Algebraic Expressions ka Sarlikaran

Class 7 Maths · Chapter 4: Letter-Numbers wale Expressions · NCERT Ganita Prakash section 4.4

Seekho

Aayat ki parimiti = lambaai + chaudaai + lambaai + chaudaai = l + b + l + b. Terms kisi bhi kram mein jud sakte hain, to ye l + l + b + b = 2l + 2b. Dono roop hamesha wahi maan dete hain: l = 3, b = 4 par dono 14. 2l + 2b ko saral roop kehte hain.

l + b + l + b = 2l + 2b

Like terms mein ek hi letter-number hota hai: 5c, 3c aur 10c like terms hain, aur 5c + 3c + 10c = (5 + 3 + 10)c = 18c. Alag aksharon wale terms, jaise 18c aur 11d, unlike hain aur jud nahi sakte: 18c + 11d pehle se saral hai. Do aayaton mein bata aakaar dikhaata hai: 4v + 3v = 7v.

5c + 3c + 10c = 18c · 4v + 3v = 7v

Expressions ghataana: x kursiyan ₹40 aur y mez ₹75 ki kiraaye par, lautane par har ek ke ₹6 aur ₹10 wapas. Tum dete ho (40x + 75y) − (6x + 10y) = 40x + 75y − 6x − 10y = 34x + 65y. Bracket kholo (minus ke baad chinh badalte hain), phir like terms jodo.

(40x + 75y) − (6x + 10y) = 34x + 65y

Barabar ya nahi? 5u = u ka 5 guna; 5 + u = u se 5 zyaada. u = 2 par 10 aur 7: alag, to barabar nahi. Waise hi 10y − 3 ≠ 10(y − 3). Par 4(x + y) − y = 4x + 4y − y = 4x + 3y har x aur y ke liye. Barabar expressions har maan par mel khaate hain.

4(x + y) − y = 4x + 3y

Explore: like terms sort karo.

1. Har term ko uske like terms ke group mein rakho.

Yaad rakho

• Like terms ke number jodkar jodo (5c + 3c = 8c); unlike terms alag rehte hain.
• Aam chinh niyam se bracket kholo, phir like terms group karo; maan rakhkar jaancho.

Quick check

Saral karo: 7p − p + 5q − 2q

1. 6p + 3q
2. 7p + 3q
3. 6p + 7q
4. 9pq

Socho

Ek quiz khiladi 21p − 9q aur doosra 23p − 7q laata hai (p sahi jawab, q penalty). Doosre ne kitna zyaada liya?

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.