Fractions ka Multiplication

Class 7 Maths · Chapter 8: Fractions ke Saath Kaam · NCERT Ganita Prakash section 8.1

Seekho

Ishaan ghante mein 3 km chalta hai, to 5 ghante mein 5 × 3 = 15 km. Uska paaltu kachhua ghante mein sirf 1/4 km; 3 ghante mein 3 × 1/4 = 1/4 + 1/4 + 1/4 = 3/4 km. Fraction aur poore number ka guna baar-baar jodne jaisa hi hai.

3 × 1/4 = 3/4

Ghante ka hissa: 1/5 ghante mein Ishaan 3 km ke 5 barabar hisson jitna: 3/5 km. 2/5 ghante mein uska do guna: 6/5 km. To 2/5 × 3 ke liye pehle denominator 5 se bhaag, phir numerator 2 se guna. Aur 1/4 × 1/2: chauthaai ka aadha 1/8.

2/5 × 3 = 6/5

Kshetrafal ka chitra: unit varg ko poora maano. 3/4 × 2/5 ke liye panktiyon mein 2/5 shade karo (5 panktiyan), phir uske 4 mein se 3 stambh lo. Varg mein 5 × 4 = 20 chhote hisse aur 6 gehre: 3/4 × 2/5 = 6/20 = 3/10. Fraction bhujaon wale aayat ka kshetrafal = unka guna.

3/4 × 2/5 = 6/20 = 3/10

Brahmagupta ka niyam (628 CE): a/b × c/d = (a × c)/(b × d). Number chhote rakhne ko pehle kaato: 12/7 × 5/24 mein 12 aur 24 ko 12 se bhaag dekar 1/7 × 5/2 = 5/14. Dono 1 se bade hon to guna-phal dono se bada; dono 0 aur 1 ke beech to dono se chhota; ek-ek ho to beech mein. Kram se farak nahi: a/b × c/d = c/d × a/b.

a/b × c/d = (a × c)/(b × d)

Explore: product shade karo.

1. 1/2 × 1/4: chauthaai ka aadha. Poore ko 8 barabar hisson mein kaato aur guna-phal shade karo.
2. 2/3 × 3/4 = 6/12. Poore ko 12 hisson mein kaato aur 6/12 shade karo.

Yaad rakho

• a/b × c/d = (a × c)/(b × d); pehle common factors kaato.
• 0 aur 1 ke beech wale se guna chhota karta hai; 1 se bade se bada.

Quick check

3/4 × 2/5 sabse chhote roop mein?

1. 3/10
2. 5/9
3. 6/9
4. 8/15

Socho

Kaunsa bhaari: 500 g ka 12/15, ya 4 kg ka 3/20?

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.