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Integers ke saath Khoj

Class 6 Maths · Chapter 10: Zero ke Us Paar · NCERT Ganita Prakash section 10.4, 10.5

Seekho

Border paheli. Ye 8 boxes ka square hai jiska beech khaali hai. Har kinaare ke teen numbers ka jod barabar hai, ye border sum hai. Jaancho: upar 5 + 1 + (−2) = 4, daayein (−2) + 2 + 4 = 4, neeche (−6) + 6 + 4 = 4, baayein 5 + 5 + (−6) = 4.

border sum = 4

Kisi side ko theek karne ke liye kami dhoondo: agar side ka jod 4 hona chahiye aur 5 aur −6 pata hain, to gayab number 4 − 5 − (−6) = +5. Har khaali box aise mil sakta hai.

4 − 5 − (−6) = 5

Patterns. 7 se 3-3 peeche gino: 7, 4, 1, −2, −5, −8 … Har baar jump −3, aur pattern zero ke paar aaraam se chalta hai.

Itihaas se: negative numbers ko maanne mein bahut samay laga. 2,000 se zyada saal pehle China ke ganitagya faayde aur karz ke liye laal aur kaali ginti ki daandiyaan use karte the, bilkul hamare hare aur coral tokens jaisi. 628 CE mein Bhaarat ke ganitagya Brahmagupta ne "dhan" (positive numbers), "rin" (negative numbers) aur zero ko jodne aur ghataane ke saaf niyam likhe. Hazaar saal baad bhi kai European ganitagya negative numbers ko "bekaar" kehte the!

Explore: border paheliyaan suljhaao.

  1. Har side ka jod 4 banao.
  2. Ab har side ka jod −2 hona chahiye.
  3. Sirf kone diye hain. Border sum 0.

Yaad rakho

  • Gayab number = kul − jaane hue numbers.
  • Integers ke patterns zero ke paar aaraam se chalte hain.

Quick check

Aage kya? 6, 2, −2, −6, ?

  1. −10
  2. −8
  3. −2
  4. 10
Answer

−10. Har baar jump −4: −6 − 4 = −10.

Socho

Border sum 0 wali paheli mein chaaron kone 0 hain. Beech ke boxes kya hone chahiye?

Ek answer

Har side = kona + beech + kona = 0 + beech + 0, to har beech wala box bhi 0 hona chahiye.

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.