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Expressions mein terms aur brackets

Short mein jawab

Terms expression ke wo hisse hain jo + chinh se jude hote hain, har ghatav ko inverse jodna maankar: 23 − 2 × 4 + 16 ke terms 23, −2 × 4 aur 16 hain. Terms kisi bhi kram mein jode ja sakte hain. Brackets se pehle minus ho to hataane pe andar ke chinh ulat jaate hain.

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Term kya hai?

Terms expression ke wo hisse hain jo + chinh se jude hote hain. 12 + 7 mein terms 12 aur 7 hain. Ghatav waale expression ke terms dhoondhne ke liye pehle har ghatav ko inverse jodne ki tarah likho; inverse matlab ulte chinh waali wahi sankhya. To 83 − 14 = 83 + (−14), jiske terms 83 aur −14 hain, aur −18 − 3 ke terms −18 aur −3 hain.

Guna aur bhaag term ke andar hi rehte hain. 6 × 5 + 3 ke terms 6 × 5 aur 3 hain, aur 2 − 10 + 4 × 6 ke terms 2, −10 aur 4 × 6. Minus chinh hamesha apne baad waale term ke saath chalta hai.

Aath expressions terms ke jod ki tarah likhe gaye, jaise 23 − 2 × 4 + 16 ke terms 23, −2 × 4 aur 16
Expressions terms ke jod ki tarah

Ghatana matlab inverse jodna

6 − 4 aur 6 + (−4) barabar kyun hain? Class 6 ka integers ka token model ye dikhata hai. 6 − 4 ke liye 6 positive tokens mein se 4 hatao: 2 bachte hain. 6 + (−4) ke liye 6 positive tokens ke paas 4 negative tokens rakho; har negative token ek positive token ke saath zero pair banakar khatm ho jaata hai, aur phir se 2 positive tokens bachte hain. Doosre jode bhi aazmaao, jaise 18 − 10 aur 18 + (−10): dono 8 hain.

Token model: 6 mein se 4 positive tokens hataane pe 2 bachte hain; 6 positive mein 4 negative tokens jodne pe 4 zero pairs bante hain aur 2 bachte hain
4 ghatana = −4 jodna

Terms ki jagah badlo, samooh banao

Madhu ka drone 6 m upar jaata hai aur phir 4 m neeche: 6 + (−4) = 2 m, terrace se upar. Terms ki jagah badlo, (−4) + 6, to bhi 2. Teen terms waale (−7) + 10 + (−11) mein pehle do terms jodo aur phir teesra, ya aakhri do aur phir pehla, ya pehle dono negative terms: har tarah −8 aata hai. Yaani jab expression mein sirf jod ho, to terms kisi bhi kram mein jode ja sakte hain. Jagah badalna addition ki commutative property kehlata hai, aur samooh banaana associative property.

(−7) + 10 + (−11) teen alag kram mein, har baar −8
Kram koi bhi, jod wahi

Isse mehnat bachti hai. Manasa ne paanch minute mein 1342, 774, 8611 aur 1022 jodkar 11749 paaya, phir dekha ki chauthi sankhya 9055 chhoot gayi. Phir se shuru karne ki zaroorat nahi: 11749 + 9055 = 20804. Par roz ke kuch kaamon mein kram maayne rakhta hai: topi aur joote kisi bhi kram mein pehen sakte ho, par moze jooton se pehle hi pehne jaate hain.

Brackets hatana

Kabhi kabhi brackets ke bina hisaab aasaan hota hai. 200 − (40 + 3) ka matlab 200 mein se 43 ghatana hai, par pehle 40 aur phir 3 bhi ghata sakte ho: 200 − 40 − 3 = 157. Irfan ke paise bhi aise hi: 100 − (15 + 56) = 100 − 15 − 56 = 29. Dono mein brackets ke andar ka + ban gaya −.

Ab 500 − (250 − 100). Agar poora 250 ghatao to zaroorat se 100 zyaada ghat gaya, isliye use waapas jodo: 500 − 250 + 100 = 350. Yahan andar ka − ban gaya +. Yaani brackets se pehle minus ho to andar ke har term ka chinh badal jaata hai. Plus ho to kuch nahi badalta: Hira ke ek thaile mein 28 aur doosre mein 35 sikke hain, aur doosre thaile se 10 sikke dost ko diye gaye, to bache 28 + (35 − 10) = 28 + 35 − 10 = 53 sikke. Niyam ratne se behtar hai expression ka matlab sochna.

