Distributive property: jod ka guna
Short mein jawab
Distributive property kehti hai ki jod ya antar ka guna, guna-phalon ke jod ya antar ke barabar hota hai: 2 × (43 + 24) = 2 × 43 + 2 × 24. Isse samajh aata hai ki brackets kyun zaroori hain, aur guna jaldi hota hai, jaise 97 × 25 = 100 × 25 − 3 × 25 = 2425.
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Do logon ka bill
Lhamo aur Norbu hotel gaye, aur dono ne ek-ek vegetable cutlet ₹43 ka aur ek-ek rasgulla ₹24 ka order kiya. Har ek ka hissa 43 + 24 hai. Kya kul bill 2 × 43 + 24 ho sakta hai? Terms mein dekho to ye 2 × 43 aur 24 ka jod hai, yaani do cutlet aur sirf ek rasgulla ka paisa. Hamein poore hisse ka dugna chahiye, aur brackets theek yahi kehte hain: 2 × (43 + 24) = 2 × 67 = 134 rupaye.
Do hisson ka bill do cutlet aur do rasgulle ke bill jaisa hi hai, isliye 2 × (43 + 24) = 2 × 43 + 2 × 24 = 86 + 48 = 134. Agar dost Sangmu bhi wahi order lekar aa jaaye, to bill 3 × (43 + 24) = 201 rupaye hoga.
Scouts aur guides ki panktiyan
Republic Day parade mein boy scouts 5-5 ki 4 panktiyon mein aur girl guides 5-5 ki 3 panktiyon mein chal rahe hain. Har samooh alag gino to 4 × 5 + 3 × 5 = 20 + 15 = 35. Pehle panktiyan gino to 4 + 3 = 7 panktiyan, har ek mein 5, yaani (4 + 3) × 5 = 35. Isliye 4 × 5 + 3 × 5 = (4 + 3) × 5.
Yahan bhi brackets matlab badalte hain: 5 × 4 + 3 = 23 hai, par 5 × (4 + 3) = 35. Aur kyunki jagah badalne se na jod badalta hai na guna, 5 × (4 + 3) = 5 × (3 + 4) = (3 + 4) × 5.
Saamaanya niyam
10 × 98 + 3 × 98 ko aise socho: das baar 98, aur phir teen baar aur 98. Ye terah baar 98 hai, isliye 10 × 98 + 3 × 98 = (10 + 3) × 98. Antar ke saath bhi aisa hi hai: chaudah baar 10 mein se chhe baar 10 hata do to aath baar 10 bachta hai, isliye 14 × 10 − 6 × 10 = (14 − 6) × 10. Shabdon mein, jod (ya antar) ka guna, guna-phalon ka jod (ya antar) hai. Chapter ki summary ise distributive property kehti hai: kisi sankhya ka bracket se guna, us sankhya ka andar ke har term se guna karne jaisa hai.
Extra: 5 × (4 + 3) ko 5 panktiyon aur 7 column waale binduon ke aayat ki tarah bhi soch sakte ho. 4th column ke baad ek rekha ise 5 × 4 aur 5 × 3 ke do hisson mein baant deti hai, isliye kul 20 + 15 = 35.
Jaldi guna
Ye property kisi jaane hue guna ko zaroorat waale guna mein badal deti hai. 53 × 18 = 954 diya hai, 63 × 18 nikaalo: 63 = 53 + 10, isliye 63 × 18 = 53 × 18 + 10 × 18 = 954 + 180 = 1134. Mushkil guna bhi aasaan ho jaate hain. 97 ko 100 − 3 likho: 97 × 25 = 100 × 25 − 3 × 25 = 2500 − 75 = 2425. Isi tarah 95 × 8 = 800 − 40 = 760, 104 × 15 = 1500 + 60 = 1560 aur 49 × 50 = 2500 − 50 = 2450. Ye aksar lambe guna se jaldi hota hai, khaas kar jab koi sankhya 10, 50, 100 ya 1000 ke kisi multiple ke paas ho, jaise 98 × 7 ya 103 × 9.
Tasveer ki sankhyaon ka jod
Ye property jod mein bhi madad karti hai. 3 by 3 grid mein paanch 4 aur chaar 8 hain: 5 × 4 + 4 × 8 = 52. Har 8 ko ek 4 ke saath jodi banao to 4 × (4 + 8) + 4 = 52 bhi aata hai. 4 by 4 grid mein aath 5 aur aath 6 hain, to jod 8 × 5 + 8 × 6 = 8 × (5 + 6) = 88, aur kyunki har pankti ka jod 22 hai, ye 4 × 22 bhi hai.
Ye kyun zaroori hai
Mann mein guna, jaldi bill aur aage chalkar algebra, sab ke peeche distributive property hai. Ye expressions ki value kaise nikalein aur terms aur brackets ke vichaaron ke saath kaam karti hai. Kitaab ke har sawaal ka jawab Chapter 2 ke NCERT solutions mein hai; poore Chapter 2 ke notes bhi dekho.
Practice karo
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Kaunsa expression (9 + 2) × 4 ke barabar hai?
Jawab dekho
Jawab: (b) 9 × 4 + 2 × 4
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104 × 15 kya hai? (100 + 4) × 15 ka use karo.
Jawab dekho
Jawab: (c) 1560
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53 × 18 = 954 diya hai. 63 × 18 kya hai?
Jawab dekho
Jawab: (b) 1134
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49 × 50 jaldi waale tareeke se nikaalo.
Jawab dekho
Jawab: 49 × 50 = (50 − 1) × 50 = 50 × 50 − 1 × 50 = 2500 − 50 = 2450.
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Khaali jagah bharo: 5 × (12 − 3) = 5 × 12 − 5 × ___.
Jawab dekho
Jawab: 3. 5 brackets ki dono sankhyaon ko guna karta hai: 5 × 12 − 5 × 3 = 60 − 15 = 45, aur 5 × 9 bhi 45 hai.
Students ke sawal
Class 7 Maths mein distributive property kya hai?
Ye niyam ki jod ya antar ka guna karna, har hisse ka alag guna karke jodne ya ghataane jaisa hai: 4 × 5 + 3 × 5 = (4 + 3) × 5 = 35. Chapter ise Lhamo aur Norbu ke hotel bill aur scouts aur guides ki panktiyon se dikhata hai, aur summary mein ise distributive property naam deta hai.
5 × 4 + 3 aur 5 × (4 + 3) barabar kyun nahi hain?
5 × 4 + 3 mein sirf 4 ka 5 se guna hota hai, phir 3 judta hai: 20 + 3 = 23. 5 × (4 + 3) mein poore jod 7 ka 5 se guna hota hai: 35. Doosra expression 5 × 4 + 5 × 3 ke barabar hai, yaani usme 3 ki jagah 5 × 3 = 15 hai.
Distributive property se guna jaldi kaise hota hai?
Ek sankhya ko gol sankhya aur chhoti sankhya ke jod ya antar mein todo, har hisse ka guna karo aur milao. 97 × 25 = (100 − 3) × 25 = 2500 − 75 = 2425, aur 104 × 15 = (100 + 4) × 15 = 1500 + 60 = 1560. Ye tab sabse kaam aata hai jab sankhya 10, 50 ya 100 ke kisi multiple ke paas ho.
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