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Fractions ke Kuch Sawaal

Class 7 Maths · Chapter 8: Fractions ke Saath Kaam · NCERT Ganita Prakash section 8.3

Seekho

Meher 1/4 litre doodh se 5 cup chai banaati hai. Har cup mein 1/4 ÷ 5 = 1/4 × 1/5 = 1/20 litre. Tanki ghante mein 7/10 bharti hai; 3/4 ghante mein 3/4 × 7/10 = 21/40. Sthiti ko guna ya bhaag mein likho, phir niyam lagaao.

1/4 ÷ 5 = 1/20

Śulbasūtra se (lagbhag 800 BCE): 1/5 unit bhuja ki kitni varg eentein 7 1/2 varg unit dhakengi? Har eent ka kshetrafal 1/5 × 1/5 = 1/25. To 15/2 ÷ 1/25 = 15/2 × 25 = 375/2 eentein, yaani 187 1/2. Ye prachin Bharatiya geometry granth fractions khulkar use karte the.

15/2 ÷ 1/25 = 375/2

Fawwaare (Pṛthūdakasvāmī, lagbhag 860 CE): chaar fawwaare tanki 1, 1/2, 1/4 aur 1/5 din mein bharte hain. Ek din mein ve 1, 2, 4 aur 5 baar bharte: milkar 12 baar. To saath mein 1/12 din.

1 + 2 + 4 + 5 = 12 → 1/12 day

Līlāvatī ka mazaak (Bhāskara II, 1150 CE): ek kanjoos ne bhikhaari ko dramma (1280 kauriyon ka chaandi ka sikka) ka 3/4 ka 2/3 ka 1/2 ka 1/5 ka 1/16 ka 1/4 diya. Multiply karo: 6/7680 = 1/1280 dramma, theek ek kauri! "Ka" hamesha guna hai.

1/4 × 1/16 × 1/5 × 1/2 × 2/3 × 3/4 = 1/1280

Explore: multiply ya divide?

  1. Har sawaal ko zaroori kriya se sort karo.

Yaad rakho

  • "Ka" matlab guna; barabar baantna matlab bhaag.
  • Dar: jo 1/k din mein hota hai, wo din mein k baar.

Quick check

Chaar paudhe kataar mein 3/4 m door hain. Pehle se aakhri kitni door?

  1. 9/4 m
  2. 3 m
  3. 3/4 m
  4. 12/4 m
Answer

9/4 m. 4 paudhon mein 3 antar: 3 × 3/4 = 9/4 = 2 1/4 m.

Socho

Sadak khet ka 1/6 leti hai. Maalkin bache ka aadha beti ko aur bache ka 1/3 bete ko deti hai. Wo kitna rakhti hai?

Ek answer

Bacha 5/6. Beti: 1/2 × 5/6 = 5/12. Beta: 1/3 × 5/6 = 5/18. Wo rakhti hai 5/6 − 5/12 − 5/18 = 30/36 − 15/36 − 10/36 = 5/36.

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.