NCERT Solutions Class 7 Maths Chapter 2: Arithmetic Expressions (Hinglish)

Ganita Prakash Grade 7 Part 1 (Reprint 2026-27) ke Chapter 2, Arithmetic Expressions, ke har sawaal ke jawab: text ke sawaal, har Figure it Out, Math Talk aur Try This, aur Expression Engineer paheliyan. Page numbers kitaab ke hisaab se hain (pages 24–45). Har value do baar nikaali gayi hai, aur paheliyan computer search se bhi jaanchi gayi hain. Chhote notes: Chapter 2 ke notes.

Simple Expressions (pages 24–26)

Apni pasandeeda sankhya chuno aur us value ke expressions likho. 36 ke liye: 30 + 6, 40 − 4, 4 × 9, 72 ÷ 2, 6 × 6 aur 18 + 18. Koi bhi sankhya chalegi; har expression hal karke jaancho.

Figure it Out (page 25)

1. (a) 13 + 4 = 17, isliye khaali jagah 11 hai, kyunki 11 + 6 = 17. (b) 6 × 5 = 30, isliye 22 + 8 = 30. (c) 64 ÷ 2 = 32, isliye 8 × 4 = 32. (d) 34 − 9 = 25.
2. Values hain (a) 67 − 19 = 48, (b) 67 − 20 = 47, (c) 35 + 25 = 60, (d) 5 × 11 = 55 aur (e) 120 ÷ 3 = 40. Badhte kram mein: 120 ÷ 3 < 67 − 20 < 67 − 19 < 5 × 11 < 35 + 25. (Bina ghataaye bhi 67 − 20 < 67 − 19, kyunki zyaada ghataane pe kam bachta hai.)

Bina lambe hisaab ke >, < ya = lagao (page 26).

• (a) 245 + 289 > 246 + 285. 245, 246 se 1 kam hai, par 289, 285 se 4 zyaada, isliye baayaan paksh 3 zyaada hai (534 aur 531).
• (b) 273 − 145 = 272 − 144. Baayaan paksh 1 upar se shuru hota hai aur 1 zyaada ghataata bhi hai (dono 128).
• (c) 364 + 587 < 363 + 589. 364 ek zyaada hai, par 587 do kam, isliye baayaan paksh 1 kam hai (951 aur 952).
• (d) 124 + 245 < 129 + 245. Wahi 245 chhoti sankhya mein juda hai (369 aur 374).
• (e) 213 − 77 < 214 − 76. Baayaan paksh 1 neeche se shuru hota hai aur 1 zyaada ghataata hai, isliye 2 kam hai (136 aur 138).

Reading and Evaluating Complex Expressions (pages 26–29)

Jaancho ki ghatav ko inverse jodne se badalne pe value wahi rehti hai. 18 − 10 = 8 aur 18 + (−10) = 8; 5 − 9 = −4 aur 5 + (−9) = −4. Har baar aisa hota hai.

Token model se samjhao ki kisi sankhya ko ghatana uske inverse ko jodne jaisa kyun hai. 6 − 4 ke liye 6 positive tokens mein se 4 hatao: 2 bachte hain. 6 + (−4) ke liye 6 positive tokens mein 4 negative tokens milao; har negative token ek positive token ke saath zero pair banata hai, aur 2 positive tokens bachte hain. Dono se 2 milta hai.

Table poori karo (page 29).

• 13 − 2 + 6 = 13 + (−2) + 6. Terms: 13, −2, 6.
• 5 + 6 × 3. Terms: 5, 6 × 3.
• 4 + 15 − 9 = 4 + 15 + (−9). Terms: 4, 15, −9.
• 23 − 2 × 4 + 16 = 23 + (−2 × 4) + 16. Terms: 23, −2 × 4, 16.
• 28 + 19 − 8 = 28 + 19 + (−8). Terms: 28, 19, −8.

Kya terms jodne ka kram badalne se value badalti hai? Nahi. Jaise 9 + (−3) + 5 = 11 aur 5 + 9 + (−3) = 11.

Swapping and Grouping (pages 29–32)

Kuch terms negative hon to bhi kya jagah badalne se jod wahi rehta hai? Haan: (−3) + (−5) = −8 = (−5) + (−3), aur 9 + (−4) = 5 = (−4) + 9.

Token model se jagah badalna samjhao. Jodne ka matlab saare tokens ek dher mein rakhna hai. Koi bhi samooh pehle rakho, dher wahi banta hai aur wahi zero pairs khatm hote hain, isliye jod kram pe nirbhar nahi karta.

