Class 7 Maths Part 2 Chapter 7: Finding the Unknown (Hinglish Notes)

Ye chapter 5 lines mein

Finding the Unknown equations ke baare mein hai: do expressions jo barabar ke nishaan se jude hon, jaise 2n + 1 = 99. Equation solve karne ke liye dono taraf ek hi operation karte hain, jaise balanced taraazu dono palde se barabar wazan hataane pe bhi seedha rehta hai, ya kisi term ko ulte operation ke saath doosri taraf le jaate hain. Equations word problems ko aasaan steps mein badal deti hain, aur chapter bijaganita pe khatm hota hai, yaani Brahmagupta aur Bhaskaracharya ka algebra.

Part 2 Chapter 7 ka mind map: equation kya hai, balance banaaye rakhna, term ko doosri taraf le jaana, problems solve karna, galtiyon se bachna, aur bijaganita — Poora chapter ek page pe

Ye chapter kis baare mein hai?

Pehle tumne n jaise letter-numbers se pattern likhe the: matchstick pattern ki position n pe 2n + 1 tiliyan lagti hain. Ye chapter sawaal ulta poochta hai. Agar Jasmine ke paas theek 99 tiliyan hain, to wo kaunsi position bana sakti hai? Iska jawab dene ke liye hum likhte hain 2n + 1 = 99 aur wo n dhoondhte hain jisse ye sahi ho. Aise kathan equations hain, aur unknown dhoondhna unhe solve karna kehlaata hai.

Anjaan wazan aur taraazu

Chapter latakne waale taraazu aur palde waale taraazu se shuru hota hai. Latakne waale taraazu pe likhi sankhya kul wazan hai, aur seedhi dandi ka matlab hai dono taraf barabar wazan. Palde waale taraazu pe paanch boriyan, do boriyon aur 21 kg ke baat ke barabar hain. Har palde se do boriyan hata do, taraazu phir bhi seedha rahega, to teen boriyan 21 kg ki hain aur ek bori 7 kg ki. Dono taraf se barabar cheez hataana, yahi is chapter ki har equation ki chaabi hai.

Taraazu pe 5 bori = 2 bori aur 21 kg; har palde se 2 bori hataane pe 3 bori = 21 kg, to ek bori 7 kg — Taraazu ko balance rakhna

Equation ka ek left hand side (LHS) aur ek right hand side (RHS) hota hai, jo barabar ke nishaan se jude hote hain. Uska solution letter-number ki wo value hai jisse dono taraf barabar ho jaayein.

Equation 2n + 1 = 99 ke LHS, RHS, letter-number aur barabar ka nishaan — Equation ke hisse

Equations ko tareeke se solve karna

Tum values andaaza lagaakar aazma sakte ho, ye trial and error hai, par isme der lag sakti hai. Ek pakka tareeka ek baat pe tika hai: dono taraf ek hi sankhya jodo, ghataao, guna karo ya bhaag do, to equation sahi rehti hai. 5x − 4 = 7 mein dono taraf 4 jodo to 5x = 11, phir dono taraf 5 se bhaag do to x = 11/5. Jawab waapas rakhkar check karo. Agar unknown dono taraf ho, jaise 6y + 7 = 4y + 21 mein, to pehle dono taraf se 4y ghataao.

Inhi steps ko jaldi likhne ka tareeka hai term ko ulte operation ke saath barabar ke nishaan ke doosri taraf le jaana: ek taraf ka + 7 doosri taraf − 7 ban jaata hai, factor 2 ban jaata hai ÷ 2, aur divisor 15 ban jaata hai × 15. Aur padho equations kaise solve karein mein.

Equation mein term ko doosri taraf le jaane ke teen niyam, udaaharan ke saath — Term ko doosri taraf le jaana

Equations se problems hal karna

Equations asli sawaalon mein kaam aati hain. Unknown ko ek akshar do, problem ki baat ko equation mein likho, solve karo aur jo poocha gaya uska jawab do. Ranjana ke tile pattern mein Step k pe 3k + 1 tiles lagti hain, to 100 tiles Step 33 mein lagengi. Madhubanti ₹500 kharch kar sakti hai, ₹25 ki ek plate aur ₹50 delivery, to 25p + 50 = 500 aur 18 log aa sakte hain: uska 5 logon ka parivaar aur 13 dost. Alag alag raftaar se bachat karne waali do saheliyon ki bachat 7 mahine baad barabar hoti hai. Tum ulta bhi chal sakte ho aur aisi equations bana sakte ho jinka solution tumne pehle se chuna ho. Dekho word problems se equation kaise banayein.

