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Class 6 Maths Chapter 10: The Other Side of Zero (Hinglish Notes)

Ye chapter 5 lines mein

Zero se chhote numbers bhi hote hain, jinhe negative numbers kehte hain, jaise −1, −2 aur −3. Zero aur positive numbers ke saath ye integers banaate hain: …, −3, −2, −1, 0, 1, 2, 3, … Number line pe negative numbers zero ke baayein hote hain, aur chhota number hamesha baayein hota hai. Jodna matlab Shuruaati position + Movement = Target, aur ghatana matlab Target − Shuruaati position = Movement; kisi number ko ghatana uske inverse ko jodne jaisa hai.

Chapter 10 ka mind map: zero se neeche ke numbers, integers, number line, inverse, jodna, ghatana aur thoda itihaas
Poora chapter ek page pe

Kya zero se kam bhi kuch hota hai?

Humne pehle counting numbers 1, 2, 3, … seekhe, phir 0, aur phir unke beech ke fractions. Ab tak ki number line 0 se shuru hokar sirf daayein jaati thi, isliye wo asal mein ek number ray thi. Kya 0 ke baayein, 0 se chhote numbers hain? Haan: zameen ke neeche ki manzilein, kisi ka udhaar, jamaav se thanda taapmaan, ya sea level ke neeche ki gehraai socho.

Bela ki Building of Fun

Bela ki Building of Fun: ground floor Floor 0 hai, upar ki manzilein +1 se +6 aur neeche ki −1 se −5
Manzilein integers ke roop mein

Bela ki Building of Fun mein zameen ke upar aur neeche manzilein hain, aur ek lift jisme do button hain: upar jaane ke liye ‘+’ aur neeche jaane ke liye ‘−’. ‘+’ do baar dabaana +2 hai; ‘−’ teen baar dabaana −3. Ground floor, Welcome Hall, Floor 0 hai. Iske upar ki manzilon ke number positive numbers (+1, +2, …) aur neeche ki manzilon ke negative numbers (−1, −2, …) hain. Zero na positive hai na negative. Aur padho negative numbers kya hain mein.

Movement ki tarah jodna aur ghatana

  • Jodna: Shuruaati floor + Movement = Target floor. Floor +2 se −3 dabaane pe Floor −1 pahunchte ho: (+2) + (−3) = −1.
  • Button dabaana milaana bhi jodna hai: +2 aur phir −3 dabaana kul −1 ka movement hai.
  • Inverse: +3 aur phir −3 dabaane se wapas aa jaate ho: (+3) + (−3) = 0. Isliye −3, +3 ka inverse hai.
  • Ghatana: Target − Shuruaati floor = Zaroori movement. Floor −2 se Floor +2 jaane ke liye +4 dabao: (+2) − (−2) = +4.

Khadaan (mine) mein zameen ke upar-neeche metre mein naape levels bhi aise hi kaam karte hain: (−90) + (−55) = −145 aur (+40) − (−50) = +90.

Integers aur number line

−10 se 10 tak number line: baayein negative integers, daayein positive integers aur beech mein zero; baayein jaane pe numbers chhote hote hain
Number line pe integers

Positive numbers hamesha chalte rehte hain, aur negative numbers bhi. Zero ke saath ye integers hain: …, −3, −2, −1, 0, 1, 2, 3, … Ek ‘infinite lift’ socho aur use leta do: wo number line ban jaati hai, jisme negative numbers 0 ke baayein hain. Chhote numbers hamesha baayein hote hain, isliye −5 < −3 < 2. Aur padho number line pe integers mein.

Jodne-ghatane ke niyam

Negative number ghatana positive number jodne jaisa hai: (+2000) − (−200) = (+2000) + (+200) = +2200. Aam taur pe, kisi number ko ghatana uske inverse ko jodne jaisa hai, isliye har ghataav ko jod mein badla ja sakta hai. Token model ye dikhata hai: ek positive aur ek negative token zero pair banaate hain jiski value 0 hai, aur zero pairs daalne ya nikaalne se value nahi badalti. Aur padho integers add subtract kaise karein mein.

Hamare aas-paas integers

Rozmarra mein integers: 0°C se neeche ka taapmaan negative, sea level ke upar ki oonchaai positive aur neeche negative, aur bank mein credit positive aur debit negative
Zero ek reference point
  • Banking: credit (aaya paisa) positive aur debit (gaya paisa) negative hai. Kuch bank kuch samay ke liye balance negative hone dete hain, aksar extra charge ke saath.
  • Geography: oonchaai sea level, 0 m, se naapi jaati hai; sea level se neeche ki jagahon ki oonchaai negative hoti hai.
  • Taapmaan: degree Celsius mein paani ke jamne ke bindu, 0°C, se neeche ka taapmaan negative hai, jaise sardiyon ki raat mein Leh mein.

