Class 7 Maths · Chapter 6
Short answer:
Class 7 Maths Chapter 6 "Number Play" numbers ke patterns aur logical puzzles ka chapter hai — supercells dhoondhna, digits rearrange karke bade/chhote numbers banana, palindrome aur reverse-and-add patterns, BODMAS ke through arithmetic expressions solve karna, aur magic squares banana. Yeh chapter rote-learning nahi, pattern-based thinking test karta hai — isliye practice hi sabse best strategy hai.
NCERT Class 7 Maths (Ganita Prakash) ka Chapter 6, "Number Play", students ko numbers ke saath khelna sikhata hai — literally. Yeh chapter traditional "solve karo aur answer likho" type nahi hai; iska poora focus pattern recognition, logical reasoning, aur number sense pe hai. Isme supercells dhoondhna (grid mein woh numbers jo apne saare neighbours se bade hain), digits ko rearrange karke sabse bada ya sabse chhota number banana, palindromic numbers ke saath reverse-and-add jaise fascinating patterns explore karna, arithmetic expressions ko correct order of operations (BODMAS) se solve karna, aur magic squares jaisi classic number puzzles shaamil hain.
Yeh chapter dikhne mein "khel-khel mein maths" jaisa lagta hai, lekin actually yeh students ki computational fluency aur pattern-based thinking ko strong karta hai — jo aage Class 8-9 ke algebra aur number theory chapters ke liye zaroori hai. Neeche diye gaye solutions har concept ko step-by-step, CBSE marking-scheme style mein explain karte hain, taaki exam mein full marks aasani se mil sakein.
Chapter 6 Summary — 5 Minute Revision
NCERT Class 7 Maths (Ganita Prakash) Chapter 6 "Number Play" numbers ke saath structured playfulness sikhata hai. Is chapter mein students ne seekha ki kaise grid ke andar supercells (apne saare neighbours se bade numbers) identify kiye jaate hain, kaise diye gaye digits ko rearrange karke sabse bada ya sabse chhota number banaya jaata hai, palindrome numbers aur reverse-and-add process ke fascinating patterns kya hote hain, arithmetic expressions ko BODMAS ke sahi order mein kaise solve karte hain, aur magic squares kaise construct kiye jaate hain jahan har row, column aur diagonal ka sum equal ho.
Yeh saare concepts pure computation se zyada pattern recognition aur logical reasoning pe based hain — jo is chapter ko baaki Class 7 Maths chapters se thoda different banata hai. In concepts ki practice aage Class 8 ke number-theory aur algebra topics ke liye strong foundation deti hai. Agla useful step hai "A Peek Beyond the Point" chapter (decimals aur unke beyond-the-point patterns) explore karna, jo isi number-sense building ko aage le jaata hai.
Yeh guide broader NCERT Class 7 Maths Ganita Prakash chapter wise solutions series ka hissa hai — isse related chapters jaise Class 7 Maths Large Numbers Around Us solutions, Class 7 Maths Arithmetic Expressions NCERT solutions, Expressions Using Letter-Numbers class 7 notes, aur Operations with Integers class 7 ncert solutions bhi explore kar sakte hain step-by-step working ke saath.
In-Text Questions — Solutions
Ek grid mein diya gaya row hai: 5, 12, 8, 20, 15, 30, 3. Isme saare supercells identify karo.
Har number ko uske dono immediate neighbours se compare karo:
12: left=5, right=8 → 12 > 5 aur 12 > 8 → Supercell ✓
20: left=8, right=15 → 20 > 8 aur 20 > 15 → Supercell ✓
30: left=15, right=3 → 30 > 15 aur 30 > 3 → Supercell ✓
Answer: Supercells hain — 12, 20, aur 30 (kul 3 supercells is row mein).
Digits 4, 0, 7, 2 use karke sabse chhota 4-digit number banao (leading zero allowed nahi).