Negative terms ke saath kya samooh badalne se jod wahi rehta hai? Haan: ((−3) + 8) + (−6) = 5 + (−6) = −1, aur (−3) + (8 + (−6)) = (−3) + 2 = −1.

Token model se samooh samjhao. Pehle dher 1 aur 2 milao ya dher 2 aur 3, aakhir mein teenon dher saath hote hain aur wahi zero pairs khatm hote hain.

(−7) + 10 + (−11): pehle −7 aur −11 jodo. (−7) + (−11) = −18 aur −18 + 10 = −8, baaki do kramon jaisa hi.

Kya kisi bhi kram mein terms jodne se wahi value milti hai, 3 se zyaada terms mein bhi? Haan. 12 + (−5) + 7 + (−9) ke liye: kram se, 7 + 7 = 14 aur 14 + (−9) = 5; pehle positive terms, 19 + (−14) = 5; jodiyon mein, (12 + (−9)) + ((−5) + 7) = 3 + 2 = 5.

Manasa se 9055 jodna chhoot gaya. Kya phir se shuru karna padega? Nahi. Terms kisi bhi kram aur samooh mein jode ja sakte hain, isliye chhooti sankhya ko jod mein milao: 11749 + 9055 = 20804. (Jaanch: 1342 + 774 + 8611 + 1022 = 11749.)

More Expressions and Their Terms (pages 32–34)

Example 7: saat dost, wahi ₹5 tip. 7 × 23 + 5 = 161 + 5 = ₹166. Terms 7 × 23 aur 5 hain.

Example 8: Ruby ne 6 × 5 + 3 kyun likha? 33 khilaadiyon ne 5-5 ke 6 group banaaye, yaani 30 khilaadi, aur 3 bahar rahe: 6 × 5 + 3 = 33.

• Teacher 4 bole to: 8 × 4 + 1, terms 8 × 4 aur 1.
• Teacher 7 bole to: 4 × 7 + 5, terms 4 × 7 aur 5.
• Apni class ke liye apni sankhyaayein lo. Jaise 40 khilaadi aur 6 ki pukaar: 6 × 6 + 4.

Example 10: terms pehchaano. 4 × 100 + 1 × 20 + 1 × 10 + 2 × 1 ke terms 4 × 100, 1 × 20, 1 × 10 aur 2 × 1 hain. 8 × 50 + 1 × 10 + 4 × 5 + 2 × 1 ke terms 8 × 50, 1 × 10, 4 × 5 aur 2 × 1 hain.

₹432 dene ke aur tareeke. 2 × 100 + 4 × 50 + 1 × 20 + 1 × 10 + 2 × 1; 4 × 100 + 6 × 5 + 2 × 1; 21 × 20 + 2 × 5 + 2 × 1. Har ek ka jod 432 hai.

Example 11: daayein arrangement ka expression. Har column mein 5 peele aur 3 neele squares hain, aur 2 column hain: 2 × (5 + 3) = 16. Ise 5 + 3 + 5 + 3 ya 5 × 2 + 3 × 2 bhi likh sakte hain.

Figure it Out (pages 34–35)

1. (a) 28 − 7 + 8 = 28 + (−7) + 8. Terms 28, −7, 8; value 29.
   (b) 39 − 2 × 6 + 11. Terms 39, −2 × 6, 11; 39 − 12 + 11 = 38.
   (c) 40 − 10 + 10 + 10. Terms 40, −10, 10, 10; value 50.
   (d) 48 − 10 × 2 + 16 ÷ 2. Terms 48, −10 × 2, 16 ÷ 2; 48 − 20 + 8 = 36.
   (e) 6 × 3 − 4 × 8 × 5. Terms 6 × 3 aur −4 × 8 × 5; 18 − 160 = −142.
2. Namoone ki kahaaniyan; tumhari alag ho sakti hain.
   (a) 89 + 21 − 10 = 100. Ek bus mein 89 yaatri hain; ek stop pe 21 chadhte hain aur 10 utarte hain. Ab bus mein 100 yaatri hain.
   (b) 5 × 12 − 6 = 54. Ek dukaan mein 12-12 ande waali 5 trays aati hain aur 6 ande toot jaate hain. 54 ande bache.
   (c) 4 × 9 + 2 × 6 = 48. School ke liye 9-9 pencil ke 4 packet aur 6-6 pencil ke 2 packet khareede gaye: 36 + 12 = 48 pencil.
3. (a) Ab Elsa ke paas 2 × 100 sikke hain aur Anna ke paas 100 ÷ 2. Expression 2 × 100 + 100 ÷ 2; terms 2 × 100 aur 100 ÷ 2; value 200 + 50 = 250 sone ke sikke.
   (b) (i) 4 × 40 + 3 × 20; terms 4 × 40 aur 3 × 20; 160 + 60 = ₹220. (ii) 2 × (3 × 40), ek hi term; 2 × 120 = ₹240. Ise 3 × 40 + 3 × 40 bhi likh sakte hain.
   (c) Khidki mein 3 cm ke 2 border, 2 cm ki 6 grill aur 5 cm ke 7 gap hain. Expression 2 × 3 + 6 × 2 + 7 × 5; terms 2 × 3, 6 × 2 aur 7 × 5; 6 + 12 + 35 = 53 cm.

