen stations aur Vahapur ke beech 4 hisse hain, aur 2 minute ke 3 thehraav. (a) t = 4 pe: 4 × 4 + 6 = 22 minute. (b) 4t + 6 minute.

7. (a) (3 + 8 − 7)a + (9 − 4)b + (−6 + 16) = 4a + 5b + 10
   (b) 9a − 9b − 8a − 4b − 16 = a − 13b − 16
   (c) 4x − 6 + 8x + 12 = 12x + 6
   (d) 8x − 2x + 3 + 12 = 6x + 15
   (e) 8h − 5 − 7h + 9 = h + 4
   (f) 23 + 24m − 12n − 8n − 3m − 18 = 21m − 20n + 5
8. (a) 13d + c − 2
   (b) 7f + 4s − 4
   (c) 8d − 14c + 9 + 16c − 11 − 9d = 2c − d − 2
   (d) −7f − 4s + 3
   (e) 0
   (f) 0
9. B mein se A ghataane ka matlab B − A.
   (a) (6a + 9b − 18) − (9a − 6b + 14) = −3a + 15b − 32
   (b) (7y − 10 + 3x) − (−15x + 13 − 9y) = 18x + 16y − 23
   (c) (11 − 10g + 3h) − (17g + 9 − 7h) = −27g + 10h + 2
   (d) (6a − 9b − 18) − (9a − 6b + 14) = −3a − 3b − 32
   (e) (−3y + 8 − 3x) − (10x + 2 + 10y) = −13x − 13y + 6
   (f) (7h − 8g + 20) − (8g + 4h − 10) = 3h − 16g + 30
10. (a) 8x + 3y: ₹x kilo ka 8 kg chaawal aur ₹y kilo ki 3 kg daal ka daam 8x + 3y rupaye.
    (b) 15x − 2x: ek dibbe mein ₹x waali 15 pencil hain, par 2 tooti hain aur nahi bikti, isliye dibbe se 15x − 2x = 13x rupaye.
11. Chitra jaisa, har mod kaatne ke liye rassi ki ek aur ladi jodta hai: bina mod 2 tukde, 1 mod 3, 2 mod 4. Isliye 10 mod se 12 tukde, aur r mod se r + 2.

12. Pehle square ko 4 teeliyan aur har naye ko 3 aur. Isliye 10 squares ko 4 + 3 × 9 = 31, aur w squares ko 4 + 3(w − 1) = 3w + 1.
13. Rang laal, peela, hara, peela chalte hain aur har 4 ke baad dohraate hain. Laal 4n − 3 pe, peela har sam position, 2n, pe, aur hara 4n − 1 pe. Isliye position 90 peela, 190 peela aur 343 (= 4 × 86 − 1) hara hai.

14. X mein Step 1 se 3 tak 5, 9 aur 13 squares hain, har baar 4 zyaada, isliye Step n mein 4n + 1: Step 4 mein 17, Step 10 mein 41 aur Step 50 mein 201. Har square ke 4 vertices hain, isliye saare squares ke milkar 4(4n + 1) = 16n + 4 vertices. (Pados ke squares ek kone pe chhoote hain, isliye alag-alag kone ke bindu 16n + 4 − 4n = 12n + 4 hain.)

15. (a) Row r mein: column 1 mein 4r − 3, column 2 mein 4r − 2, column 3 mein 4r − 1 aur column 4 mein 4r.
    (b) (i) 124 = 4 × 30 + 4: row 31, column 4; (ii) 147 = 4 × 36 + 3: row 37, column 3; (iii) 201 = 4 × 50 + 1: row 51, column 1.
    (c) 4(r − 1) + c, yaani 4r + c − 4.
    (d) 3 ke guna-phal baari-baari columns 3, 2, 1, 4, 3, 2, 1, 4, … mein aate hain. Aur patterns: column 4 mein 4 ke guna-phal; columns 2 aur 4 mein sam sankhyaayein aur columns 1 aur 3 mein visham; aur har row ka jod 16r − 6.

Chhote notes topic pages pe hain: letter-numbers kya hain, expressions simplify kaise karein aur algebra se patterns.