Class 7 Maths · Chapter 12
Short answer: Class 7 Maths Ganita Prakash Chapter 12 — "Another Peek Beyond the Point" — Chapter 3 ("A Peek Beyond the Point") mein decimals ka basic intro hua tha; ye chapter usi concept ko aage le jaake decimal numbers ki multiplication, division aur real-life applications (paisa, measurement, science data) pe deep-dive karta hai. Neeche step-by-step solutions, formulas, common mistakes aur FAQs diye gaye hain.
Ganita Prakash Class 7 Maths ka Chapter 12, "Another Peek Beyond the Point," apne naam ke hisaab se hi Chapter 3 "A Peek Beyond the Point" ka natural extension hai. Jahan Chapter 3 mein decimal numbers ka introduction — place value, decimal ko fraction mein convert karna, aur basic addition-subtraction — cover hua tha, wahin ye chapter decimal numbers ki multiplication aur division, unke real-world applications (paise ka hisaab, lambai-chaudai ki measurement, science ke data readings), aur estimation skills pe focus karta hai. Chapter 3 poore Class 7 decimal-number understanding ki neev hai — aur Chapter 12 uspe operations ki chhat khadi karta hai.
Is post mein hum NCERT Class 7 Maths Ganita Prakash chapter wise solutions series ka hissa banate hue "Another Peek Beyond the Point class 7 solutions" cover karenge. Agar aap poori series dhoondh rahe ho to yaad rakhiye ki isme Class 7 Maths Large Numbers Around Us solutions (Chapter 1), Class 7 Maths Arithmetic Expressions NCERT solutions (Chapter 2), "A Peek Beyond the Point" (Chapter 3), Expressions Using Letter-Numbers class 7 notes (Chapter 4), Parallel and Intersecting Lines class 7 questions (Chapter 5), Number Play class 7 maths ncert solutions (Chapter 6), A Tale of Three Intersecting Lines class 7 solutions (Chapter 7), Working with Fractions class 7 exercise solutions (Chapter 8), Geometric Twins class 7 congruence solutions (Chapter 9), Operations with Integers class 7 ncert solutions (Chapter 10), Finding Common Ground class 7 maths HCF LCM (Chapter 11), aur is Chapter 12 ke baad Connecting the Dots class 7 maths solutions, Constructions and Tilings class 7 practical geometry, aur Finding the Unknown class 7 simple equations solutions bhi shamil hain. Ye poora set mila kar aapke Ganita Prakash class 7 important questions ki tayyari complete karta hai.
Chapter 12 ke andar aap seekhoge: decimal × decimal multiplication (jaise 3.5 × 1.2), decimal ÷ whole number aur decimal ÷ decimal division, decimal numbers ko 10, 100, 1000 se multiply/divide karne ka shortcut (decimal point shift), aur real-life word problems — jaise dukaan ka bill, kapde ki lambai, ya petrol ka average — jinme decimal operations use hote hain.
Chapter 12 Summary — 5 Minute Revision
Chapter 12 "Another Peek Beyond the Point" decimal numbers ke operations (multiplication aur division) ko practical context mein sikhata hai. Do decimals ko multiply karte waqt pehle unhe whole numbers ki tarah multiply karo, phir dono numbers ke decimal digits ginkar answer mein utne hi decimal places wapas rakho. Division mein divisor ko whole number banane ke liye dono numbers ko 10/100/1000 se multiply karo. Ye skills daily life — shopping bills, measurement, average speed, science readings — mein directly use hoti hain, isliye NCERT is chapter ko strong conceptual base ke saath sikhata hai, sirf mechanical rules ratt-kar nahi.
In-Text Questions — Solutions
Figure it out: 2.5 × 3 ka value kya hoga?
2.5 × 3 = 25 × 3 ÷ 10 = 75 ÷ 10 = 7.5
Step-by-step: pehle decimal ko ignore karke 25 × 3 = 75 nikalo, phir jitne decimal places original number (2.5) mein the (yahan 1), utne hi answer mein wapas rakho — 7.5.
0.6 × 0.4 ka product nikaliye.
0.6 × 0.4 = 6 × 4 ÷ 100 = 24 ÷ 100 = 0.24
Dono numbers mein 1-1 decimal place hai, total 2 decimal places, isliye answer 0.24 (2 decimal places) hoga, sirf 2.4 nahi.
12.5 ÷ 5 ka value kya hoga?