Removing Brackets I (pages 35–36)

Jaancho ki 500 − (250 − 100) aur 500 − 250 − 100 barabar nahi hain. 500 − (250 − 100) = 500 − 150 = 350, par 500 − 250 − 100 = 150. Doosra 200 kam hai, kyunki 100 waapas jodne ki jagah ghata diya gaya.

Tinker the Terms I (pages 36–37)

• Pehla column: 54 + (−16) = 38, kyunki 54, 53 se 1 zyaada hai. 53 + (−15) = 38, kyunki −15, −16 se 1 zyaada hai.
• Doosra column: 52 + (−16) = 36, kyunki 52, 53 se 1 kam hai. 53 + (−17) = 36, kyunki −17, −16 se 1 kam hai.
• Teesra column: −87 + (−16) = −103. −88 + (−15) = −103: ek term 1 kam aur doosra 1 zyaada. −86 + (−18) = −104: 1 zyaada aur 2 kam, yaani 1 kam. −97 + (−26) = −123: 10 kam aur 10 kam, yaani 20 kam.

Figure it Out (pages 37–38)

1. (a) 24 + (6 − 4) = 24 + 6 − 4.
   (b) 38 + (9 − 4) = 38 + 9 − 4.
   (c) 24 − (6 + 4) = 24 − 6 − 4.
   (d) 24 − 6 − 4 = 24 − 6 − 4.
   (e) 27 − (8 + 3) = 27 − 8 − 3.
   (f) 27 − (8 − 3) = 27 − 8 + 3.
2. (a) 14 + (12 + 10) = 14 + 12 + 10 = 36.
   (b) 14 − (12 + 10) = 14 − 12 − 10 = −8.
   (c) 14 + (12 − 10) = 14 + 12 − 10 = 16.
   (d) 14 − (12 − 10) = 14 − 12 + 10 = 12.
   (e) −14 + (12 − 10) = −14 + 12 − 10 = −12.
   (f) 14 − (−12 − 10) = 14 + 12 + 10 = 36. Dhyaan do ki (a) aur (f) ki value ek hai.
3. (a) (6 + 10) − 2 = 14 aur 6 + (10 − 2) = 14: barabar.
   (b) 16 − (8 − 3) = 16 − 8 + 3 = 11, par (16 − 8) − 3 = 5: barabar nahi.
   (c) 27 − (18 + 4) = 27 − 18 − 4 = 5 aur 27 + (−18 − 4) = 27 − 18 − 4 = 5: barabar.
   Do expressions tab barabar hote hain jab brackets sahi tarah hataane ke baad unke terms ek jaise hon.
4. (a) 319 − 537 aur −537 + 319 ke terms ek hain, 319 aur −537, isliye ye barabar hain. 319 + 537 ke terms 319 aur 537 hain, aur 537 − 319 ke 537 aur −319, isliye ye mel nahi khaate.
   (b) Kitaab mein pehle teen expressions ek hi chhape hain, 87 + 46 − 109, isliye wo barabar hain. 87 − 46 + 109 aur (87 − 46) + 109 ke terms ek hain, 87, −46 aur 109, isliye barabar hain. 87 − (46 + 109) = 87 − 46 − 109 mein 109 ki jagah −109 hai, isliye ye alag hai.
5. (a) 34 − (9 + 12) = 34 − 21 = 13.
   (b) (56 − 14) − 8 = 42 − 8 = 34. Brackets ke bina bhi expression ka yahi matlab hai; 56 − (14 − 8) se 50 aata.
   (c) −22 − (12 + 10) + 22 = −22 − 22 + 22 = −22.
6. (a) 419, 423 se 4 kam hai, isliye daayein ki khaali jagah baayein waali se 4 zyaada honi chahiye: jaise 423 + 1 = 419 + 5, ya 423 + 419 = 419 + 423.
   (b) 210, 207 se 3 zyaada hai, isliye 3 aur ghataana hoga: 207 − 68 = 210 − 71.
7. 2, 3 aur 5 ko ek-ek baar, + aur − aur brackets ke saath use karke chhe values milti hain: 2 + 3 + 5 = 10, 3 + 5 − 2 = 6, 2 + 5 − 3 = 4, 2 + 3 − 5 = 0, 3 − (2 + 5) = −4 aur 2 − (3 + 5) = −6. Saari values sam (even) hain, kyunki 2 + 3 + 5 = 10 sam hai aur kisi + ko − banaane se jod us sankhya ke dugne se ghatta hai. Agar pehli sankhya se pehle bhi minus lagaane ki chhoot ho, to −(2 + 3 + 5) = −10 ek aur value hai.
8. (a) Haan, Jasoda ka jawab hamesha sahi aata hai. 9 ghatana matlab 10 − 1 ghatana, isliye 36 − 9 = 36 − (10 − 1) = 36 − 10 + 1 = 27.
   (b) Haan. 8 ghatane ke liye 10 ghatao aur 2 jodo: 55 − 8 = 45 + 2 = 47. 9 jodne ke liye 10 jodo aur 1 ghatao: 47 + 9 = 57 − 1 = 56. 99 ghatane ke liye 100 ghatao aur 1 jodo: 350 − 99 = 250 + 1 = 251.

