Galti Pakdo, Galti Sudhaaro

Class 7 Maths · Chapter 15: Anjaan ko Dhoondhna · NCERT Ganita Prakash section P2 7.3–7.4

Seekho

Neel 7 − 8z = 5 hal karke likhta hai "−8z = 5 + 7 = 12". Galti! 7 hataane ke liye dono taraf se 7 ghataana tha: −8z = 5 − 7 = −2, to z = 1/4. Jaancho: 7 − 8 × 1/4 = 7 − 2 = 5 ✓. Jaanchne se zyaadatar galtiyan pakdi jaati hain.

7 − 8z = 5 → −8z = −2 → z = 1/4

Aam galtiyan: sirf ek taraf bhaag dena; coefficient se bhaag ki jagah use ghataana (3x = 12 se x = 9 nahi); bracket ke har term ko guna bhoolna (2(x + 5) = 2x + 10, 2x + 5 nahi); aur term hataate samay minus chinh khona.

Itihaas ki chutki: Bharat mein algebra ko bījagaṇita kehte the: jaise beej (bīja) mein ped chhupa hai, waise anjaan mein jawaab. Brahmagupta (628 CE) ne anjaan numbers ke niyam likhe, unhe yā, kā, nī … kaha; 2x + 1 ko "yā 2 rū 1" likhte the. Ye vichaar Al-Khwarizmi (lagbhag 825 CE) tak pahunche, jinki kitaab al-jabr se algebra shabd aaya.

2x + 1 → yā 2 rū 1

Bhāskarāchārya ke ghode (1150 CE): ek aadmi ke paas ₹300 aur 6 ghode; doosre ke 10 ghode aur ₹100 ka karz. Dono barabar ameer. Ghode ke daam x: 300 + 6x = 10x − 100, to 400 = 4x aur x = 100. Brahmagupta ka formula: Ax + B = Cx + D ka hal x = (D − B) ÷ (A − C). 650m + 4000 = 500m + 5050 ke liye: m = 1050 ÷ 150 = 7.

x = (D − B) ÷ (A − C)

Explore: steps kram mein.

1. 4x + 7 = x + 22 hal karne ke steps kram mein lagao.

Yaad rakho

• Har hal ko equation mein waapas rakhkar jaancho.
• Dhyaan do: ek taraf badlaav, chinh, aur bracket ke har term ka guna.

Quick check

Kaunsa kadam galat? 2(x + 5) = 16 → 2x + 5 = 16 → 2x = 11 → x = 5.5

1. bracket kholna: 2x + 10 hona chahiye
2. 2x = 11
3. x = 5.5
4. koi galti nahi

Socho

Jiraaf ki oonchaai apni aadhi oonchaai se 2.5 m zyaada hai. Kitna ooncha?

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.