Fraction kya hai?

Barabar hisse ke roop mein fraction

Ek roti 2 bachchon mein barabar baanto to har ek ko 1/2 (aadhi) roti milti hai. Wahi roti 4 bachchon mein baanto to har ek ko 1/4 (ek quarter). Doosra hissa chhota hai, kyunki wahi roti zyada bachche baant rahe hain, isliye 1/2 > 1/4.

Matlab fraction ek seedhe sawal ka jawab hai: jab poori cheez barabar baanti jaaye, to har hissa kitna hai?

Fractional units

Jab ek poore ko barabar hisson mein baanta jaata hai, to har hissa fractional unit, ya unit fraction, kehlata hai: 1/2, 1/3, 1/4, 1/5, … , 1/10, … , 1/100.

1/5 aur 1/9 mein bada kaun hai? Bahut se bachche kehte hain 1/9, kyunki 9, 5 se bada hai. Hisse ke baare mein socho. Ek roti 5 bachchon mein baanto to tukda bada hoga, 9 bachchon mein baanto to chhota. Isliye 1/9 < 1/5, aur isi tarah 1/200 < 1/100.

Poore ke hisse

Ek poori chikki ko kai tareekon se barabar tukdon mein toda ja sakta hai. Use do alag tareekon se 6 barabar tukdon mein kaato, to tukdon ki shape alag ho sakti hai, par har tukda phir bhi chikki ka 1/6 hai, kyunki wo 6 barabar hisson mein se ek hai. Zaroori ye hai ki hisse barabar hon, ye nahi ki wo ek jaise dikhein.

Fractional units se naapna

Kaagaz ki ek patti lo aur uski lambai ko 1 unit maano. Use aadha modo: har hissa 1/2 hai. Phir aadha modo: 4 barabar hisse, har ek 1/4. Ek baar aur modo to 1/8 ke 8 hisse milte hain.

Ab in units se naap sakte hain. 1/4 ke teen hisse milkar 3/4 banate hain:

3/4 = 1/4 + 1/4 + 1/4 = 3 baar 1/4

3/4 ko aksar “three quarters” ya “three upon four” padhte hain. Ise “3 baar 1/4” padhna bahut kaam ka hai, kyunki isse fractional unit (1/4) aur uski ginti (3), dono dikhte hain. Fraction 5/6 mein upar ka number 5 numerator hai aur neeche ka number 6 denominator.

Number line pe fractions

Number line pe 0 se 1 tak ki doori 1 unit hai. Ise 4 barabar hisson mein baanto to har hissa 1/4 hai. 0 se 1/4 ki teen chhalaangein 3/4 pe pahunchti hain. 5 barabar hisson mein baanto to marks 1/5, 2/5, 3/5, 4/5 hain.

Har fraction ka number line pe apna point hota hai. 0 aur 1 ke beech kitne fractions hain? Anginat: kinhi do ke beech hamesha ek aur aa jaata hai.

1 se bade fractions: mixed fractions

1/2, 3/4 aur 2/5 ko dekho: numerator denominator se chhota hai, aur har fraction 1 se kam hai. 3/2, 5/2 aur 7/4 mein numerator bada hai, aur har ek 1 se zyada hai.

Aise fraction mein kitne poore hain, ye dekhne ke liye uske fractional units ko poore mein jodo:

• 7/2 = 2/2 + 2/2 + 2/2 + 1/2 = 3 + 1/2, likhte hain 3 1/2.
• 8/3 = 3/3 + 3/3 + 2/3 = 2 + 2/3, likhte hain 2 2/3, padhte hain “two and two thirds”.

Mixed fraction (ya mixed number) mein ek poora hissa aur 1 se chhota fractional hissa hota hai. Wapas jaane ke liye fractional units gino: 3 3/4 = 4/4 + 4/4 + 4/4 + 3/4 = 15/4. Jab numerator denominator ka multiple ho, to fractional hissa bachta hi nahi: 8/4 = 2, ek poora number.

Hamari bhashaon mein fractions ke shabd

India mein fractions ke naam bahut purane zamaane se hain. Rig Veda mein 3/4 ko tri-pada kaha gaya hai, bilkul roz ki Hindi ke “teen paav” aur Tamil ke “mukkaal” jaisa. Hindi mein paav (1/4), aadha (1/2), sava (1 1/4), dedh (1 1/2) aur dhai (2 1/2) jaise shabd bhi hain. Ghar pe poochho ki tumhare parivaar mein kaun se shabd bole jaate hain. Aage dekho ki alag fractions ek hi hissa kaise dikha sakte hain: equivalent fractions kaise nikalein.