Equivalent fractions kya hain aur kaise nikalein?

Fraction wall kya dikhati hai?

Ek jaisi lambai ki kaagaz ki pattiyan lo. Ek ko halves mein, ek ko quarters mein aur ek ko eighths mein modo, aur unhe ek ke neeche ek rakho. 1/2 ka kinaara bilkul 2/4 aur 4/8 ke kinaare se milta hai. Lambai same hai, isliye

1/2 = 2/4 = 4/8

Aise fractions, jo ek hi lambai ya hissa dikhate hain par alag fractional units use karte hain, equivalent fractions kehlate hain. Thirds, fifths, sixths wagairah ki pattiyan jodte jaao, to fraction wall ban jaati hai.

Wall se: 1/3 = 2/6, 2/3 = 4/6, aur 1/6 ke 3 tukde milkar 1/2 banate hain.

Barabar hisse se equivalent fractions

1 roti 2 bachchon mein, 2 rotiyan 4 bachchon mein, ya 3 rotiyan 6 bachchon mein baanto. Har baar har bachche ko utna hi milta hai, isliye 1/2 = 2/4 = 3/6.

Isi tarah 2 cake 5 bachchon mein aur 4 cake 10 bachchon mein baantne se barabar hissa milta hai: 2/5 = 4/10. Aur 2 rotiyan 3 bachchon mein, 4 rotiyan 6 mein aur 6 rotiyan 9 mein baantne se 2/3 = 4/6 = 6/9.

Baantne ko facts ke roop mein bhi likh sakte hain. Jab 3 rotiyan 4 bachchon mein baanti jaayein:

• division fact: 3 ÷ 4 = 3/4;
• addition fact: 3 = 3/4 + 3/4 + 3/4 + 3/4;
• multiplication fact: 3 = 4 × 3/4.

Equivalent fraction kaise banate hain?

2/3 = 4/6 = 6/9 ko dekho. Numerator aur denominator dono ko ek hi number se guna kiya gaya:

2/3 = (2 × 2)/(3 × 2) = 4/6, aur 2/3 = (2 × 3)/(3 × 3) = 6/9.

Ye kyun chalta hai? Denominator ko 2 se guna karne ka matlab hai har hisse ko 2 chhote hisson mein kaatna. Ab hisse dugne hain aur har ek aadha, isliye hume dugne hisse chahiye: numerator bhi dugna ho jaata hai. Hissa khud nahi badalta.

Do fractions ko ek hi fractional unit dena

3/4 aur 7/10 compare karne ke liye hum dono ko ek hi fractional unit mein chahte hain. Equivalent fractions likho:

• 3/4 = 6/8 = 9/12 = 12/16 = 15/20 = … = 30/40
• 7/10 = 14/20 = 21/30 = 28/40

Dono list denominator 20 pe pahunchti hain, isliye 3/4 = 15/20 aur 7/10 = 14/20. Denominators ka guna (4 × 10 = 40) hamesha common denominator ka kaam karta hai, par chhota common multiple, yahan 20, numbers ko chhota rakhta hai. Iska use fractions compare kaise karein mein hoga.

Fraction lowest terms mein kab hai?

Fraction lowest terms (ya simplest form) mein tab hai jab uske numerator aur denominator ka 1 ke alawa koi common factor na ho.

Kya 16/20 lowest terms mein hai? Nahi: 4, 16 aur 20 ka common factor hai. Dono ko 4 se bhaag do: 16/20 = 4/5. Ab 4 aur 5 ka 1 ke alawa koi common factor nahi, isliye 4/5, 16/20 ka simplest form hai.

Ye steps mein bhi kar sakte ho. 36/60 ke liye:

1. Dono even hain: 36/60 = 18/30.
2. Dono phir even hain: 18/30 = 9/15.
3. Dono 3 ke multiples hain: 9/15 = 3/5.

Ya seedha dekho ki 36 = 3 × 12 aur 60 = 5 × 12, isliye 36/60 = 3/5. Dono tareekon se same jawab aata hai, kyunki highest common factor (yahan 12) se bhaag dene pe ek hi step mein pahunch jaate hain.