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Class 7 Maths Chapter 4: Expressions using Letter-Numbers (Hinglish Notes)

Ye chapter 5 lines mein

Expressions using Letter-Numbers algebra se parichay karaata hai. a ya n jaisa letter-number kisi sankhya ki jagah aata hai, isliye Shabnam ki umar Aftab se 3 saal zyaada hai jaisa rishta s = a + 3 ban jaata hai. Letter-numbers waale expressions ki value letters ki jagah sankhya rakhkar nikalti hai, like terms jodkar aur brackets kholkar ve simplify hote hain, aur patterns ko samjhaate hain.

Chapter 4 ka mind map: letter-numbers, formulas, value nikaalna, simplify karna, barabar ya nahi, aur patterns
Poora chapter ek page pe

Ye chapter kis baare mein hai?

Shabnam ki umar Aftab se 3 saal zyaada hai. Aftab ki umar jo bhi ho, Shabnam ki umar ke liye 3 jodna hai. Aftab ki umar ke liye a likhne se ye ek chhota niyam ban jaata hai, s = a + 3, jo har umar ke liye chalta hai. Ye chapter sankhyaon ki jagah letters use karke aise rishte chhote mein likhne, unke saath kaam karne, aur patterns kyun chalte hain ye samjhaane ke baare mein hai.

Letter-numbers aur formulas

Sankhyaon ki jagah aane waale a aur s jaise letters letter-numbers hain, aur unwaale expressions, jaise a + 3, algebraic expressions hain. Maachis ka ek L 2 teeliyon se banta hai, isliye n L ke liye 2 × n. Ketaki ke laddu ke saamaan ka daam c nariyal aur j kg gud ke liye c × 35 + j × 60 rupaye hai. q bhuja waale square ki parimiti 4 × q hai. Aise likhe aam rishte formulas kehlaate hain. Aur padho letter-numbers kya hain mein.

Aftab ki umar 4, 10, 23 aur a, aur Shabnam ki umar 7, 13, 26 aur a + 3
Shabnam ki umar 3 saal zyaada
Parimiti ke formulas: niyamit aakaaron ke liye 3q, 4q, 5q aur 6q, aur rectangle ke liye 2l + 2b
Parimiti ke formulas

Chhota likhna aur value nikaalna

4 ke guna-phal 4, 8, 12, … hain, isliye nth term 4 × n hai, jise hum chhota karke 4n likhte hain: sankhya pehle aur guna ka chinh hata dete hain. Algebraic expression ki value tab milti hai jab har letter-number ki jagah sankhya rakhi jaaye. Isliye k = 4 pe 7k = 28, aur m = 2 pe 5m + 3 = 5 × 2 + 3 = 13. Chinhon aur brackets ka dhyaan zaroori hai: a = −4 ho to 10 − a = 10 + 4 = 14.

Nau value jaanchi gayin: diye gaye jawab, galtiyan kati hui, aur sahi values
Mind the Mistake: values

Expressions simplify karna

Sankhyaon ke niyam letter-numbers pe bhi chalte hain. Rectangle ki parimiti l + b + l + b ko jamaakar 2l + 2b banta hai, jo uska simplified roop hai; l = 3 aur b = 4 pe dono 14 dete hain. 5c, 3c aur 10c jaise ek jaise letter-numbers waale terms like terms hain aur distributive property se judkar ek term, 18c, bante hain. 18c aur 11d jaise terms unlike hain aur jud nahi sakte. Bracket se pehle minus ho to andar ka har chinh badal jaata hai: (40x + 75y) − (6x + 10y) = 34x + 65y. Padho expressions simplify kaise karein.

Bante rectangles ka kshetrafal: 4v + 3v = 7v, aur 12n − 4n = 8n
Kshetrafal se distributive property

Barabar ya nahi?

Do expressions tab barabar hain jab unke letter-numbers ki har value pe ek hi value milein. Simplified aur asli roop hamesha aisa karte hain. Par 5u (u ka 5 guna) aur 5 + u (u se 5 zyaada) u = 2 pe 10 aur 7 dete hain, isliye barabar nahi; 10y − 3 aur 10(y − 3) bhi nahi.

Values ki table: 5u aur 5 + u alag, aur 10y − 3 aur 10(y − 3) bhi alag
Barabar ya nahi? Values aazmaao

Patterns aur rishte

Algebra patterns dhoondhne aur samjhaane mein madad karta hai. Jo number machine 5 aur 2 se 8, aur 8 aur 1 se 15 deti hai, wo formula 2a − b pe chalti hai. A, B, C dohraane waali saree ki kinaari mein nth C position 3n pe, nth B 3n − 1 pe aur nth A 3n − 2 pe hai, isliye position 122 pe B hai. Calendar ke kisi bhi 2 × 2 square mein, upar-baayein taareekh a ho to sankhyaayein a, a + 1, a + 7 aur a + 8 hain, isliye dono vikarn ka jod 2a + 8 hai: pattern har square ke liye sahi hai. Maachis ke triangles ki line mein step y pe 2y + 1 teeliyan lagti hain. Padho algebra se patterns.

