Integers ka Multiplication

Class 7 Maths · Chapter 10: Integers par Kriyaayein · NCERT Ganita Prakash section P2 2.2

Seekho

Thaile mein tokens: 4 × 2 ka matlab khaali thaile mein 2 positive 4 baar daalo: 8 positive, yaani 8. Aur 4 × (−2) matlab 2 negative 4 baar daalo: 8 negative, yaani −8. Positive multiplier matlab daalna.

4 × (−2) = −8

Negative multiplier matlab nikaalna. (−4) × 2 ke liye khaali thaile se 4 baar 2 positive nikaalo. Hain hi nahi, to pehle zero pairs daalo, phir positive nikaalo: 8 negative bachte hain, yaani −8. (−4) × (−2) ke liye 4 baar 2 negative nikaalo: 8 positive bachte hain, yaani +8!

(−4) × (−2) = 8

Pattern bhi yahi kehte hain: 2 × 3 = 6, 1 × 3 = 3, 0 × 3 = 0, to (−1) × 3 = −3, (−2) × 3 = −6. Aur 1 × (−3) = −3, 0 × (−3) = 0, to (−1) × (−3) = 3: har kadam 3 jodta hai. Niyam: maap = maapon ka guna; ek jaise chinh → positive, alag → negative.

same signs: + · different signs: −

Gun: 1 × a = a aur (−1) × a = −a. Adla-badli se farak nahi: a × b = b × a. Brahmagupta ne 628 CE mein ye niyam dhana (positive) aur ṛṇa (negative, karz) se likhe: "do karzon ka guna dhan hai." Udaharan: 30 sahi +5 ke aur 20 galat −2 ke: 150 + (−40) = 110 ank.

30 × 5 + 20 × (−2) = 110

Explore: tokens se multiply.

1. (−4) × 2: thaile mein kya bacha? Dikhao.
2. (−3) × (−3): bacha hua dikhao.

Yaad rakho

• Ek jaise chinh: positive guna-phal; alag chinh: negative.
• (−1) × a = −a, aur har integer ke liye a × b = b × a.

Quick check

123 × 456 = 56088. (−123) × (−456) kya hai?

1. 56088
2. −56088
3. 0
4. −123

Socho

Quiz mein sahi ke +4 aur galat ke −2. Kabir ne saare kiye aur 15 sahi se 40 ank. Kitne sawaal the?

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.