₹500 ki patti: ₹25 ki 18 plates, 5 parivaar ke liye aur 13 doston ke liye, aur ₹50 delivery — Madhubanti ki party

Mind the Mistake

Chapter kuch hal kiye hue sawaal dikhata hai jinme galtiyan chhupi hain, jinhe tumhe dhoondhna hai. Aam galtiyan hain: doosri taraf le jaate waqt term ka sign na badalna, kisi taraf ki sirf ek term ko bhaag dena, ulta bhaag dena, aur bracket kholte waqt sign ki chook.

A Pinch of History

Bharat mein algebra ko bijaganita kaha jaata tha. Brahmagupta ne 628 CE mein unknowns ke saath kaam karne ke niyam likhe, aur Ax + B = Cx + D ke liye unka niyam seedha x = (D − B) ÷ (A − C) deta hai. Ye vichaar Arabic mein gaye aur baad mein Europe pahunche, jahan Al-Khwarizmi ki kitaab ke naam ke shabd al-jabr se algebra shabd bana. Bhaskaracharya ki Bijaganita (1150 CE) mein ghode ki keemat ka ek mashhoor sawaal hai. Padho bijaganita: pracheen Bharat mein algebra. Har sawaal ka jawab, paheliyan, machines aur Start se End tak ka raasta bhi, Part 2 Chapter 7 ke NCERT solutions mein hai.

Bakhshali Manuscript se Bhaskaracharya tak bijaganita ki timeline, aur Arabic aur Latin ke zariye algebra ka failna — Algebra kaise badha

Key terms (zaroori shabd)

Term	Matlab
Equation	Aisa kathan ki do algebraic expressions barabar hain, beech mein barabar ka nishaan likhkar, jaise 3x + 4 = 7 ya 2z + 4 = 5z − 14.
Letter-number (unknown)	x, n ya y jaisa akshar jo kisi aisi sankhya ki jagah hai jo abhi pata nahi.
LHS aur RHS	Equation ka left hand side aur right hand side: barabar ke nishaan se pehle aur baad mein jo likha hai.
Solution (hal)	Unknown ki wo value jisse LHS aur RHS barabar ho jaayein. 2n + 1 = 99 ka solution n = 49 hai.
Trial and error	Ek ke baad ek value aazmaana jab tak dono taraf barabar na ho jaayein. Ye chalta hai, par isme kai koshishein lag sakti hain.
Dono taraf ek hi operation	Dono taraf ek hi sankhya jodna, ghataana, guna ya bhaag karna equation ko sahi rakhta hai (zero se bhaag mana hai).
Inverse operations	Ek doosre ko ulat dene waale operations: jod aur ghataana, guna aur bhaag.
Term ko doosri taraf le jaana	Term ko ulte operation ke saath doosri taraf likhna: + 7 ban jaata hai − 7, factor 2 ban jaata hai ÷ 2, aur divisor 15 ban jaata hai × 15. Ise transposing bhi kehte hain.
Additive inverse	Wo sankhya jo di gayi sankhya mein jodne pe 0 de. 7 ka additive inverse −7 hai, aur −5 ka 5.
Solution check karna	Value ko waapas equation mein rakhkar dekhna ki LHS aur RHS barabar aate hain ya nahi.
Bijaganita	Algebra ka puraana Bharatiya naam. Bija matlab beej: jaise ped beej mein chhupa hota hai, waise hi jawab unknown mein chhupa hota hai.
Brahmagupta ka niyam	Ax + B = Cx + D jaisi equation ka hal hai x = (D − B) ÷ (A − C).