Brackets hatana: pehle plus ho to chinh wahi rehte hain; minus ho to ulat jaate hain
Brackets hatana

Terms badlo, value dekho

Ek term badalne pe value ka kya hota hai? 53 + (−16) = 37 se shuru karo. 54 + (−16) mein pehla term 1 zyaada hai, to value bhi 1 zyaada, 38. 53 + (−15) mein doosra term 1 zyaada hai, kyunki −15, −16 se 1 zyaada hai, to value phir 38. Isi tarah 52 + (−16) aur 53 + (−17) dono 36 hain. Badlaav ek doosre ko kaat bhi sakte hain: −88 + (−15) mein −87 + (−16) ki tulna mein ek term 1 kam aur doosra 1 zyaada hai, isliye dono −103 hain.

53 + (−16) = 37 ya −87 + (−16) = −103 ka ek term badalkar nayi value ka andaaza
Term badlo, value ka andaaza lagao

Jasoda ka shortcut

Jasoda ka tareeka: 9 ghatana ho to 10 ghatao aur 1 jodo, jaise 36 − 9 = 26 + 1 = 27. Ye hamesha kaam karta hai, kyunki 36 − 9 = 36 − (10 − 1) = 36 − 10 + 1. Isi vichaar se aur shortcuts bante hain: 8 ghatane ke liye 10 ghatao aur 2 jodo, aur 9 jodne ke liye 10 jodo aur 1 ghatao.

Number line: 36 se 10 peeche 26 aur 1 aage 27, yaani 36 − 9 = 27; − 8, + 9, − 99 aur − 19 ke aur shortcuts
Jasoda ka shortcut

Ye kyun zaroori hai

Expression ko terms ka jod samajhne se tum suvidha ke kram mein jod sakte ho, bina galti brackets hata sakte ho, aur andaaza laga sakte ho ki kisi badlaav se jawab kitna badlega. Hal karne ka kram expressions ki value kaise nikalein mein hai, aur jod ka guna distributive property kya hai mein. Kitaab ke har sawaal ka jawab Chapter 2 ke NCERT solutions mein hai; poore Chapter 2 ke notes bhi dekho.

Practice karo

  1. 39 − 2 × 6 + 11 ke terms kya hain?

    1. (a) 39, 2, 6 aur 11
    2. (b) 39, −2 × 6 aur 11
    3. (c) 37, 6 aur 11
    4. (d) 39 − 2 aur 6 + 11
    Jawab dekho

    Jawab: (b) 39, −2 × 6 aur 11

  2. Kaunsa expression 14 − (12 − 10) ke barabar hai?

    1. (a) 14 − 12 − 10
    2. (b) 14 + 12 − 10
    3. (c) 14 − 12 + 10
    4. (d) 14 + 12 + 10
    Jawab dekho

    Jawab: (c) 14 − 12 + 10

  3. 53 + (−16) = 37. To 53 + (−17) kya hai?

    1. (a) 38
    2. (b) −36
    3. (c) 37
    4. (d) 36
    Jawab dekho

    Jawab: (d) 36

  4. Brackets hatao aur value nikaalo: 14 − (−12 − 10).

    Jawab dekho

    Jawab: Brackets se pehle minus hai, isliye andar ke dono chinh ulat jaate hain: 14 − (−12 − 10) = 14 + 12 + 10 = 36.

  5. Manasa ne sankhyaon ki lambi list jodkar 11749 paaya, phir dekha ki 9055 chhoot gaya. Kya use phir se shuru karna padega?

    Jawab dekho

    Jawab: Nahi. Terms kisi bhi kram aur kisi bhi samooh mein jode ja sakte hain, isliye chhooti hui sankhya ko jod mein mila do: 11749 + 9055 = 20804.

Students ke sawal

Arithmetic expression mein term kya hai?

Expression ka wo hissa jo baaki se + chinh se juda ho. Pehle har ghatav ko inverse jodne ki tarah likho: 4 + 15 − 9 = 4 + 15 + (−9), isliye iske terms 4, 15 aur −9 hain. 6 × 5 jaise guna ya 16 ÷ 2 jaise bhaag ke andar + chinh nahi hota, isliye wo ek hi term hai.

Brackets se pehle minus ho to andar ke chinh kyun badalte hain?

Kyunki poora bracket ghataaya ja raha hai. 200 − (40 + 3) mein 40 aur 3 dono ghatne chahiye, isliye ye 200 − 40 − 3 ke barabar hai. 500 − (250 − 100) mein poora 250 ghatane se 100 zyaada ghat jaata hai, isliye 100 waapas jodte hain: 500 − 250 + 100 = 350.

Addition ki commutative aur associative property kya hain?

Jodne ke do niyamon ke naam. Commutative: do terms ki jagah badalne se jod nahi badalta, jaise 6 + (−4) = (−4) + 6. Associative: teen terms ka samooh kaise bhi banao, jod wahi rehta hai, jaise ((−7) + 10) + (−11) = (−7) + (10 + (−11)) = −8. Dono milkar kehte hain ki terms kisi bhi kram mein jode ja sakte hain.

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