Digits ascending order mein: 0, 2, 4, 7. Lekin number ka first digit 0 nahi ho sakta, isliye sabse chhota non-zero digit (2) ko first position pe rakho, baaki digits ascending order mein rakho.
Sabse chhota number = 2047
Answer: 2047 (0 ko second position pe rakha gaya kyunki leading zero se number 4-digit nahi rahega).
Expression 15 − 3 + 6 ÷ 2 × 4 ki value nikalo.
Step 1 (Division aur Multiplication left to right):
6 ÷ 2 = 3
3 × 4 = 12
Expression: 15 − 3 + 12
Step 2 (Addition-Subtraction left to right):
15 − 3 = 12
12 + 12 = 24
Answer: 24
Exercise Questions — Solutions (Q1–Q6)
Ek 5×5 grid mein numbers likhe gaye hain jahan har row left se right badhte hue arrange hai. Supercells (apne saare horizontal neighbours se bade numbers) ko identify karo aur circle karo. Kya ek row mein ek se zyada supercell ho sakta hai? Reasoning do.
Jab numbers strictly increasing order mein left se right arrange ho, to sirf sabse right wala number apne dono neighbours (sirf left neighbour hota hai last cell ke liye) se bada hoga.
Row: 12, 45, 67, 89, 93 → sirf 93 hi supercell hai kyunki uska koi right neighbour nahi aur woh left neighbour (89) se bada hai.
Answer: Ek strictly increasing row mein sirf ek hi supercell ban sakta hai — sabse last (sabse bada) number. Agar row monotonic nahi hai (ups and downs hain) to multiple supercells ban sakte hain, jaise 12, 45, 30, 67, 20 mein 45 aur 67 dono supercell hain.
7 alag-alag digits (jaise 2, 5, 8, 1, 9, 3, 6) use karke sabse bada aur sabse chhota 7-digit number banao. In dono ke beech ka difference nikalo.
Step 1: Digits ko descending order mein arrange karo sabse bada number banane ke liye.
Digits: 1, 2, 3, 5, 6, 8, 9 → Sabse bada = 9865321
Step 2: Digits ko ascending order mein arrange karo sabse chhota number banane ke liye (agar 0 na ho to koi restriction nahi).
Sabse chhota = 1235689
Step 3: Difference nikalo.
9865321 − 1235689 = 8629632
Answer: Difference = 8,629,632
Ek number palindrome kehlata hai agar woh aage se aur peeche se same padhe (jaise 121, 3443). 237 ko lo. Isme aur reverse (732) ko add karo. Yeh process (reverse-and-add) repeat karo jab tak palindrome na mil jaye. Kitne steps lagte hain?
Step 1: 237 + 732 = 969
969 khud hi palindrome hai (aage se peeche se same padhta hai — 9, 6, 9).
Answer: Sirf 1 step mein palindrome mil gaya: 969. Yeh reverse-and-add process bahut interesting hai — kai numbers 1-2 steps mein palindrome ban jaate hain, kuch (jaise 196) known cases mein bahut zyada steps lete hain ya palindrome nahi milta (unsolved problem, ise 'Lychrel number' kehte hain).
Ek arithmetic expression di gayi hai: 8 + 4 × 3 − 6 ÷ 2. BODMAS/operator precedence use karke iski value nikalo, step by step.
Step 1 (Division pehle, left to right BODMAS ke hisaab se):
6 ÷ 2 = 3
Expression ban gaya: 8 + 4 × 3 − 3
Step 2 (Multiplication):
4 × 3 = 12
Expression ban gaya: 8 + 12 − 3
Step 3 (Addition aur Subtraction, left to right):
8 + 12 = 20
20 − 3 = 17
Answer: 17
Kisi bhi 3-digit number ko lo jiske digits sab alag hon (jaise 4 3 2). Isse aur iske digits ko reverse karke bana number ka difference lo, phir reverse-and-add na karke sirf ek baar subtract karo — yeh Kaprekar-type puzzle hai. 432 aur 234 ka difference nikalo aur check karo yeh 9 se divisible hai kya.
