Class 7 Maths · Chapter 4
Short answer:
Chapter 4: Expressions Using Letter-Numbers — Class 7 Maths Ganita Prakash ka ye chapter algebra ka pehla formal introduction hai jahan letters (n, x, y, t) ko numbers ki jagah use karke general expressions banana sikhaya jaata hai. Number-machines, matchstick patterns, aur real-life situations se expression-writing aur simplification cover hoti hai. Ye chapter aage 'Finding the Unknown' (simple equations) ki neev banata hai.
Chapter 4 poore Class 7 Maths ke algebra section ki neev hai — yahan se students formal tareeke se 'letter-numbers' (variables) ka use seekhte hain, jo aage Chapter 15 'Finding the Unknown' aur high-school algebra tak kaam aata hai. NCERT Class 7 Maths Ganita Prakash chapter wise solutions is series mein hum har chapter ko is Expressions Using Letter-Numbers class 7 notes wale format mein detail se cover kar rahe hain — real-life examples (jaise pocket money, matchstick patterns, number machines) se shuru karke abstract expression-writing tak.
Is chapter mein number ki jagah letters (n, x, y, t) use karke general rule likhna sikhaya jaata hai, jisse ek hi expression multiple values ke liye kaam kar sake. Ye skill sirf is chapter tak seemit nahi — Number Play class 7 maths ncert solutions aur Arithmetic Expressions jaise dusre chapters mein bhi yehi foundational thinking use hoti hai.
Chapter 4 Summary — 5 Minute Revision
Chapter 4 "Expressions Using Letter-Numbers" Class 7 Maths ke Ganita Prakash textbook ka ek foundational algebra chapter hai jisme letters ko unknown ya changing numbers represent karne ke liye use kiya jaata hai. Chapter number-input-output machines se shuru hota hai, jahan ek fixed rule (jaise "double karo aur 3 jodo") ko letter-number expression ki form mein likhna sikhaya jaata hai — jaise 2n + 3. Iske baad real-life scenarios (pocket money, umar ka farak, shopping bills) ko expressions mein convert karna cover hota hai.
Dusra major hissa hai like aur unlike terms ka concept — sirf same letter-number wale terms ko hi combine kiya ja sakta hai (5x + 3x = 8x), jabki alag letter-numbers (5x + 3y) simplify nahi hote. Distributive rule (a(b+c) = ab+ac) bhi is chapter mein introduce hoti hai jo brackets khol kar expression expand karne mein kaam aati hai.
Teesra important skill hai substitution — given value ko letter-number ki jagah rakh kar expression ki numeric value nikaalna, jo verify karne ka tareeka bhi hai ki do expressions equivalent hain ya nahi. Matchstick aur dot patterns se general expression nikaalna is chapter ka visual-thinking component hai, jo students ko pattern se algebra tak ka connection samjhata hai. Poora chapter aage Class 7 ke hi "Finding the Unknown" (simple equations) chapter aur high-school algebra ki direct neev banata hai — isliye is chapter ki practice thorough honi chahiye.
In-Text Questions — Solutions
Ek number machine 'n' input leti hai aur usmein 3 jodkar output deti hai. n = 8 ke liye output expression aur value likho.
Expression: n + 3
n = 8 pe: 8 + 3 = 11
x = 4 hone par 2x + 5 ki value nikaalo.
2x + 5 = 2(4) + 5 = 8 + 5 = 13
Simplify karo: 7y − 3y + 2y
Sabhi like terms hain (y ke terms), inhe combine karo:
7y − 3y + 2y = (7 − 3 + 2)y = 6y
Do consecutive numbers ka sum agar pehla number 'n' hai to expression likho.
Consecutive number matlab agla number = n + 1
Sum = n + (n + 1) = 2n + 1
Exercise Questions — Solutions (Q1–Q6)
Figure Out 4.1 Q1: Ekta har roz ₹y bachati hai. Uske bade bhai Sunny use har roz ₹5 extra deta hai. To Sunny ke paas total kitna paisa hoga, agar woh apna paisa bhi jodta hai jo already usme hai — expression likho jab Sunny ke paas already ₹x hai.
