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Letter-numbers aur algebraic expressions

Short mein jawab

Letter-number a, n ya x jaisa letter hai jo kisi sankhya ki jagah aata hai. Letter-numbers waala expression, jaise a + 3 ya 2n, algebraic expression hai, aur aise likha aam rishta formula hai. Expression ki value nikaalne ke liye har letter ki jagah uski sankhya rakho: m = 2 pe 5m + 3 = 13.

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Shabdon se letters tak

Shabnam ki umar Aftab se 3 saal zyaada hai. Aftab ki umar 10 ho to Shabnam ki 13; Aftab ki umar 18 ho to Shabnam ki 21. Shabdon mein niyam hai: Shabnam ki umar = Aftab ki umar + 3. Aftab ki umar ke liye a aur Shabnam ki umar ke liye s likhne se ye s = a + 3 ban jaata hai. a = 23 ho to s = 23 + 3 = 26. Niyam ulta bhi chalta hai: Aftab ki umar 3 saal kam hai, isliye a = s − 3, aur Shabnam ki umar 20 ho to Aftab ki umar 17.

Aftab ki umar 4, 10, 23 aur a, aur Shabnam ki umar 7, 13, 26 aur a + 3
Shabnam ki umar 3 saal zyaada

Sankhyaon ki jagah aane waale a aur s jaise letters letter-numbers kehlaate hain, aur inwaale expressions, jaise a + 3, algebraic expressions. Koi bhi letter chalega; hum yaad rakhne mein aasaan letter chunte hain.

Formulas likhna

Parthiv maachis ke L agal-bagal rakhta hai, aur har L 2 teeliyon se banta hai. Isliye 5 L ke liye 5 × 2 teeliyan, 45 L ke liye 45 × 2, aur n L ke liye 2 × n. Ketaki ₹35 ka ek nariyal aur ₹60 kilo gud khareedti hai: c nariyal aur j kg gud ka daam c × 35 + j × 60 rupaye hai, isliye 10 nariyal aur 5 kg ka ₹650, aur 8 nariyal aur 9 kg ka ₹820. q bhuja waale square ki parimiti 4 × q hai. Letter-numbers mein likhe aise rishte formulas kehlaate hain.

Maachis ke L: har ek mein 2 teeliyan, isliye 1, 5, 7, 45 aur n L ke liye 2, 10, 14, 90 aur 2n
Har L mein 2 teeliyan

Formulas ek saath kai sawaalon ka jawab dete hain. Saari bhujaayein q waale triangle ki parimiti 3q, niyamit pentagon ki 5q aur niyamit hexagon ki 6q hai. 20 m ke pipe mein k m ka pipe jodne se 20 + k metre bante hain. Vaakya bhi expressions bante hain: kisi sankhya x se 5 zyaada x + 5, 4 kam x − 4, uske 13 gune se 2 kam 13x − 2, aur 2 gune se 13 kam 2x − 13.

Parimiti ke formulas: niyamit aakaaron ke liye 3q, 4q, 5q aur 6q, aur rectangle ke liye 2l + 2b
Parimiti ke formulas

Guna ka chinh hataana

4 ke guna-phal 4, 8, 12, 16, … ka kram banaate hain. Teesra term 4 × 3 aur 29va term 4 × 29 hai, isliye nth term 4 × n hai. Ek maanak tareeke se hum 4 × n ko chhota karke 4n likhte hain: sankhya pehle aur × ka chinh hata dete hain. Isi tarah 5m + 3 matlab 5 × m + 3.

Value nikaalna

Har letter-number ki jagah sankhya rakhne pe algebraic expression ki ek value milti hai. Isliye k = 4 pe 7k = 7 × 4 = 28, aur m = 2 pe 5m + 3 = 5 × 2 + 3 = 13. Arithmetic ke niyam ab bhi lagte hain: terms nikaalo, aur brackets pehle. 23 − 10 × 2 ke terms 23 aur −10 × 2 hain, isliye value 23 + (−20) = 3 hai.

Aam galtiyan tab hoti hain jab letters ka matlab bhool jaate hain. d = 6 ho to 3d = 3 × 6 = 18, do ankon ki sankhya 36 nahi. r = 8 ho to 2r + 1 = 17, 29 nahi. s = 7 ho to 3s − 2 = 21 − 2 = 19, 3 × 5 = 15 nahi. m = −6 ho to 3(m + 1) = 3 × (−5) = −15. h = 5 aur n = 6 ho to h − (3 − n) = 5 − (−3) = 8.

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

Ye kyun zaroori hai

Formulas har jagah kaam aate hain, bills aur recipes se lekar parimiti aur kshetrafal tak, kyunki ek expression har value pe chalta hai. Aage dekho expressions ko saaf kaise karte hain, expressions simplify kaise karein mein, aur ye patterns kaise samjhaate hain, algebra se patterns mein. Har sawaal ka jawab Chapter 4 ke NCERT solutions mein hai; poore Chapter 4 ke notes bhi dekho.

Practice karo

  1. Kisi sankhya p se 4 kam kaunsa expression hai?

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

    Jawab: (b) p − 4

  2. r = 8 ho to 2r + 1 kitna hai?

    1. (a) 29
    2. (b) 17
    3. (c) 18
    4. (d) 11
    Jawab dekho

    Jawab: (b) 17

  3. Aate ki chakki chalu hone mein 10 second aur har kg pisne mein 8 second leti hai. y kg pisne mein kitna samay lagega?

    1. (a) 10 + 8 + y
    2. (b) (10 + 8) × y
    3. (c) 10 + 8 × y
    4. (d) 10 × y + 8
    Jawab dekho

    Jawab: (c) 10 + 8 × y

  4. Kisi sankhya k ke 13 gune se 2 kam ka expression likho, aur k = 3 pe uski value nikaalo.

    Jawab dekho

    Jawab: 13k − 2. k = 3 pe ye 13 × 3 − 2 = 39 − 2 = 37 hai.

  5. Krithika ke paas ₹100 ke x, ₹20 ke y aur ₹5 ke z note hain. Kitne paise hain?

    Jawab dekho

    Jawab: 100x + 20y + 5z rupaye. Jaise 3, 5 aur 6 note hon to 300 + 100 + 30 = ₹430.

Students ke sawal

Class 7 Maths mein letter-number kya hai?

Wo letter jo kisi sankhya ki jagah aata hai. Ye badalti maatra, jaise Aftab ki umar a, ya abhi anjaan sankhya ho sakti hai. Letters se hum ek rishta sab maamlon ke liye ek baar likh dete hain: Shabnam ki umar, jo Aftab se 3 saal zyaada hai, hamesha a + 3 saal hai, a jo bhi ho.

4 × n ki jagah 4n kyun likhte hain?

Ye ek maanak chhota tareeka hai: sankhya aur letter-number ke beech guna ka chinh hata dete hain, aur sankhya pehle likhte hain. Isliye 4n matlab 4 × n, 5m + 3 matlab 5 × m + 3, aur 2l + 2b matlab 2 × l + 2 × b.

Algebraic expression ki value kaise nikaalte hain?

Har letter-number ki jagah uske liye di gayi sankhya rakho aur arithmetic expression ko terms aur brackets ke aam niyamon se hal karo. Jaise f = 3 aur g = 1 ho to 2f − 2g = 2 × 3 − 2 × 1 = 6 − 2 = 4.

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