9. 73 − 14 + 1 ke barabar hain (b) 73 − (14 − 1) aur (c) 73 + (−14 + 1); teenon 60 hain. 73 − 14 − 1 ke barabar hain (a) 73 − (14 + 1) aur (d) 73 + (−14 − 1); teenon 58 hain.

Removing Brackets II (pages 38–40)

Sangmu bhi wahi cheezein order kare, to kul bill ka expression kya hoga? 3 × (43 + 24) = 3 × 67 = ₹201, jo 3 × 43 + 3 × 24 = 129 + 72 ke barabar hai.

5 × 4 + 3 ≠ 5 × (4 + 3) kyun? 5 × 4 + 3 = 20 + 3 = 23, par 5 × (4 + 3) = 5 × 7 = 35. Pehle mein sirf 4 ka 5 se guna hota hai; doosre mein 4 aur 3 dono ka.

Kya 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5? Haan, teenon 35 hain. Brackets ke andar sankhyaon ki jagah badalne se jod nahi badalta, aur guna ki do sankhyaon ki jagah badalne se guna-phal nahi badalta.

Page 40 pe kitaab mein “98 × 10 + 9 × 83 = 98 (10 + 3)” chhapa hai; sahi line 98 × 10 + 98 × 3 = 98 × (10 + 3) hai, jaisa agli line dikhaati hai.

Tinker the Terms II (pages 40–41)

Example 18: value nikaalo. 97 × 25 = 100 × 25 − 3 × 25 = 2500 − 75 = 2425.

Is tareeke se nikaalo. (a) 95 × 8 = (100 − 5) × 8 = 800 − 40 = 760. (b) 104 × 15 = (100 + 4) × 15 = 1500 + 60 = 1560. (c) 49 × 50 = (50 − 1) × 50 = 2500 − 50 = 2450.

Kya ye aam tareeke se jaldi hai? Aksar haan, kyunki har step mein ek gol sankhya ka guna aur ek chhota guna hota hai, jo mann mein ho jaata hai.

Aur kaunse guna aise jaldi ho sakte hain? Jinme koi sankhya 10, 50, 100 ya 1000 ke kisi multiple ke paas ho: 98 × 7 = 700 − 14 = 686; 103 × 9 = 900 + 27 = 927; 51 × 12 = 600 + 12 = 612; 999 × 6 = 6000 − 6 = 5994.