Calendar ka 2 × 2 square a, a + 1, a + 7, a + 8 aur barabar vikarn jod 2a + 8, aur plus aakaar jiska jod 5a hai
Calendar ke patterns

Aage badhne se pehle

Algebraic expressions maatraon ke beech rishton ko dikhate hain, sankhyaon ke hi niyamon pe chalte hain, aur jo baat shabdon mein lambi hoti, wo kuch chinhon mein keh dete hain. Har sawaal, dono Mind the Mistake aur teeno Figure it Out ke jawab Chapter 4 ke NCERT solutions mein hain.

Key terms (zaroori shabd)

TermMatlab
Letter-numbera, n ya x jaisa letter jo kisi badalti ya abhi anjaan sankhya ki jagah aata hai.
Algebraic expressionLetter-numbers waala ganit ka expression, jaise a + 3, 2n ya 35c + 60j.
FormulaLetter-numbers mein likha aam rishta, jaise q bhuja waale square ki parimiti 4q.
Expression ki valueHar letter-number ki jagah sankhya rakhne pe milne waali sankhya: m = 2 ho to 5m + 3 = 13.
TermExpression ka wo hissa jo baaki se + chinh se juda ho, jaise 7p − 3q mein 7p aur −3q.
Like termsEk jaise letter-numbers waale terms, jaise 5c, 3c aur 10c; inhe jodkar ek term banta hai.
Unlike termsAlag letter-numbers waale terms, jaise 18c aur 11d; inhe joda nahi ja sakta.
Simplest formBrackets hata kar aur like terms aur number terms jodkar bana roop, jaise l + b + l + b ka 2l + 2b.
Distributive propertyJod ka guna, guna-phalon ka jod hai: 4(x + y) = 4x + 4y, aur 5c + 3c = (5 + 3)c.

Is chapter ke topics

Is chapter ke NCERT solutions Chapter ke saare exercise questions, step-by-step jawab ke saath.

Practice karo

  1. Aftab ki umar a saal hai aur Shabnam ki umar 3 saal zyaada. Shabnam ki umar kaunsa expression deta hai?

    1. (a) 3a
    2. (b) a + 3
    3. (c) a − 3
    4. (d) 3 − a
    Jawab dekho

    Jawab: (b) a + 3

  2. m = 2 ho to 5m + 3 ki value kya hai?

    1. (a) 55
    2. (b) 13
    3. (c) 10
    4. (d) 25
    Jawab dekho

    Jawab: (b) 13

  3. 5c + 3c + 10c ka simplest form kya hai?

    1. (a) 18c
    2. (b) 18 + c
    3. (c) 150c
    4. (d) 8c
    Jawab dekho

    Jawab: (a) 18c

  4. a = −4 ho to 10 − a kitna hai?

    1. (a) 6
    2. (b) −14
    3. (c) 14
    4. (d) −6
    Jawab dekho

    Jawab: (c) 14

  5. A, B, C, A, B, C, … pattern mein position 122 pe kaunsa design hai?

    1. (a) A
    2. (b) B
    3. (c) C
    4. (d) Pata nahi chal sakta
    Jawab dekho

    Jawab: (b) B

  6. l lambaai aur b chaudaai waale rectangle ki parimiti kaunsa expression hai?

    1. (a) l × b
    2. (b) 2l + 2b
    3. (c) l + b
    4. (d) 4l
    Jawab dekho

    Jawab: (b) 2l + 2b

Students ke sawal

Class 7 Maths Chapter 4 ke mukhya topics kya hain?

Letter-numbers aur algebraic expressions; umar, daam aur parimiti ke formulas likhna; arithmetic expressions dohraana; guna ka chinh hataana; expression ki value nikaalna; like terms aur brackets se expressions simplify karna; do expressions barabar hain ya nahi jaanchna; aur number machines, saree, calendar aur maachis ki teeliyon ke patterns ko algebra se samjhaana.

Kya Expressions using Letter-Numbers nayi Ganita Prakash kitaab mein hai?

Haan. Ye Ganita Prakash, Class 7 Maths ki kitaab Part 1 (Reprint 2026-27) ka Chapter 4 hai, pages 81 se 105 tak. Ye Shabnam se shuru hota hai, jiski umar Aftab se 3 saal zyaada hai, aur dikhata hai ki Aftab ki umar ke liye a likhne se ye rishta a + 3 ban jaata hai.

Letter-number kya hota hai?

Kisi sankhya ki jagah likha letter. Ye kisi badalti sankhya, jaise kisi ki umar ya maachis ke L ki ginti, ya kisi anjaan sankhya ke liye ho sakta hai. L ki ginti ke liye n likhne se hum har pattern ke liye ek saath keh sakte hain ki teeliyan 2n hongi.

Algebraic expression ko simplify kaise karte hain?

Brackets hataao, ye yaad rakhte hue ki bracket se pehle minus ho to andar ke har term ka chinh badal jaata hai, aur jahan koi sankhya bracket ko guna kare wahan distributive property lagaao. Phir like terms, yaani ek jaise letter-numbers waale terms, aur number terms jodo. Jaise 4(x + y) − y = 4x + 4y − y = 4x + 3y.

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