12.5 ÷ 5 = 125 ÷ 10 ÷ 5 = 25 ÷ 10 = 2.5
Divisor whole number hai isliye seedha long division use karke 12.5 ÷ 5 = 2.5 milta hai — 12 ÷ 5 = 2 remainder 2, phir 2.5 ÷ 5 = 0.5, total 2.5.
3.6 ÷ 0.4 ka value kya hoga?
3.6 ÷ 0.4 = 36 ÷ 4 = 9
Divisor ko whole number banane ke liye dono numbers ko 10 se multiply karo: 3.6 × 10 = 36 aur 0.4 × 10 = 4. Phir simple division 36 ÷ 4 = 9.
Ek dukaan mein 1 kg seb ka daam ₹85.50 hai. 3.5 kg seb ka kul daam kya hoga?
85.50 × 3.5 = 8550 × 35 ÷ 1000
8550 × 35 = 299250
299250 ÷ 1000 = 299.25
Kul daam ₹299.25 hoga. Ye real-life application decimal multiplication ko shopping bill ke context mein dikhata hai.
Ek car 156.8 km, 8 litre petrol mein tay karti hai. 1 litre mein car kitni km chalegi?
156.8 ÷ 8 = 1568 ÷ 10 ÷ 8 = 196 ÷ 10 = 19.6
Car 1 litre mein 19.6 km chalegi — ye average calculation ka real-world example hai jisme decimal division use hoti hai.
Exercise Questions — Solutions (Q1–Q6)
12.34 × 100 aur 12.34 ÷ 100 ka value nikaliye.
12.34 × 100 = 1234.0 = 1234
Rule: 10 ki power se multiply karne pe decimal point utni hi jagah right shift hota hai. 100 mein 2 zero hain, isliye point 2 jagah right shift hoga: 12.34 → 1234.
12.34 ÷ 100 = 0.1234
Divide karne pe decimal point utni hi jagah left shift hota hai: 12.34 → 0.1234.
7.25 + 3.6 × 2 ka value nikaliye (BODMAS follow karte hue).
BODMAS ke rule se pehle multiplication phir addition:
3.6 × 2 = 7.2
7.25 + 7.2 = 14.45
Answer: 14.45
Ek kapde ki dukaan mein 1 metre kapda ₹142.50 ka hai. 6.5 metre kapda kharidne ka kul kharcha kya hoga?
142.50 × 6.5 = 14250 × 65 ÷ 1000
14250 × 65 = 926250
926250 ÷ 1000 = 926.25
Kul kharcha ₹926.25 hoga.
25.5 litre dudh ko 3 barabar bartano mein baantna hai. Har bartan mein kitna dudh aayega?
25.5 ÷ 3 = 255 ÷ 10 ÷ 3 = 85 ÷ 10 = 8.5
Har bartan mein 8.5 litre dudh aayega. Check: 8.5 × 3 = 25.5 ✓
Ek dhaage ka tukda 0.75 m lamba hai. Agar aise 8 tukde jode jayein, to kul lambai kya hogi?
0.75 × 8 = 75 × 8 ÷ 100
75 × 8 = 600
600 ÷ 100 = 6.0
Kul lambai 6 metre hogi.
Compare karo: 0.5, 0.05, aur 0.55 — inhe chhote se bade order mein arrange kijiye, aur bataiye 2.4 kg chawal ko agar 0.6 kg ke packet mein baanta jaye to kitne packet banenge.
Ascending order (chhote se bade): 0.05 < 0.5 < 0.55
Reasoning: place value se dekhein — 0.05 mein tenths digit 0 hai, 0.5 aur 0.55 dono mein 5 hai lekin 0.55 mein hundredths digit bhi 5 hai isliye 0.55 sabse bada hai.
2.4 ÷ 0.6 = 24 ÷ 6 = 4
Kul 4 packet banenge.