Diya hai: Ekta bachati hai = ₹y roz. Sunny deta hai = ₹5 extra roz. Sunny ke paas already = ₹x.
Sunny ke total paisa ka expression = x + 5
Yahan y sirf Ekta ki bachat batata hai, Sunny ke total mein directly nahi judta jab tak explicitly na kaha jaye — is tarah ke letter-number sawaalon mein pehle carefully identify karo ki kaunsa letter kis quantity ko represent kar raha hai, phir hi expression banao.
Figure Out 4.1 Q2: Jinput-output machine mein agar input number 'n' hai aur machine har number mein 7 jodkar double kar deti hai, to output ka expression likho.
Step 1: n mein 7 jodo → n + 7
Step 2: is result ko double karo → 2 × (n + 7)
Output expression = 2(n + 7)
Bracket lagana zaroori hai kyunki pehle addition hoga, uske baad multiplication — BODMAS rule follow karo.
Simplify karo agar t = 3: 5t + 2t − t
Pehle letter-numbers ko combine karo (jaise terms):
5t + 2t − t = (5 + 2 − 1)t = 6t
Ab t = 3 substitute karo:
6t = 6 × 3 = 18
Ek rectangle ki length 'l' aur breadth 'b' hai. Agar length ko 3 se badhaya jaaye aur breadth ko waise hi rakha jaaye, to naye rectangle ka perimeter ka expression likho.
Naya length = l + 3, breadth = b (same)
Perimeter ka formula = 2 × (length + breadth)
Perimeter = 2 × ((l + 3) + b) = 2(l + b + 3)
Isko expand bhi kar sakte hain: 2l + 2b + 6
Verify karo ki 3(x + 4) aur 3x + 12 same expression hain jab x = 2.
Pehla expression: 3(x + 4) = 3(2 + 4) = 3 × 6 = 18
Dusra expression: 3x + 12 = 3(2) + 12 = 6 + 12 = 18
Dono ka answer same (18) aaya, isliye 3(x + 4) = 3x + 12 — yeh distributive property ka example hai.
Ek number machine mein input 'p' hai. Pehle usmein 2 subtract kiya jata hai, phir 4 se multiply kiya jata hai, aur end mein 1 add hota hai. Output ka expression likho aur p = 5 ke liye value nikaalo.
Step-by-step expression banate hain:
Step 1: p − 2
Step 2: 4 × (p − 2) = 4(p − 2)
Step 3: 4(p − 2) + 1
Final expression = 4(p − 2) + 1
Ab p = 5 daalo:
4(5 − 2) + 1 = 4(3) + 1 = 12 + 1 = 13
Important Equations — Ek Nazar Me
| Rule / Concept | Explanation |
|---|---|
| Like terms | Same letter-number wale terms — inhe hi add/subtract kar sakte hain. Jaise 5x + 3x = 8x |
| Unlike terms | Alag letter-number wale terms — inhe combine nahi kar sakte. Jaise 5x + 3y ko simplify nahi kiya ja sakta |
| Distributive rule | a(b + c) = ab + ac — bracket khol kar expand karna |
| Order of operations (BODMAS) | Bracket → Of → Division → Multiplication → Addition → Subtraction ke order mein expression solve karo |
| Substitution | Letter-number ki jagah given value rakh kar expression ki numeric value nikalna |
| Coefficient | Letter-number ke saath multiply hone wala number — jaise 6t mein 6 coefficient hai |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Unlike terms ko combine kar dena — jaise 3x + 2y ko galti se 5xy ya 5(x+y) likhna, jabki ye simplify hi nahi ho sakta kyunki x aur y alag letter-numbers hain.
- Bracket ke andar operation order galat karna — pehle multiplication phir addition kar dena jab expression 3(x+4) jaisa ho, jabki bracket ke andar ka operation pehle priority leta hai ya distributive rule use karni padti hai.
- Substitution karte waqt sign ki galti — negative letter-number value substitute karte waqt (jaise x = −2) sign bhool jaana aur galat answer nikaalna.
- Coefficient aur letter-number ko alag treat karna — jaise 6t ko 6 + t samajh lena, jabki 6t ka matlab hai 6 × t (multiplication, not addition).