Thoda itihaas

Negative numbers pehle hisaab-kitaab mein use hue. China mein The Nine Chapters on Mathematical Art (pehli ya doosri sadi CE) mein positive aur negative numbers laal aur kaali chhadon se dikhaaye gaye. India mein Kautilya ke Arthaśhāstra (lagbhag 300 BCE) mein credit aur debit ki baat hai, aur Bakhshali manuscript (lagbhag 300 CE) mein negative number ke baad ek khaas nishaan lagaakar likha gaya. 628 CE mein Brahmagupta ne positive numbers, negative numbers aur zero ko barabar maana aur unke saath kaam karne ke saaf niyam diye. Ye vichaar 9th sadi tak Arab duniya aur 13th sadi tak Europe pahunche. Chapter ke har sawal ka jawab Chapter 10 ke NCERT solutions mein hai.

Key terms (zaroori shabd)

TermMatlab
Negative number (rinaatmak sankhya)Zero se chhota number, jiske aage ‘−’ ka nishaan hota hai, jaise −4. Number line pe ye 0 ke baayein hota hai.
Positive number (dhanaatmak sankhya)Zero se bada number, kabhi ‘+’ ke saath likha jaata hai, jaise +4 ya bas 4.
Integers (poornank)…, −3, −2, −1, 0, 1, 2, 3, … yaani positive numbers, negative numbers aur zero.
ZeroReference point. Zero na positive hai na negative.
Inverse (additive inverse)Wo number jo diye gaye number mein jodne pe zero de. +3 ka inverse −3 hai, aur −3 ka +3.
Zero pairEk positive aur ek negative token saath mein. Inki kul value zero hai, isliye ye kat jaate hain.
Number lineBeech mein 0 waali line, daayein positive aur baayein negative numbers, jo dono taraf hamesha chalti rehti hai.
Unmarked number lineAisi number line jisme sirf 0 dikhaaya ho; bade integers jodne-ghatane ke liye baaki numbers kalpana karte hain.
Credit aur debitBank khaate mein daala gaya paisa (credit, positive) aur nikaala gaya paisa (debit, negative).
Sea level (samudra tal)Oonchaai ke liye reference level, 0 m: iske upar positive, neeche negative.
Brahmagupta ke niyamPositive numbers, negative numbers aur zero ko jodne-ghatane ke niyam, jo Brahmagupta ne 628 CE mein diye.

Is chapter ke topics

Is chapter ke NCERT solutions Chapter ke saare exercise questions, step-by-step jawab ke saath.

Practice karo

  1. Inme se negative number kaunsa hai?

    1. (a) +4
    2. (b) 0
    3. (c) −4
    4. (d) 4
    Jawab dekho

    Jawab: (c) −4

  2. −7 ka inverse kya hai?

    1. (a) −7
    2. (b) 0
    3. (c) +7
    4. (d) +1
    Jawab dekho

    Jawab: (c) +7

  3. Sahi tulna kaunsi hai?

    1. (a) −3 < −4
    2. (b) −4 < −3
    3. (c) −3 = −4
    4. (d) 0 < −4
    Jawab dekho

    Jawab: (b) −4 < −3 Number line pe −4, −3 ke baayein hai (aur Floor −4, Floor −3 ke neeche hai), isliye −4 chhota hai.

  4. (+5) + (−8) kitna hai?

    1. (a) +13
    2. (b) +3
    3. (c) −3
    4. (d) −13
    Jawab dekho

    Jawab: (c) −3 Paanch zero pairs kat jaate hain, aur teen negative tokens bachte hain.

  5. 2 − (−3) kitna hai?

    1. (a) −1
    2. (b) −5
    3. (c) 1
    4. (d) 5
    Jawab dekho

    Jawab: (d) 5 −3 ghatana +3 jodne jaisa hai: 2 + 3 = 5.

Students ke sawal

Class 6 Maths Chapter 10 mein kya padhte hain?

Bela ki Building of Fun se negative numbers, integers ko movement ki tarah jodna-ghatana, inverse, integers ki tulna, number line, token model, banking, geography aur taapmaan mein integers, integer grids ke saath khojbeen, aur negative numbers ka thoda itihaas.

Kya The Other Side of Zero nayi Ganita Prakash book mein hai?

Haan. The Other Side of Zero (Integers) Ganita Prakash ka Chapter 10, yaani aakhri chapter hai, jo 2026-27 session mein Class 6 Maths ki textbook hai.

Negative numbers ke niyam kisne diye?

Brahmagupta ne 628 CE mein apne Brāhma-sphuṭa-siddhānta mein positive numbers, negative numbers aur zero ko jodne, ghatane, guna aur bhaag karne ke saaf niyam diye.

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