Class 6 Maths · Chapter 10
Short answer: "
Class 6 Maths Ganita Prakash ke chapter \"The Other Side of Zero\" ki complete NCERT solutions yahan hain — negative numbers, integers, number line extension, aur real-life applications (temperature, sea level, lift floors) sab step-by-step CBSE marking-scheme style explain kiya gaya hai, saath me common mistakes aur practice questions.
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Chapter 10 poore Class 6 Maths ke number-system foundation ka agla bada step hai — yahan pehli baar bachhon ko zero ke \"doosri taraf\" ki duniya se milwaya jaata hai. Ab tak counting sirf 0, 1, 2, 3... tak simit thi, lekin real life me temperature minus me ja sakti hai, bank balance overdraft ho sakta hai, aur lift basement floors me neeche ja sakti hai — in sab situations ko represent karne ke liye negative numbers chahiye.
'The Other Side of Zero' Ganita Prakash (NEP-aligned rationalised syllabus, 2026-27 session) ka woh chapter hai jo integers — positive aur negative dono whole numbers — ka concept build karta hai. Yeh chapter number line ko dono directions me extend karke dikhata hai ki zero koi \"end point\" nahi, balki ek center point hai.
Is chapter ka connection pichle chapters se bhi hai — jis tarah NCERT Class 6 Maths Ganita Prakash chapter 1 Patterns in Mathematics me number patterns explore hue the, aur Class 6 Maths chapter 5 Prime Time me Goldbach conjecture jaisi unsolved-problem thinking introduce hui thi, waise hi yahan number system ka scope integers tak expand hota hai. Yeh foundation aage Class 7-8 me rational numbers samajhne ke liye zaroori hai.
"Chapter 10 Summary — 5 Minute Revision
"'The Other Side of Zero' Class 6 Maths (Ganita Prakash, rationalised syllabus 2026-27) ka chapter hai jo negative numbers aur integers ka foundation build karta hai. Is chapter me bachhe seekhte hain ki number line zero ke dono taraf extend hoti hai, integers ko kaise compare aur order karte hain, aur addition-subtraction ke rules kaise sign ke saath apply hote hain.
Real-life applications — jaise temperature below zero, sea level se neeche depth, aur lift ke basement floors — is chapter ko practical banate hain. Yeh chapter NCERT Class 6 Maths chapter 1 Patterns in Mathematics aur chapter 5 Prime Time jaise earlier chapters ke number-sense foundation par build hota hai, aur aage Perimeter and Area, Fractions, Lines and Angles, Symmetry, aur Data Handling and Presentation jaise chapters ke saath milkar Class 6 Maths ka poora rationalised syllabus (10 chapters, purani 14-chapter Mathematics book se consolidated) complete karta hai.
Exam preparation ke liye number line practice, sign rules ki repetition, aur word problems ka daily solving sabse effective strategy hai — Class 6 Maths chapter wise important questions CBSE pattern follow karte hue integers ke concept ko thoroughly revise karo.
"In-Text Questions — Solutions
Number line par −5 aur 3 ke beech kitni units ka gap hai?
−5 se 3 tak jaane ke liye zero cross karna padta hai: 5 units (−5 se 0) + 3 units (0 se 3) = 8 units.
Ek submarine sea level se 120 m neeche hai, use kaunsa integer represent karega?
−120, kyunki sea level ko 0 maante hain aur neeche jaana negative direction hai.
−4 aur −9 me bada kaun hai?
−4 bada hai, kyunki number line par woh zero ke zyada kareeb (daayi taraf) hai.
Exercise Questions — Solutions (Q1–Q6)
Write the integer that is 5 more than −7.
−7 + 5 = −2. Number line par −7 se 5 ghar right (dayin taraf) chalo, tab −2 pe pahunchte ho.
Represent the temperature change: a city's temperature was 4°C at morning and it fell by 9°C by night. Find the night temperature.
4 − 9 = 4 + (−9) = −5°C. Yeh negative temperature dikhata hai, matlab freezing point se neeche.
Arrange in increasing order: −8, 5, 0, −3, 9, −1.
Number line pe left se right order lagao: −8 < −3 < −1 < 0 < 5 < 9. Yaad rakho — negative numbers me jo zero se jitna door hai (bina sign dekhe) utna hi chhota hota hai agar sign negative hai.
A lift is at floor 3 (above ground). It goes down 7 floors. At which floor (basement level) does it stop?
3 − 7 = 3 + (−7) = −4, matlab lift Basement 4 (B4) pe rukega. Yahan floors ko integers ki tarah treat karte hain — ground floor = 0, upar positive, neeche negative.
Find the value: (−12) + (−8) − (−15).
(−12) + (−8) = −20
−20 − (−15) = −20 + 15 = −5
(−12) + (−8) − (−15) = −5
On a number line, a frog is at −2. It jumps 6 steps to the right and then 10 steps to the left. Where does it land?
Step 1: −2 + 6 = 4
Step 2: 4 − 10 = 4 + (−10) = −6
Frog −6 par land karta hai.
