Class 6 Maths Chapter 7: Fractions (Hinglish Notes)
Ye chapter 5 lines mein
Fraction batata hai ki jab poori cheez ko barabar hisson mein baanta jaaye, to har hissa kitna hai. Har barabar hissa ek fractional unit hai, jaise 1/4, aur 3/4 ka matlab hai 3 baar 1/4. 1 se bade fractions mixed fraction mein likhe ja sakte hain, jaise 7/4 = 1 3/4. Equivalent fractions, jaise 1/2 = 2/4, ek hi hissa dikhate hain. Fractions ko compare karne, jodne ya ghatane se pehle unka denominator ek jaisa karte hain (Brahmagupta ka tareeka).
Fraction kya hai?
Jab kuch cheezein barabar baanti jaati hain, to fraction batata hai ki har hissa kitna hai. Ek roti 2 bachchon mein barabar baanto to har bachche ko 1/2 roti milti hai; 4 bachchon mein baanto to har ek ko 1/4 roti. Doosra hissa chhota hai, kyunki wahi roti zyada bachchon mein bati, isliye 1/2 > 1/4.
Fractional units kya hain?
Jab ek poore ko barabar hisson mein baanta jaata hai, to har hissa ek fractional unit (ya unit fraction) hai: 1/2, 1/3, 1/4, … , 1/10, … , 1/100. Jitne zyada hisse, utna chhota har hissa, isliye 1/9 < 1/5 aur 1/200 < 1/100. Ek hi fractional unit ke tukde alag shape ke ho sakte hain aur phir bhi barabar size ke hote hain, bas wo ek hi poore ke barabar hisse hone chahiye. Aur padho: fraction kya hai.
Fractions kaise padhte aur naapte hain?
Kisi maatra ko hum fractional units gin ke naapte hain. Kaagaz ki patti ko do baar aadha modo to 4 barabar hisse milte hain: unme se 3 milkar 3/4 banate hain, yaani 3 baar 1/4. Fraction 5/6 mein upar ka number 5 numerator hai aur neeche ka number 6 denominator.
Number line pe fractions aur mixed fractions
0 se 1 tak ki lambai ko barabar hisson mein baanto, to har fraction ko number line pe apna point mil jaata hai. Jab numerator denominator se bada ho, to fraction 1 se bada hota hai aur use mixed fraction mein likh sakte hain: ek poora hissa aur 1 se chhota fractional hissa. Jaise 7/2 = 3 1/2 aur 8/3 = 2 2/3. Ulta, 3 3/4 = 15/4.
Equivalent fractions kya hain?
Jo fractions ek hi hissa dikhate hain, wo equivalent fractions hain. Fraction wall dikhati hai ki 1/2 = 2/4 = 3/6 = 4/8. Baantne se bhi yahi milta hai: 2 cake 5 bachchon mein aur 4 cake 10 bachchon mein, dono mein har bachche ko 2/5 = 4/10 milta hai. Numerator aur denominator ko ek hi number se guna ya bhaag karne pe equivalent fraction milta hai. Fraction lowest terms mein tab hai jab numerator aur denominator ka 1 ke alawa koi common factor na ho, isliye 16/20 lowest terms mein 4/5 hai. Dekho: equivalent fractions kaise nikalein.
Fractions compare kaise karte hain?
Denominator same ho to numerators compare karo: 5/8 > 3/8. Numerator same ho to chhote denominator wala fraction bada hota hai: 4/7 > 4/8. Warna pehle dono fractions ko ek jaise denominator se likho: 4/5 = 36/45 aur 7/9 = 35/45, isliye 4/5 > 7/9. Dekho: fractions compare kaise karein.
Fractions jodte aur ghatate kaise hain?
Denominator same ho to numerators jodo ya ghatao: 2/5 + 1/5 = 3/5 aur 6/7 − 4/7 = 2/7. Denominator alag ho to pehle common denominator wale equivalent fractions banao: 1/4 + 1/3 = 3/12 + 4/12 = 7/12, aur 3/4 − 2/3 = 9/12 − 8/12 = 1/12. Ye Brahmagupta ka tareeka (628 CE) hai. Dekho: fractions ko jodna aur ghatana.
