Class 7 Maths · Chapter 15
Short answer:
NCERT Class 7 Maths Ganita Prakash Chapter 15 "Finding the Unknown" simple equations ka chapter hai — ek unknown letter-number (jaise x ya y) waali equation ko solve karke uski exact value nikalna sikhata hai. Ye chapter seedha Chapter 3 "Expressions Using Letter-Numbers" ke upar build hota hai, isliye pehle wahan ka concept clear hona zaroori hai.
Chapter 15 poore Class 7 algebra ki neev hai. Pichle chapters me humne dekha tha letter-numbers (variables) use karke expressions kaise banate hain — jaise x + 5, ya 3y − 2. Ab is chapter me hum ek kadam aage badhte hain: agar humein pata chal jaaye ki koi expression kisi specific value ke barabar hai (jaise x + 5 = 12), toh x ki value kaise nikaalein?
Isi process ko "Finding the Unknown" kehte hain — yaani equation solve karna. Ye NCERT Class 7 Maths Ganita Prakash chapter wise solutions series ka ek zaroori chapter hai kyunki simple equations aage Class 8, 9, 10 ke poore algebra (linear equations, quadratic equations) ki neev banata hai. Agar yahan concept clear nahi hua, toh aage har jagah dikkat aayegi.
Is chapter me hum seekhenge: equation kya hoti hai aur expression se kaise alag hai, balance method se equation solve karna, verification (check) karna ki solution sahi hai ya nahi, aur real-life word problems ko equation ki form me likhna. Har concept ke saath NCERT textbook ke exercise questions ka step-by-step CBSE marking-scheme style solution diya gaya hai — jaise poore Ganita Prakash class 7 important questions series me hota hai.
Chapter 15 Summary — 5 Minute Revision
Is chapter ka core idea simple hai: equation ek aisa statement hai jisme do expressions "=" sign se jude hote hain, aur unknown (letter-number) ki woh value dhoondhni hoti hai jispar dono side barabar ho jaayein. Sabse reliable tareeka hai balance method — jo bhi operation ek side par karo, wahi doosri side bhi karo, taaki equation "balanced" rahe (jaise ek tarazu/scale).
Steps hamesha yeh hote hain: (1) equation ko dhyan se padho aur samjho kaunsa letter-number unknown hai, (2) constant terms (plain numbers) ko unknown wale term se alag karo — addition/subtraction ka opposite operation dono side karke, (3) agar unknown ke saath koi coefficient (multiplying number) hai, toh division/multiplication ka opposite operation dono side karke unknown ko akela chhodo, (4) mili hui value ko original equation me wapas daal kar verify karo ki LHS = RHS ban raha hai ya nahi.
Word problems solve karte waqt sabse zaroori step hai real-life statement ko equation me convert karna — jaise "kisi number me 7 jodne par 20 milta hai" ko x + 7 = 20 likhna. Yehi skill Class 7 Maths me sabse zyada exam me poochi jaati hai, aur Class 8 ke "Linear Equations in One Variable" chapter me seedha aage badhti hai.
In-Text Questions — Solutions
Equation aur expression me kya farak hai?
Expression sirf ek mathematical phrase hoti hai jisme numbers aur letter-numbers operations (+, −, ×, ÷) se jude hote hain, jaise x + 5. Isme koi "=" sign nahi hota, isliye isko solve nahi kiya ja sakta — sirf simplify kiya ja sakta hai.
Equation me do expressions "=" sign se jude hote hain, jaise x + 5 = 12. Yahan hum unknown x ki woh specific value dhoondh sakte hain jispar dono side barabar ho.
Balance method se x + 8 = 15 kaise solve karte hain?
x + 8 = 15
Dono side se 8 ghataao (subtract) taaki x akela reh jaaye:
x + 8 − 8 = 15 − 8
x = 7
Verification: x = 7 ko original equation me daalo → 7 + 8 = 15 ✓ (LHS = RHS, sahi hai)
3x = 21 jaisi equation solve karne ka tareeka?
3x = 21
Dono side ko 3 se divide karo (kyunki x ke saath 3 multiply ho raha hai):
3x ÷ 3 = 21 ÷ 3
x = 7
Verification: 3 × 7 = 21 ✓ sahi hai.
Do-step equation jaise 2x + 5 = 17 kaise solve hoti hai?
2x + 5 = 17
Step 1 — pehle constant number hatao (dono side 5 ghataao):
2x + 5 − 5 = 17 − 5
2x = 12
Step 2 — ab coefficient hatao (dono side 2 se divide karo):
x = 6
Verification: 2(6) + 5 = 12 + 5 = 17 ✓
Ek word problem ko equation me kaise convert karte hain? Example: "Ek number ko 4 se guna karke 9 jodne par 33 milta hai."
Unknown number ko x maano. Statement ko step by step equation me todo:
4x + 9 = 33
Ab solve karo:
4x = 33 − 9 = 24
x = 24 ÷ 4 = 6
Verification: 4(6) + 9 = 24 + 9 = 33 ✓ Number hai 6.
Exercise Questions — Solutions (Q1–Q6)
Solve karo: y − 9 = 14
y − 9 = 14
Dono side 9 jodo:
y − 9 + 9 = 14 + 9
y = 23
Check: 23 − 9 = 14 ✓
Solve karo: x/5 = 8
x/5 = 8
Dono side 5 se multiply karo:
(x/5) × 5 = 8 × 5
x = 40
Check: 40/5 = 8 ✓
Solve karo: 5x − 3 = 22
5x − 3 = 22
Step 1 — dono side 3 jodo:
5x = 25
Step 2 — dono side 5 se divide karo:
x = 5
Check: 5(5) − 3 = 25 − 3 = 22 ✓
Solve karo: 4(x + 2) = 28
4(x + 2) = 28
Dono side 4 se divide karo:
x + 2 = 7
Dono side 2 ghataao:
x = 5
Check: 4(5 + 2) = 4 × 7 = 28 ✓
Ravi ki age uski behan se 4 saal zyada hai. Agar Ravi 17 saal ka hai, toh behan ki age nikalne ke liye equation banao aur solve karo.