Step 1: Original number = 432, Reversed number = 234
432 − 234 = 198
Step 2: Check divisibility by 9 — digit sum nikalo.
1 + 9 + 8 = 18, aur 18 ÷ 9 = 2 (exact)
Answer: Difference = 198, jo 9 se poori tarah divisible hai. Yeh property hamesha true hoti hai — kisi bhi number aur uske digits ke reverse ka difference hamesha 9 ka multiple hota hai, kyunki place-value ka har term 9 ka multiple banata hai (100a + 10b + c) − (100c + 10b + a) = 99(a − c), jo 9 se divisible hai.
Ek 3×3 magic square banao jisme har row, column, aur dono diagonals ka sum same ho, using numbers 1 se 9 tak (har number sirf ek baar).
Step 1: Total sum of 1 to 9 nikalo.
1+2+3+4+5+6+7+8+9 = 45
Step 2: Magic sum (har row ka sum) = Total ÷ 3 rows = 45 ÷ 3 = 15
Step 3: Standard magic square (Lo Shu square) banao jisme center mein 5 ho (kyunki 5 average hai aur symmetric):
| 2 | 7 | 6 |
| 9 | 5 | 1 |
| 4 | 3 | 8 |
↔ Table ko side me swipe karein
Verification: Row 1: 2+7+6=15, Row 2: 9+5+1=15, Row 3: 4+3+8=15, Column 1: 2+9+4=15, Diagonal: 2+5+8=15, Diagonal: 6+5+4=15 — sab 15 hai. Answer: Magic sum = 15, aur upar diya gaya arrangement ek valid magic square hai.
Important Equations — Ek Nazar Me
| Concept | Rule / Formula |
|---|---|
| Supercell condition | Cell value > left neighbour AND Cell value > right neighbour |
| Largest number from given digits | Digits ko descending (badte se ghatte) order mein arrange karo |
| Smallest number from given digits | Digits ko ascending order mein arrange karo (agar 0 ho to leading zero avoid karo) |
| Order of operations (BODMAS) | Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction (L→R) |
| Number minus its reverse (3-digit, digits a,b,c) | (100a+10b+c) − (100c+10b+a) = 99(a−c), hamesha 9 aur 11 dono se divisible |
| Magic sum for n×n square (1 to n²) | Magic Sum = n(n²+1) / 2 |
| Palindrome test | Number = Reverse of Number |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Supercell dhoondhte waqt sirf ek direction (sirf left ya sirf right neighbour) compare karna — dono neighbours check karna zaroori hai, warna wrong supercell mark ho jaata hai.
- Digits se sabse chhota number banate waqt 0 ko first position pe rakh dena — isse number ki digit-count kam ho jaati hai (jaise 0247 actually 247 hai, 4-digit nahi). Sabse chhota non-zero digit ko first position pe rakhna chahiye.
- BODMAS mein Division aur Multiplication ko strict order (pehle sab division, phir sab multiplication) samajh lena — yeh galat hai. In dono ki priority same hai, jo pehle left se aaye woh pehle solve hoga.
- Palindrome check karte waqt sirf number ko dekh kar guess kar lena, poora reverse karke compare na karna — especially 4+ digit numbers mein manual error ho sakta hai.
- Magic square banate waqt sirf ek row ka sum check karke satisfied ho jaana — sabhi rows, columns, AUR dono diagonals ka sum verify karna zaroori hai, tabhi woh true magic square kehlata hai.
- Number minus its reverse ka result hamesha 9 se divisible hota hai — is property ko yaad na rakhne ki wajah se students calculation lambi kar dete hain jab shortcut se hi answer verify ho sakta tha.
Board-Style Important Questions
- Grid-based supercell identification questions — diagram diya jaata hai aur students se saare supercells circle karke unki reasoning likhne ko kaha jaata hai.
- Given digits se sabse bada aur sabse chhota number banao, phir dono ka difference nikalo — yeh format har saal aata hai with different digit sets.