Figure it Out (pages 41–42)

1. Part (a) aur (b) pure udaaharan hain.
   (c) 3 × (5 + 8) = 3 × 5 + 3 × 8.
   (d) (9 + 2) × 4 = 9 × 4 + 2 × 4.
   (e) 3 × (10 + 4) = 3 × 10 + 3 × 4. 10 ki jagah koi bhi sankhya chalegi, agar dono jagah wahi ho.
   (f) (13 + 6) × 4 = 13 × 4 + 6 × 4.
   (g) 3 × (5 + 2) = 3 × 5 + 3 × 2.
   (h) (2 + 3) × 4 = 2 × 4 + 3 × 4.
   (i) 5 × (9 − 2) = 5 × 9 − 5 × 2.
   (j) (5 − 2) × 7 = 5 × 7 − 2 × 7.
   (k) 5 × (8 − 3) = 5 × 8 − 5 × 3.
   (l) (8 − 3) × 7 = 8 × 7 − 3 × 7.
   (m) 5 × (12 − 3) = 5 × 12 − 5 × 3. 3 ki jagah koi bhi sankhya chalegi, agar dono jagah wahi ho.
   (n) (15 − 6) × 7 = 15 × 7 − 6 × 7.
   (o) 5 × (9 − 4) = 5 × 9 − 5 × 4.
   (p) (17 − 9) × 7 = 17 × 7 − 9 × 7.
2. (a) (8 − 3) × 29 > (3 − 8) × 29. 8 − 3 = 5 aur 3 − 8 = −5, isliye baayaan paksh positive aur daayaan negative hai.
   (b) 15 + 9 × 18 < (15 + 9) × 18. Daayaan paksh 15 × 18 + 9 × 18 hai, aur 15 × 18, 15 se bahut zyaada hai.
   (c) 23 × (17 − 9) < 23 × 17 + 23 × 9. Baayaan paksh 23 × 17 − 23 × 9 hai: jo daayaan jodta hai, wo baayaan ghataata hai.
   (d) (34 − 28) × 42 = 34 × 42 − 28 × 42, distributive property se.
3. Kuch aur tareeke: 2 × (3 + 4), 2 × (2 + 5), 7 × (1 + 1) aur 1 × (9 + 5). Aur bhi bahut hain, jaise 1 × (6 + 8).
4. Tasveer I mein paanch 4 aur chaar 8 hain. Tareeka 1: 5 × 4 + 4 × 8 = 20 + 32 = 52. Tareeka 2: har 8 ki ek 4 ke saath jodi: 4 × (4 + 8) + 4 = 48 + 4 = 52. Tareeka 3: panktiyan jodo: 16 + 20 + 16 = 52.
   Tasveer II mein aath 5 aur aath 6 hain. Tareeka 1: 8 × 5 + 8 × 6 = 40 + 48 = 88. Tareeka 2: 8 × (5 + 6) = 8 × 11 = 88. Tareeka 3: har pankti 5 + 6 + 6 + 5 = 22 hai, isliye 4 × 22 = 88.

Figure it Out (pages 42–44)

1. (a) Dono milkar roz 9 + 11 kg aam dete hain, isliye ek hafte mein 7 × (9 + 11) = 7 × 20 = 140 kg. (Ya 7 × 9 + 7 × 11 = 63 + 77.)
   (b) 12 × 20,000 − 12 × (5,000 + 5,000 + 2,000) = 2,40,000 − 1,44,000 = ₹96,000. Har mahine ₹8,000 ki bachat hoti hai.
   (c) Har din-raat mein ghonga 3 − 2 = 1 cm upar badhta hai, isliye 7 din-raat baad wo 7 cm pe hai. 8ve din wo 3 cm chadhkar raat se pehle 10 cm pe pahunch jaata hai: 7 × (3 − 2) + 3 = 10. Treat 8ve din milti hai, 10ve din nahi, kyunki upar pahunchne ke baad phisalne ka sawaal nahi.

2. Hafte mein 7 − 2 = 5 din padhaai hoti hai, isliye 8 hafton mein 40 kahaaniyan. Is sthiti ko batane waale expressions hain (b) (7 − 2) × 8 aur (g) 7 × 8 − 2 × 8. (a) 5 × 2 × 8 = 80 pages ginta hai, kahaaniyan nahi.

