Products ke Pattern

Class 7 Maths · Chapter 1: Hamare Aas-paas Bade Numbers · NCERT Ganita Prakash section 1.5–1.6

Seekho

Shortcut: 5 se multiply karna = 2 se bhaag dekar 10 se multiply karna, kyunki 5 = 10 ÷ 2. To 116 × 5 = (116 ÷ 2) × 10 = 58 × 10 = 580. Waise hi 25 = 100 ÷ 4 aur 125 = 1000 ÷ 8: 824 × 25 = (824 ÷ 4) × 100 = 20,600.

824 × 25 = (824 ÷ 4) × 100 = 20,600

Dobara group karke aasaan banao: 2 × 1768 × 50 = (2 × 50) × 1768 = 100 × 1768 = 1,76,800. Aur 125 × 40 × 8 × 25 = (125 × 8) × (40 × 25) = 1000 × 1000 = 10,00,000. Aise jode dhoondho jo 10, 100 ya 1000 banaayein.

125 × 8 = 1000 · 40 × 25 = 1000

Product kitna lamba? Do 2-ank ke numbers: sabse chhota product 10 × 10 = 100 (3 ank), aur har product 100 × 100 = 10,000 (5 ank) se kam. To product mein 3 ya 4 ank. Aam taur par a-ank × b-ank mein (a + b − 1) ya (a + b) ank: 3-ank × 3-ank se 5 ya 6 ank.

a-digit × b-digit → (a + b − 1) or (a + b) digits

Kabhi socha…? Kya 1 crore 24 lakh ke shahar ke sab log 1 lakh buses mein aa jaayenge? Agar ek bus mein 50 aate hain, to 1 lakh × 50 = 50 lakh log, kaafi nahi. Bade sawaal kadam-kadam hal karo: din mein 100 km → saal mein 36,500 km → 10 saal mein 3,65,000 km, chaand ki 3,84,400 km doori se thoda kam!

100 × 365 × 10 = 3,65,000 km

Explore: product mein kitne ank?

1. Har guna ko uske product ki sambhav lambaai se milaao.

Yaad rakho

• × 5 = ÷ 2 phir × 10; × 25 = ÷ 4 phir × 100; × 125 = ÷ 8 phir × 1000.
• a-ank × b-ank ke product mein (a + b − 1) ya (a + b) ank; bade sawaal kadam-kadam hal karo.

Quick check

Jaldi nikaalo: 72 × 125

1. 9,000
2. 7,200
3. 90,000
4. 8,750

Socho

Agar tum bina ruke har second 1 sikka gino, to kya ek din mein 10 lakh sikke gin sakte ho?

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.