- Pattern se expression banate waqt starting value ignore karna — matchstick ya number-machine pattern mein sirf 'rate of change' pakadna aur fixed starting number (constant term) chhod dena, jisse expression jaise 3n ki jagah sahi 3n + 1 nahi ban paata.
- Expression aur equation ko confuse karna — expression (jaise 2x + 5) ko equation (jaise 2x + 5 = 11) samajh kar 'x nikaalne' ki koshish karna, jabki plain expression sirf simplify ya evaluate hoti hai, solve nahi.
Board-Style Important Questions
- NCERT Ganita Prakash Class 7 textbook ke 'Figure Out' aur 'Let Us Explore' sections mein is chapter ke practice questions diye gaye hain — koi official CBSE board-exam PYQ database is naye syllabus ke liye abhi public available nahi hai (2026-27 session recent hai).
- School-level periodic tests mein is chapter se number-machine based expression-writing questions frequently puchhe jaate hain.
- Matchstick pattern se general expression nikaalne wale questions school unit tests mein common hain.
- Simplification of like/unlike terms wale short-answer questions class tests mein regularly aate hain.
- Substitution-based value-finding questions (given x = value, find expression value) bhi common assessment format hai.
Aksar Poochhe Jaane Wale Sawaal
Class 7 Maths Chapter 4 'Expressions Using Letter-Numbers' ka main topic kya hai?
Ye chapter algebra ki neev hai — isme sikhte hain ki kaise letters (jaise x, y, n, t) ko numbers ki jagah use karke general expressions banaye jaate hain. Input-output number machines, matchstick patterns, aur real-life situations (jaise Ekta-Sunny ka paisa wala example) se letter-numbers ka concept build hota hai. Simplifying expressions aur unhe verify karna bhi is chapter ka core part hai.
Letter-number aur variable mein kya farak hai — NCERT Ganita Prakash isko kis naam se bulata hai?
Naye Ganita Prakash textbook mein 'variable' ki jagah 'letter-number' term use hui hai kyunki students ke liye ye zyada intuitive hai — letter ek unknown ya changing number ko represent karta hai. Concept wahi hai jo purane NCERT mein 'variable' ke naam se padhaya jaata tha, sirf naming approach zyada beginner-friendly bana di gayi hai.
Expression simplify karte waqt sabse common mistake kya hoti hai?
Sabse common mistake hai unlike terms ko combine karna — jaise 3x + 2y ko galti se 5xy ya 5(x+y) likh dena. Yaad rakho, sirf like terms (same letter-number) hi add ya subtract ho sakte hain. Dusri common mistake hai bracket ke andar operation ka order galat karna — hamesha BODMAS follow karo.
Kya is chapter mein equations bhi solve karni padti hain?
Nahi, Chapter 4 mein sirf expressions banana aur simplify karna sikhaya jaata hai — equal-to sign wale equations solve karna (jaise x + 5 = 12) alag chapter 'Finding the Unknown' mein cover hota hai jo Ganita Prakash ke baad wale chapters mein aata hai.
Matchstick patterns wale sawaal is chapter mein kyun important hain?
Matchstick pattern questions students ko dikhate hain ki real, visual patterns se bhi general expression nikala ja sakta hai — jaise 'n' squares banane ke liye matchsticks ka expression 3n + 1 hota hai. Ye pattern-recognition skill algebra ki understanding ko concrete banati hai, sirf abstract formula rata-fication nahi rehti.
Class 7 Maths ke saare Ganita Prakash chapters kahan milenge solved format mein?
NCERT Class 7 Maths Ganita Prakash chapter wise solutions is series mein cover ho rahe hain — jaise Large Numbers Around Us, Arithmetic Expressions, A Peek Beyond the Point, Parallel and Intersecting Lines, Number Play, A Tale of Three Intersecting Lines, Working with Fractions, Geometric Twins, Operations with Integers, Finding Common Ground, Connecting the Dots, Constructions and Tilings, aur Finding the Unknown. Har chapter ke liye step-by-step solved notes available hain jo current 2026-27 session ke syllabus ke hisaab se hain.
Class 7 Maths — Saare Chapters
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