3. (a) Tareeka 1, padosiyon ki jodi: (1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + (9 − 10) = 5 × (−1) = −5. Tareeka 2, visham aur sam alag: (1 + 3 + 5 + 7 + 9) + (−2 − 4 − 6 − 8 − 10) = 25 + (−30) = −5. Tareeka 3: 1 + (−2 + 3) + (−4 + 5) + (−6 + 7) + (−8 + 9) − 10 = 1 + 4 − 10 = −5.
   (b) Tareeka 1: (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) = 0. Tareeka 2: paanch 1 aur paanch −1, 5 + (−5) = 0. Tareeka 3: 1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + (−1 + 1) − 1 = 1 + 0 − 1 = 0.
4. (a) 49 − 7 + 8 = 49 − 7 + 8: dono taraf ek hi expression hai.
   (b) 83 × 42 − 18 > 83 × 40 − 18: 83 × 42, 83 × 40 se 2 × 83 zyaada hai.
   (c) 145 − 17 × 8 < 145 − 17 × 6: baayaan paksh zyaada ghataata hai.
   (d) 23 × 48 − 35 > 23 × (48 − 35): daayaan paksh 23 × 48 − 23 × 35 hai, jo 23 guna zyaada ghataata hai.
   (e) (16 − 11) × 12 = −11 × 12 + 16 × 12: daayaan paksh 16 × 12 − 11 × 12 hai, bas terms ki jagah badli hai.
   (f) (76 − 53) × 88 > 88 × (53 − 76): baayaan paksh positive aur daayaan negative hai.
   (g) 25 × (42 + 16) = 25 × (43 + 15): dono brackets 58 hain.
   (h) 36 × (28 − 16) > 35 × (27 − 15): dono brackets 12 hain, aur 36 × 12, 35 × 12 se zyaada hai.
5. (a) 83 − 37 − 12 ke barabar hain (i) 84 − 38 − 12, jisme ek term 1 zyaada aur doosra 1 kam hai, aur (iv) −37 + 83 − 12, jiske terms wahi hain. (ii) 84 − (37 + 12) ek zyaada hai, aur (iii) 83 − 38 − 13 do kam.
   (b) 93 + 37 × 44 + 76 ke terms 93, 37 × 44 aur 76 hain. Sirf (iv) 37 × 44 + 93 + 76 ke terms wahi hain. (i) aur (ii) alag sankhyaon ka guna karte hain, aur (iii) do jodon ka guna karta hai.
6. 36 ke liye: 30 + 6, 40 − 4, 4 × 9, 72 ÷ 2, 6 × 6, 18 + 18, 3 × 10 + 6, 50 − 2 × 7, (2 + 4) × 6 aur 100 − 64. Koi bhi sankhya chuno aur apne har expression ko jaancho.

Expression Engineer (page 45)

Chaar 4 se 1 se 20 tak har value. +, −, ×, ÷ aur brackets se: 1 = (4 + 4) ÷ (4 + 4); 2 = 4 ÷ 4 + 4 ÷ 4; 3 = (4 + 4 + 4) ÷ 4; 4 = 4 + (4 − 4) × 4; 5 = (4 × 4 + 4) ÷ 4; 6 = 4 + (4 + 4) ÷ 4; 7 = 4 + 4 − 4 ÷ 4; 8 = 4 + 4 + 4 − 4; 9 = 4 + 4 + 4 ÷ 4; 12 = (4 − 4 ÷ 4) × 4; 15 = 4 × 4 − 4 ÷ 4; 16 = 4 + 4 + 4 + 4; 17 = 4 × 4 + 4 ÷ 4; 20 = (4 + 4 ÷ 4) × 4. Computer search dikhata hai ki in operations se theek chaar 4 se 10, 11, 13, 14, 18 ya 19 nahi bante. Agar 44 likhne ki chhoot ho, to 10 = (44 − 4) ÷ 4. Baaki ke liye is chapter se aage ke auzaar chahiye, jaise decimals ya square root, isliye teacher se poocho ki kaunse auzaar chalenge.

1, 2, 3, 4 aur 5 ek-ek baar, −10 se +10 tak ki values. Computer search dikhata hai ki −10 se 10 tak ki har poorn sankhya ban sakti hai. Kuch udaaharan: 1 + 2 + 3 + 4 − 5 = 5; 5 + 4 + 3 − 2 − 1 = 9; 4 + 5 + 3 − 2 × 1 = 10; 5 − 4 + 3 − 2 − 1 = 1; 1 − 2 × 5 − 4 + 3 = −10; (5 − 4 − 1) × 2 × 3 = 0. Sirf + aur − se value hamesha visham (odd) aati hai, kyunki 1 + 2 + 3 + 4 + 5 = 15 visham hai, isliye sam values ke liye × ya ÷ chahiye.

0 se 9 tak har digit ek baar, value 100. 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 × 9 = 28 + 72 = 100.

Aise aur kaunse sawaal pooch sakte ho? Jaise: 1 se 9 tak ke digits kram se rakhkar 100 banao (1 + 2 + 3 − 4 + 5 + 6 + 78 + 9 = 100), ya dekho ki paanch 5 se 1 se 10 tak kaunsi values banti hain.