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Fractions ko kaise jodein aur ghatayein?

Short mein jawab

Same denominator wale fractions jodne ya ghatane ke liye numerators jodo ya ghatao aur denominator wahi rakho: 2/5 + 1/5 = 3/5. Denominators alag hon to pehle dono ko common denominator se likho: 1/4 + 1/3 = 3/12 + 4/12 = 7/12. Aakhir mein simplify karo. Yahi Brahmagupta ka tareeka hai.

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Same denominator wale fractions jodna

Meena ne chikki ka 1/2 khaya aur uske chhote bhai ne 1/4. Dono ne milkar kitna khaya? Chikki ko do halves mein kaato, aur bache hue half ko do quarters mein. Meena ka half 2 quarters hai, aur bhai ne 1 quarter khaya, isliye milkar unhone 1/4 + 1/4 + 1/4 = 3/4 chikki khayi. Jo 1/4 bacha, wahi bachi hui chikki hai.

Jab fractions ka fractional unit pehle se same ho, to jodna bas units ginna hai:

  • 2/5 + 1/5 = 3/5 (2 fifths aur 1 fifth milkar 3 fifths).
  • 4/7 + 6/7 = 10/7 = 7/7 + 3/7 = 1 3/7.

Number line pe 4/7 se shuru karo aur 1/7 ki 6 aur chhalaangein lagao. Tum 10/7 pe pahunchoge, jo 1 se 3/7 aage hai.

Alag denominators wale fractions jodna

1/4 aur 1/3 alag size ke hisse hain, isliye unhe seedha nahi gin sakte. Pehle unhe ek hi size ke hisson mein badlo. 4 aur 3 dono 12 ko poora bhaag dete hain:

  • 1/4 = (1 × 3)/(4 × 3) = 3/12
  • 1/3 = (1 × 4)/(3 × 4) = 4/12

Ab 1/4 + 1/3 = 3/12 + 4/12 = 7/12.

Pattiyon se 1/2 + 1/3: sixths mein kaat ke 5/6, aur 3/4 − 1/2 ko 3/4 − 2/4 = 1/4 ke roop mein dikhaya gaya
Pehle hisse ek size ke karo

Brahmagupta ka tareeka

Kitne bhi fractions jodne ka ye tareeka sabse pehle poori tarah Brahmagupta ne 628 CE mein bataya:

  1. Denominators ke common multiple (unka guna, ya sabse chhota common multiple) se ek hi fractional unit wale equivalent fractions banao.
  2. Numerators jodo aur denominator wahi rakho.
  3. Zaroorat ho to jawab lowest terms mein likho.

Example: 2/3 + 1/5. 3 aur 5 ka sabse chhota common multiple 15 hai, isliye 2/3 = 10/15 aur 1/5 = 3/15. Jod hai 13/15.

Example: 1/6 + 1/3. 6 aur 3 ka sabse chhota common multiple 6 hai, isliye 1/3 = 2/6 aur jod 1/6 + 2/6 = 3/6. 3 se bhaag dekar lowest terms mein ye 1/2 hai.

Fractions ghatana

Brahmagupta ka tareeka ghatane mein bhi chalta hai. Denominator same ho to numerators ghatao: 6/7 − 4/7 = 2/7 (6 sevenths mein se 4 hata do).

Denominators alag hon to pehle ek jaise karo. 3/4 − 2/3 ke liye 12 lo:

  • 3/4 = (3 × 3)/(4 × 3) = 9/12 (3 se guna, kyunki 4 × 3 = 12)
  • 2/3 = (2 × 4)/(3 × 4) = 8/12 (4 se guna, kyunki 3 × 4 = 12)

Isliye 3/4 − 2/3 = 9/12 − 8/12 = 1/12. Phir ho sake to simplify karo.

Word problems

  • Ravi bus stop tak 3/5 km paidal chalta hai aur bus se utar ke school tak 1/4 km. Wo kul 3/5 + 1/4 = 12/20 + 5/20 = 17/20 km chalta hai.
  • Ek bottle mein 7/8 litre tel hai, aur 1/2 litre use hua. 7/8 − 1/2 = 7/8 − 4/8 = 3/8 litre bacha.

Dhyan do: jab hisse saath milte hain to jodo, aur jab koi hissa hataya jaaye ya fark nikaalna ho to ghatao.

Thoda itihaas

Fractions likhne ka aaj ka tareeka India se shuru hua. Lagbhag 300 CE ki Bakshali manuscript mein aadha 1 ke neeche 2 likh ke dikhaya gaya hai. Brahmagupta ne fractions jodne-ghatane ke niyam likhe, jo kai sadiyon baad Arabon ke zariye Europe pahunche. Purane Egypt ke log zyadatar fractions ko alag-alag unit fractions ke jod ke roop mein likhte the, jaise 19/24 = 1/2 + 1/6 + 1/8. Kya tum teen alag unit fractions dhoondh sakte ho jinka jod 1 ho? Iska sirf ek tareeka hai: 1/2 + 1/3 + 1/6 = 1. Jodne se pehle fractions compare kaise karein jaanna kaam aata hai.

Practice karo

  1. 3/8 + 2/8 kitna hai?

    1. (a) 5/16
    2. (b) 5/8
    3. (c) 6/8
    4. (d) 1/8
    Jawab dekho

    Jawab: (b) 5/8

  2. 1/2 − 1/5 kitna hai?

    1. (a) 0
    2. (b) 3/10
    3. (c) 1/3
    4. (d) 4/10
    Jawab dekho

    Jawab: (b) 3/10 1/2 = 5/10 aur 1/5 = 2/10, isliye 5/10 − 2/10 = 3/10.

  3. Ek jug mein 5/6 litre paani hai aur 2/3 litre aur daala gaya. Ab kitna paani hai?

    1. (a) 7/9 litre
    2. (b) 1 1/2 litre
    3. (c) 7/18 litre
    4. (d) 1 1/6 litre
    Jawab dekho

    Jawab: (b) 1 1/2 litre 5/6 + 2/3 = 5/6 + 4/6 = 9/6 = 3/2 = 1 1/2.

  4. 2/5 + 1/4 nikaalo.

    Jawab dekho

    Jawab: 20, 5 aur 4 ka common multiple hai: 2/5 = 8/20 aur 1/4 = 5/20, isliye jod 13/20 hai.

  5. Ek ribbon 3/4 m lamba hai. Usme se 1/3 m kaata gaya. Kitna bacha?

    Jawab dekho

    Jawab: 3/4 − 1/3 = 9/12 − 4/12 = 5/12 m.

Students ke sawal

Alag denominators wale fractions kaise jodte hain?

Unhe common denominator wale equivalent fractions mein likho, numerators jodo, denominator wahi rakho, aur simplify karo. Jaise 2/3 + 1/5 = 10/15 + 3/15 = 13/15.

Denominators kyun nahi jod sakte?

Denominator hisson ka size batata hai. 1/4 aur 1/3 alag size ke hisse hain, isliye pehle dono ko ek hi size ke hisson, twelfths, mein kaatte hain aur phir hisse ginte hain.

Brahmagupta ka tareeka kya hai?

Bharat ke mathematician Brahmagupta ne 628 CE mein bataya ki koi bhi fractions kaise jodein aur ghatayein: unhe common denominator pe laao, phir numerators jodo ya ghatao. Hum aaj bhi yahi tareeka use karte hain.

Poore number mein se fraction kaise ghatate hain?

Poore number ko same denominator wale fraction mein likho. Jaise 1 − 3/4 = 4/4 − 3/4 = 1/4.

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