- Palindrome se related reverse-and-add process wale questions, jahan students se steps dikhate hue palindrome tak pahunchna hota hai.
- Arithmetic expression ko BODMAS follow karke step-by-step solve karna, marks step-wise diye jaate hain.
- 3×3 ya usse bade magic square complete karna jab kuch cells already filled ho aur baaki blank cells fill karne ho.
- Number aur uske reverse ka difference nikal kar uski divisibility (9 ya 11 se) verify karna, general property explain karte hue.
Aksar Poochhe Jaane Wale Sawaal
NCERT Class 7 Maths (Ganita Prakash) Chapter 6 'Number Play' mein kya-kya topics cover hote hain?
Yeh chapter numbers ke saath patterns, puzzles aur logical reasoning develop karta hai — supercells (neighbours se bade numbers dhoondhna), digit rearrangement se sabse bada/chhota number banana, palindromic numbers, reverse-and-add patterns, arithmetic expressions ka correct order of operations, aur magic squares jaisi number puzzles is chapter ka core hain. Yeh purely computational chapter nahi hai — is chapter ka focus number sense aur pattern recognition build karna hai, jo aage ke algebra aur number theory chapters ke liye foundation banata hai.
'Number Play' chapter exam ke liye kitna important hai?
Yeh chapter conceptual understanding pe based hai, rote-learning pe nahi — isliye questions typically application-based hote hain jahan diye gaye numbers/grids pe pattern dhoondhna padta hai. Practice karte waqt digit-manipulation puzzles (largest/smallest number formation), supercell identification, aur magic square logic pe extra focus do, kyunki yehi concepts is chapter ke exercises mein baar-baar aate hain.
Supercell kya hota hai aur ise kaise identify karte hain?
Supercell woh number hai jo grid mein apne saare immediate horizontal (ya jaisa bhi diagram define kare) neighbours se bada ho. Identify karne ka tarika simple hai — har cell ko uske left aur right (ya jo bhi neighbours diye gaye hon) ke saath compare karo. Agar woh dono se bada hai, to woh supercell hai. Isme common mistake yeh hoti hai ki students sirf ek direction (sirf left ya sirf right) check karte hain — dono neighbours check karna zaroori hai.
Reverse-and-add process kya hota hai aur yeh palindrome se kaise related hai?
Reverse-and-add ek process hai jahan kisi number ko uske digits reverse karke bane number mein add kiya jata hai, aur yeh process repeat kiya jata hai jab tak result ek palindrome (jo aage-peeche same padhta ho) na ban jaye. Zyadatar numbers 1-4 steps mein palindrome ban jaate hain, lekin kuch numbers (jaise 196) is process se palindrome nahi banate — inhe Lychrel numbers kehte hain, aur yeh ek open mathematical question hai ki 196 kabhi palindrome banega ya nahi.
Arithmetic expressions solve karte waqt operations ka sahi order kya hai?
Standard convention (jise BODMAS/PEMDAS kehte hain) follow karo: pehle Brackets, phir Orders/Exponents, phir Division aur Multiplication (left se right, jo pehle aaye), aur last mein Addition aur Subtraction (left se right, jo pehle aaye). Division aur Multiplication ek hi priority level pe hain — jo pehle expression mein left se aata hai, woh pehle solve hota hai. Same rule Addition aur Subtraction ke liye bhi lagu hoti hai.
Magic square banane ka trick kya hai?
Sabse pehle total sum nikalo (agar 1 se n² tak numbers hain, to sum = n²(n²+1)/2), phir usse total rows se divide karke magic sum nikalo. 3×3 magic square (1-9 numbers) ke liye center cell mein hamesha average number (5) aata hai, aur opposite corners ka sum bhi symmetric pattern follow karta hai. Practice ke through pattern samajhna sabse effective tarika hai, formula ratt-lena nahi.
Class 7 Maths — Saare Chapters
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