Behan ki age ko x maano. Statement: Ravi ki age = behan ki age + 4
x + 4 = 17
x = 17 − 4 = 13
Behan ki age 13 saal hai. Check: 13 + 4 = 17 ✓
Ek number ka 3 guna, us number me 10 jodne se prapt sankhya se 5 kam hai. Number nikalo.
Number ko x maano. Statement ke anusaar:
3x = (x + 10) − 5
3x = x + 5
Dono side se x ghataao:
2x = 5
x = 2.5
Check: 3(2.5) = 7.5; aur (2.5 + 10) − 5 = 12.5 − 5 = 7.5 ✓
Important Equations — Ek Nazar Me
| Rule / Concept | Explanation |
|---|---|
| Equation ka structure | LHS = RHS (Left Hand Side = Right Hand Side, ek "=" sign se jude) |
| Balance method (addition) | x − a = b ⟹ dono side a jodo ⟹ x = b + a |
| Balance method (subtraction) | x + a = b ⟹ dono side a ghataao ⟹ x = b − a |
| Balance method (multiplication) | x/a = b ⟹ dono side a se multiply karo ⟹ x = b × a |
| Balance method (division) | ax = b ⟹ dono side a se divide karo ⟹ x = b/a |
| Two-step equation | ax + b = c ⟹ pehle b hatao (subtract), phir a se divide karo |
| Bracket wali equation | a(x + b) = c ⟹ pehle a se divide karo, phir b ghataao |
| Verification rule | Solution ko wapas original equation me daalo — LHS = RHS aana chahiye |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Equation ke ek side operation karke doosri side bhool jaana — balance method me hamesha DONO side same operation karna zaroori hai, warna equation balanced nahi rahegi.
- Coefficient aur constant me confuse ho jaana — 3x + 5 = 20 me pehle constant (5) hatana hai, coefficient (3) baad me, warna galat order se calculation mistake hoti hai.
- Negative sign ko sahi se handle na karna — jab equation ke dono side minus number aata hai, sign ki galti se final answer ulta (positive ki jagah negative) aa jaata hai.
- Word problem ko equation me convert karte waqt "se zyada" aur "se kam" ko ulta likh dena — jaise "5 zyada" ko x + 5 ki jagah x − 5 likh dena.
- Solution nikal kar verify na karna — bina check kiye submit karne se calculation errors exam me pakde nahi jaate, isliye har answer ko wapas equation me daal kar confirm karna chahiye.
- Fraction wali equation (jaise x/4 = 9) me multiply/divide ka opposite operation galat apply karna — divide ki jagah galti se subtract kar dena, jo poora answer galat kar deta hai.
Board-Style Important Questions
- Class 7 school tests me equation solve karne ke 2-3 marks ke direct sawaal (jaise 2x + 7 = 19) common hain.
- Word problems jisme age, number, ya money se related real-life situation ko equation me convert karke solve karna hota hai — CBSE-style schools me practice questions me frequently aata hai.
- Bracket wali equations [jaise 3(x − 2) = 18] school unit tests me practice ke liye diye jaate hain.
- Verification/check step likhne wale questions — kai schools marking scheme me verification step ke alag marks rakhte hain.
- Do-step aur multi-step equations combine karke banaye gaye application-based questions periodic tests me dekhne ko milte hain.
Aksar Poochhe Jaane Wale Sawaal
NCERT Class 7 Maths Chapter 15 "Finding the Unknown" kis topic ke baare me hai?
Ye chapter simple equations solve karna sikhata hai — yaani ek letter-number (unknown, jaise x) waali equation di jaaye toh uski exact value kaise nikaali jaaye, balance method use karke.
Equation solve karne ka sabse aasan tareeka kya hai?
Balance method sabse reliable tareeka hai — jo bhi operation (jodna, ghatana, multiply, divide) equation ke ek side par karo, wahi exactly same operation doosri side bhi karo, taaki equation balanced rahe.
Expression aur equation me kya main farak hai?
Expression me "=" sign nahi hota (jaise x + 5), isliye woh solve nahi ho sakti, sirf simplify hoti hai. Equation me "=" sign hota hai (jaise x + 5 = 12), isliye unknown ki specific value nikaali ja sakti hai.
Solution nikalne ke baad verify karna kyun zaroori hai?
Verification confirm karta hai ki nikali gayi value sahi hai — solution ko wapas original equation me daalo, agar LHS = RHS ban jaaye toh answer sahi hai. Ye galtiyaan pakadne ka sabse aasan tareeka hai.
Word problems ko equation me convert karna kaise practice karein?
Pehle unknown quantity ko x (ya koi letter) maano, phir statement ko line-by-line padh kar mathematical operations me todo. Practice ke liye NCERT ke exercise questions aur Ganita Prakash class 7 important questions dono useful hain.
Ye chapter aage kaunse topics ke liye zaroori hai?
Finding the Unknown, Class 8 ke "Linear Equations in One Variable" aur Class 9-10 ke poore algebra (linear/quadratic equations) ki neev banata hai. Isliye balance method ka concept achhi tarah clear hona chahiye.
Class 7 Maths — Saare Chapters
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