Thoda itihaas
Purane India mein fraction ko bhinna, yaani ‘toota hua’, kehte the, aur bhaga ya ansha, yaani ‘hissa’, bhi. Aaj poori duniya jis tarah fractions likhti hai, wo India se shuru hua: lagbhag 300 CE ki Bakshali manuscript mein aadha 1 ke neeche 2 likh ke dikhaya gaya hai. Dono numbers ke beech ki line baad mein, 12vi sadi mein, Morocco ke mathematician Al-Hassar ne joda. Brahmagupta ke fractions ke niyam Arabon ke zariye Europe pahunche, aur aaj bhi wahi niyam use hote hain.
Key terms (zaroori shabd)
| Term | Matlab |
|---|---|
| Fraction (bhinn) | Wo number jo batata hai ki barabar baantne pe har hissa kitna hai, jaise 3/4. |
| Fractional unit (unit fraction) | Ek poori cheez ko barabar baantne pe bana ek hissa, jaise 1/2, 1/3 ya 1/10. |
| Numerator (ansh) | Fraction ka upar wala number. 5/6 mein ye 5 hai: kitne fractional units hain. |
| Denominator (har) | Fraction ka neeche wala number. 5/6 mein ye 6 hai: kitne barabar hisse milkar ek poora banate hain. |
| Mixed fraction (mixed number) | Ek poora number aur 1 se chhota fraction saath mein, jaise 8/3 ke liye 2 2/3. |
| Equivalent fractions (tulya bhinn) | Wo fractions jo ek hi hissa ya lambai dikhate hain, jaise 1/2, 2/4 aur 3/6. |
| Lowest terms (simplest form) | Wo fraction jiske numerator aur denominator ka 1 ke alawa koi common factor nahi, jaise 4/5. |
| Common denominator | Do ya zyada fractions ko diya gaya ek jaisa denominator, taaki sab ek hi fractional unit use karein. |
| Fraction wall | Ek jaisi lambai ki pattiyan jo halves, thirds, quarters wagairah mein kati hon, barabar lambaiyan dekhne ke liye. |
| Brahmagupta ka tareeka | Fractions jodne ya ghatane ka tareeka: denominators ek jaise karo, phir numerators jodo ya ghatao. Brahmagupta ne 628 CE mein bataya. |
| Bhinna | Fraction ke liye Sanskrit shabd, matlab ‘toota hua’. Fractions ko bhaga ya ansha, yaani ‘hissa’, bhi kehte the. |
Is chapter ke topics
Practice karo
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1/5 aur 1/9 mein bada kaun hai?
Jawab dekho
Jawab: (b) 1/5, kyunki poora kam hisson mein baanta gaya hai
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Fraction 7/12 mein denominator kya hai?
Jawab dekho
Jawab: (b) 12
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11/4 ko mixed fraction mein likho:
Jawab dekho
Jawab: (a) 2 3/4 11/4 = 8/4 + 3/4 = 2 + 3/4.
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Kaunsa fraction 2/3 ke equivalent hai?
Jawab dekho
Jawab: (c) 6/9 Numerator aur denominator dono ko 3 se guna karo: (2 × 3)/(3 × 3) = 6/9.
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1/4 + 1/3 kitna hai?
Jawab dekho
Jawab: (b) 7/12 1/4 = 3/12 aur 1/3 = 4/12, to jod 7/12 hai.
Students ke sawal
Class 6 Maths Chapter 7 mein kya padhte hain?
Fractional units aur barabar hisse, poore ke hisse ke roop mein fractions, fractional units se naapna, number line pe fractions, mixed fractions, equivalent fractions aur lowest terms, fractions compare karna, Brahmagupta ke tareeke se jodna-ghatana, aur fractions ka thoda itihaas.
Kya Fractions nayi Ganita Prakash book mein hai?
Haan. Fractions Ganita Prakash ka Chapter 7 hai, jo 2026-27 session mein Class 6 Maths ki textbook hai.
Brahmagupta ka tareeka kya hai?
Ye wahi tareeka hai jisse hum aaj bhi fractions jodte-ghatate hain: fractions ka denominator ek jaisa karo, numerators jodo ya ghatao, aur jawab lowest terms mein likho. Brahmagupta ne ise 628 CE mein bataya tha.
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