Important Equations — Ek Nazar Me
| Rule / Concept | Formula ya Tarika |
|---|---|
| Decimal × Decimal | Numbers ko whole number samajh kar multiply karo, phir dono ke decimal places jod kar utne hi places answer mein right se count karo |
| Decimal ÷ Whole number | Normal long division karo, quotient mein dividend ke decimal point ke seedha upar decimal point lagao |
| Decimal ÷ Decimal | Dono numbers ko 10, 100 ya 1000 se multiply karke divisor ko whole number banao, phir divide karo |
| × 10, 100, 1000 se multiply | Decimal point utni hi jagah RIGHT shift karo jitne zero hain |
| ÷ 10, 100, 1000 se divide | Decimal point utni hi jagah LEFT shift karo jitne zero hain |
| Decimal comparison | Pehle whole number part compare karo, phir tenths, phir hundredths — jagah jagah zero add karke digits barabar lambe bana lo |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Decimal point ko sirf 'aankh se guess' karke lagana instead of decimal-places ginkar sahi jagah rakhna — jaise 2.5 × 1.2 ko 3.0 samajh lena jabki sahi answer 3.00 → 3.0 hi hai, isliye is case mein luck se sahi ho sakta hai lekin method galat hai.
- Multiplication mein dono numbers ke total decimal places add karna bhool jaana — 0.6 × 0.4 = 0.24 hota hai (2 decimal places), na ki 2.4.
- Division mein divisor ko whole number banate waqt sirf divisor ko multiply karna, dividend ko multiply karna bhool jaana — dono ko sath multiply karna zaroori hai warna value badal jaati hai.
- × 10/100/1000 aur ÷ 10/100/1000 ke decimal-shift direction (right vs left) ko ulta kar dena.
- Word problems mein units mismatch — jaise kilogram aur gram, ya metre aur centimetre ko bina convert kiye seedha operation kar dena.
- Long division mein remainder ke baad zero add karke decimal continue karna bhool jaana, jisse answer beech mein hi galat truncate ho jaata hai.
Board-Style Important Questions
- Chapter-end 'Figure it out' sections mein diye gaye decimal multiplication aur division ke real-life word problems (shopping bills, measurement, average calculation) NCERT exercise se practice ke liye important hain.
- Class 7 school unit tests aur term exams mein decimal operations pe application-based word problems (jaise cloth shop, milk distribution, petrol average) commonly poochhe jaate hain.
- 10, 100, 1000 se multiply/divide karne ka decimal-shift shortcut concept school assessments mein frequently test hota hai.
- Comparing decimals aur unhe ascending/descending order mein arrange karna — ye conceptual question type regularly practice worksheets mein aata hai.
Aksar Poochhe Jaane Wale Sawaal
Chapter 12 'Another Peek Beyond the Point' mein kya naya seekhne ko milega jo Chapter 3 mein nahi tha?
Chapter 3 'A Peek Beyond the Point' mein decimal numbers ka basic introduction — place value, fraction-decimal conversion, aur simple addition-subtraction — tha. Chapter 12 isi foundation pe decimal numbers ki multiplication aur division sikhata hai, saath hi real-life applications jaise shopping bills, measurement, aur average calculation.
Decimal numbers ko multiply karte waqt decimal point kahan lagega?
Pehle dono numbers ko whole number maan kar normal multiply karo. Fir dono original numbers ke decimal places (point ke baad ke digits) count karke jod do, aur answer mein right se utni hi jagah count karke decimal point laga do.
Decimal ko decimal se divide karna kyun mushkil lagta hai aur asaan tarika kya hai?
Mushkil isliye lagta hai kyunki divisor bhi decimal hota hai. Asaan tarika ye hai ki dono numbers (dividend aur divisor) ko 10, 100 ya 1000 se multiply kar do taaki divisor whole number ban jaye — phir normal division jaisa hi solve hota hai.
Kya ye chapter class 7 exam ke liye important hai?
Haan, decimal operations daily-life numeracy ka core skill hain aur school assessments mein application-based word problems ke roop mein regularly poochhe jaate hain, isliye practice zaroori hai.
Poore Ganita Prakash Class 7 syllabus mein kitne chapters hain aur ye chapter kahan fit hota hai?
Current rationalised Ganita Prakash (2026-27 session) syllabus mein Large Numbers Around Us se shuru hoke Finding the Unknown tak kai chapters hain. 'Another Peek Beyond the Point' Chapter 12 ke position pe aata hai aur decimal-number operations ko cover karta hai — Chapter 3 ke concepts ko aage badhata hai.
Decimal multiplication aur division practice karne ka sabse accha tarika kya hai?
NCERT textbook ke 'Figure it out' aur end-of-chapter exercises step-by-step solve karo, real-life word problems (bill, measurement, average) pe extra practice karo, aur har answer mein decimal places double-check karne ki habit banao.
Class 7 Maths — Saare Chapters
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