Lagnever AI English

Integers ko kaise jodein aur ghatayein?

Short mein jawab

Jodna hai Shuruaati position + Movement = Target: 3 se −5 chalne pe −2 milta hai, isliye 3 + (−5) = −2. Ghataav zaroori movement batata hai: Target − Shuruaat = Movement, isliye 4 − (−3) = +7. Kisi number ko ghatana uska inverse jodne jaisa hai. Tokens mein positive aur negative token zero pair banke kat jaate hain.

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Movement ka hisaab rakhne ke liye jodna

Bela ki Building of Fun mein Food Court (Floor +1) se shuru karke +2 dabao: tum Floor +3 pe Book Store pahunchte ho. Ise aise likhte hain:

Shuruaati floor + Movement = Target floor, yaani (+1) + (+2) = +3.

Floor +2 se −3 dabaane pe teen manzil neeche Floor −1 pahunchte ho: (+2) + (−3) = −1. Button dabaana milaana bhi jodna hai: Toy Store mein Gurmit ne galti se do baar + aur phir teen baar − dabaaya, kul movement (+2) + (−3) = −1, yaani ek manzil neeche.

Do number lines: 3 se −5 ka movement −2 pe pahunchata hai, isliye 3 + (−5) = −2; −3 se 4 tak zaroori movement +7 hai, isliye 4 − (−3) = +7
Movement ki tarah jodna aur ghatana

Movement nikaalne ke liye ghatana

Ghataav ka matlab ‘barabar karna’, yaani jodne waala gayab number dhoondhna, bhi ho sakta hai: 6 + ? = 10 aur 10 − 6 = ? ek hi baat hai. Manzilon ke liye:

Target floor − Shuruaati floor = Zaroori movement.

  • Floor −2 se Floor −1 tak 1 upar: (−1) − (−2) = +1.
  • Floor +3 se Floor −1 tak 4 neeche: (−1) − (+3) = −4.
  • Floor −2 se Floor +2 tak 4 upar: (+2) − (−2) = +4.

Ghatana yaani inverse jodna

−200 se +2000 tak jaane ke liye 0 tak 200 upar aur phir 2000 aur: +2200. Isliye (+2000) − (−200) = (+2000) + (+200) = +2200. Negative number ghatana positive number jodne jaisa hai. Aam taur pe ghataaye ja rahe number ki jagah uska inverse rakh ke jod sakte hain:

GhataavJod ki tarahJawab
(+7) − (+5)(+7) + (−5)+2
(−3) − (+8)(−3) + (−8)−11
(+8) − (−2)(+8) + (+2)+10
(+6) − (−9)(+6) + (+9)+15

Token model

Lift attendant har baar ‘+’ dabaane pe ek positive (hara) token aur ‘−’ dabaane pe ek negative (laal) token leta hai. Ek positive aur ek negative token kat jaate hain, kyunki saath mein inki value 0 hai: ye zero pair banaate hain. Jodne ke liye tokens milao aur zero pairs hatao.

Tokens: (+5) + (−8) mein paanch zero pairs hate aur teen negative bache; (+4) − (−6) mein chhe zero pairs daale aur chhe negative nikaale, das positive bache
Zero pairs kuch nahi badalte

Ghataane ke liye tokens nikaalo. Agar sahi tarah ke kaafi tokens na hon, to pehle zero pairs daalo, jo value nahi badalte. (+5) − (+6) ke liye ek zero pair daalo, chhe positive nikaalo, aur ek negative bachta hai: −1. (+4) − (−6) ke liye chhe zero pairs daalo, chhe negative nikaalo, aur das positive bachte hain: +10.

Brahmagupta ke niyam

628 CE mein Brahmagupta ne aise niyam likhe jo aaj bhi har integer pe chalte hain:

  • do positive milkar positive, aur do negative milkar negative: (−2) + (−3) = −5;
  • ek positive aur ek negative ke liye bade mein se chhota ghatao aur bade ka nishaan rakho: −5 + 3 = −2;
  • number aur uska inverse milkar zero, aur number mein zero jodne se wahi number;
  • negative number ghatana positive number jodne jaisa hai: 2 − (−3) = 2 + 3.

Building of Fun ya number line se tab tak abhyaas karo jab tak ye niyam aasaan na lagein. Har integer ka matlab dekhne ke liye padho negative numbers kya hain.

Practice karo

  1. (−6) + (+4) kitna hai?

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

    Jawab: (c) −2

  2. (−8) − (−4) kitna hai?

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

    Jawab: (b) −4 −4 ghatana +4 jodna hai: −8 + 4 = −4.

  3. Tokens se (+5) − (+6) karne ke liye pehle kya karna hoga?

    1. (a) ek zero pair daalna
    2. (b) saare tokens hatana
    3. (c) chhe positive daalna
    4. (d) kuch nahi; ye ho hi nahi sakta
    Jawab dekho

    Jawab: (a) ek zero pair daalna Chhe nikaalne ke liye paanch positive kaafi nahi, isliye ek zero pair daalo; chhe positive nikaalne pe ek negative bachta hai: −1.

  4. Tokens se (−3) − (+5) nikaalo.

    Jawab dekho

    Jawab: 3 negatives se shuru karo. 5 positive nikaalne ke liye 5 zero pairs daalo. 5 positive nikaalo: 8 negative bachte hain, isliye (−3) − (+5) = −8.

  5. (+6) − (−9) ko jod ki tarah likho aur jawab nikaalo.

    Jawab dekho

    Jawab: −9 ki jagah uska inverse +9 rakh ke jodo: (+6) + (+9) = +15.

Students ke sawal

Positive aur negative integer kaise jodte hain?

Bade number (bina nishaan) mein se chhota number ghatao aur jawab ko bade number ka nishaan do. Jaise −5 + 3 = −2 aur 2 + (−3) = −1. Ye Brahmagupta ka ek niyam hai.

Integers ke liye ghataav ka kya matlab hai?

Ye batata hai ki shuruaati number se target number tak jaane ke liye kitna movement chahiye: Target − Shuruaat = Movement. Jaise 3 se −1 tak jaane ke liye −4 chalte ho, isliye (−1) − 3 = −4.

Negative number ghatana jodne jaisa kyun hai?

−200 se +2000 tak jaane ke liye 0 tak 200 upar aur phir 2000 aur jaana padta hai, kul +2200. Isliye 2000 − (−200) = 2000 + 200. Kisi number ko ghatana hamesha uske inverse ko jodne ke barabar hai.

Zero pair kya hai?

Ek positive token aur ek negative token. Saath mein inki value 0 hai, isliye inhe daalne ya hataane se value nahi badalti.

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