Is chapter ke topics

Jaldi revision

Equation batati hai ki do expressions barabar hain; use solve karna matlab unknown ki wo value dhoondhna jisse LHS = RHS ho.
Seedha taraazu dono taraf barabar dikhata hai, aur dono palde se barabar wazan hataane pe bhi seedha rehta hai: 5 bori = 2 bori + 21 kg se 3 bori = 21 kg, yaani ek bori 7 kg.
Matchstick triangles mein position n pe 2n + 1 tiliyan lagti hain, to 99 tiliyon se 2n + 1 = 99 aur n = 49; 200 tiliyan mumkin nahi, kyunki 2n + 1 hamesha odd hai.
Trial and error chalta hai par dheema hai; dono taraf ek hi operation karna pakka tareeka hai.
Pehle jod aur ghataana ulto, phir guna aur bhaag: 5x − 4 = 7 se 5x = 11, phir x = 11/5.
Term ko doosri taraf le jaana: judi hui term doosri taraf ghat jaati hai, factor doosri taraf bhaag deta hai, aur divisor guna karta hai.
Dono taraf unknown ho to pehle unhe ek taraf lao: 6y + 7 = 4y + 21 se 2y + 7 = 21, yaani y = 7.
Jawab ko hamesha waapas equation mein rakhkar check karo.
Word problem mein: unknown ka naam rakho, equation likho, solve karo, aur jo poocha gaya wahi jawab do; 25p + 50 = 500 se p = 18, to Madhubanti 13 dost bula sakti hai.
Solution se shuru karke dono taraf ek hi operation karte jaao to nayi equations banti hain, jaise y + 1 = 6 aur 3y = 15 waali chains.
Aam galtiyan: term le jaate waqt uska sign na badalna, sirf ek term ko bhaag dena, aur bracket mein sign ki chook.
Bijaganita Bharat mein Aryabhata (499 CE), Brahmagupta (628 CE) aur Bhaskaracharya (1150 CE) ke saath badha; Al-Khwarizmi ke al-jabr ke zariye isne duniya ko algebra shabd diya.

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

Practice karo

Inme se equation kaunsi hai?
1. (a) 3x + 4
2. (b) 3x + 4 = 7
3. (c) 5y
4. (d) x + y + 2
Jawab dekho

Jawab: (b) 3x + 4 = 7
2n + 1 = 99 ka solution kya hai?
1. (a) n = 50
2. (b) n = 49
3. (c) n = 98
4. (d) n = 100
Jawab dekho

Jawab: (b) n = 49
Left side ka + 7 right side pe le jaayein to wo ban jaata hai:
1. (a) + 7
2. (b) − 7
3. (c) × 7
4. (d) ÷ 7
Jawab dekho

Jawab: (b) − 7
3u − 7 = 2u + 3 solve karo.
1. (a) u = 4
2. (b) u = −10
3. (c) u = 10
4. (d) u = 1
Jawab dekho

Jawab: (c) u = 10
Ramesh ke paas Suresh se 30 kanche zyaada hain, aur dono ke paas milkar 60 hain. Suresh ke paas kitne hain?
1. (a) 30
2. (b) 15
3. (c) 45
4. (d) 20
Jawab dekho

Jawab: (b) 15
Ax + B = Cx + D ke liye x = (D − B) ÷ (A − C) ka niyam kisne diya?
1. (a) Al-Khwarizmi
2. (b) Brahmagupta
3. (c) Euclid
4. (d) Pythagoras
Jawab dekho

Jawab: (b) Brahmagupta

Students ke sawal

Class 7 Maths Part 2 Chapter 7 ke mukhya topics kya hain?

Taraazu pe anjaan wazan aur matchsticks ke patterns; equation kya hoti hai; equations ko pehle trial and error se aur phir dono taraf ek hi operation karke ya term ko doosri taraf le jaakar solve karna; equations se word problems hal karna; diye gaye solution se equations banaana; solutions mein galtiyan pakadna; aur Bharat mein bijaganita, yaani algebra, ka itihaas.

Kya Finding the Unknown naye Ganita Prakash Part 2 mein hai?

Haan. Ye Ganita Prakash, Class 7 Maths ki kitaab Part 2 (2026-27) ka Chapter 7 aur aakhri chapter hai, pages 164 se 190 tak. Ye Constructions and Tilings ke baad aata hai aur pichhle chapters ke letter-numbers se anjaan values dhoondhta hai.

Equation solve karne ka sabse aasaan tareeka kya hai?

Unknown ko ek taraf akela karo. Jo joda ya ghataaya gaya hai use ulto, phir jo guna ya bhaag hua hai use ulto, aur har baar dono taraf wahi karo. Phir jawab ko waapas equation mein rakhkar check karo ki dono taraf barabar hain.

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