Important Equations — Ek Nazar Me
"| Rule | Statement | Example |
|---|---|---|
| Addition of a negative number | a + (−b) = a − b | 5 + (−3) = 2 |
| Subtraction of a negative number | a − (−b) = a + b | 7 − (−4) = 11 |
| Sum of a number and its opposite | a + (−a) = 0 | 9 + (−9) = 0 |
| Two negatives added | (−a) + (−b) = −(a + b) | (−6) + (−4) = −10 |
| Comparing integers | Number line par jo daayi taraf hai woh bada hai; har negative number har positive number se chhota hai | −100 < 1 |
| Absolute distance from zero | |a| = a agar a ≥ 0; |a| = −a agar a < 0 | |−7| = 7 |
↔ Table ko side me swipe karein
"Common Mistakes — Yahan Marks Kat te Hain
- Subtraction ko addition me convert karte waqt sign flip bhool jaana — jaise 5 − (−3) ko galti se 5 − 3 = 2 likh dena, jabki correct answer 5 + 3 = 8 hai.
- Negative numbers ko compare karte waqt bina sign dekhe sirf number ki magnitude compare kar lena — jaise −8 ko −3 se bada maan lena, jabki number line par −3, −8 se bada hai.
- Real-life word problems me sign assign karte waqt confuse ho jaana — jaise 'neeche jaana' ko positive aur 'upar jaana' ko negative maan lena, jabki convention ulta hota hai.
- Number line par jump ki direction galat le lena — right (positive) ki jagah left (negative) move kar dena ya vice versa.
- Do negative numbers add karte waqt sign 'cancel' ho jaayega yeh maan lena — (−6) + (−4) ko galti se +10 ya −2 likh dena, jabki correct answer −10 hai.
- Zero ko 'kuch nahi' samajh kar usse integer set ka hissa na maanna — zero na positive hai na negative, lekin woh ek valid integer hai.
Board-Style Important Questions
- School-level periodic test me common: 'Ek shehar ka temperature din me 6°C tha, raat ko 11°C gir gaya — raat ka temperature nikaalo' type word problems integers application se poochhe jaate hain.
- Number line par integers ko represent karke unhe ascending/descending order me arrange karne wale questions frequently practice worksheets me aate hain.
- Lift/elevator basement floor scenario (jahan ground floor 0 ho aur neeche floors negative ho) ek classic real-life integer application question hai jo school assessments me repeat hoti hai.
- Addition aur subtraction of integers ke direct computation questions (jaise (−15) + 22, ya 8 − (−9)) step-by-step working ke saath poochhe jaate hain.
- Missing integer find karne wale fill-in-the-blank type questions — jaise ___ + (−7) = 0 — number properties (additive inverse) test karte hain.
- Comparing aur ordering integers on a number line ke saath diagram-based questions bhi practice papers me common hain.
Aksar Poochhe Jaane Wale Sawaal
Class 6 Maths chapter 'The Other Side of Zero' kis chapter number pe aata hai?
Rationalised Ganita Prakash textbook (2026-27 session) me yeh negative numbers aur integers wala chapter book ke baad ke hisse me aata hai. Exact chapter numbering edition-wise thoda vary kar sakti hai, isliye apni school ki copy ka index page zaroor cross-check karo.
Negative number aur integer me kya farak hai?
Integer ek broader set hai jisme sab whole numbers (0, 1, 2, 3...) aur unke negative counterparts (−1, −2, −3...) dono aate hain. Negative number sirf zero se chhoti values hoti hain (−1, −2, −3...). Matlab har negative number ek integer hai, lekin har integer negative nahi hota.
NCERT Class 6 Maths Ganita Prakash PDF 2026-27 kahan se download karein?
Official NCERT PDF hamesha ncert.nic.in ki textbook section se free download hoti hai — vahi latest rationalised (10-chapter) version hoga. Kisi third-party site se download karne se pehle chapter list match zaroor kar lo, kyunki purane 14-chapter 'Mathematics' textbook ki copies abhi bhi internet par circulate ho rahi hain.
Is chapter ka connection Class 6 ke doosre chapters se kaise hai — jaise Prime Time ya Number Play?
'The Other Side of Zero' number system ko extend karta hai jo chapter 1 Patterns in Mathematics aur Number Play me shuru hua tha. Jaise Prime Time me Goldbach conjecture jaisi unsolved-problem thinking introduce hoti hai, waise hi yeh chapter number line ko dono directions me extend karke 'negative space' ka naya concept deta hai.
Real life me negative numbers kahan use hote hain?
Temperature (sub-zero degrees), bank account overdraft/debt, sea level se neeche elevation, lift ke basement floors, aur profit-loss statements — sab jagah negative numbers ka practical use dikhta hai. Isliye is chapter ko sirf abstract math na samajh kar real-world tool ki tarah dekho.
Exam me integers ke questions me sabse zyada marks kaha katte hain?
Sabse common mistake sign handling me hoti hai — especially subtraction ko addition me convert karte waqt sign flip bhool jaana. Step-by-step working dikhana aur har operation ke baad number line pe verify karna galtiyan kam karta hai.
Class 6 Maths — Saare Chapters
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