Ratio Ka Simplest Form | Class 8 Maths Book 1 Ch 7

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📘 Class 8 · Ganita Prakash Book 1Ch 7 · Proportional Reasoning-1Post 3 / 9⏱ 25–30 min
Ratio Ka Simplest Form ✂️
IS POST MEIN
Pehle Yeh Aata Hai?KahaniConceptDeep ConceptExamplesReal LifeGalti10 MCQsFAQsPracticeHOTSOlympiadRecap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

  1. 450 aur 300 ka HCF?
  2. 3/4 aur 1/6 ka LCM (4, 6)?
  3. a : b ka matlab (Post 2 — Ratio Kya Hai?)?
Answers dekho
  1. 150
  2. 12
  3. Har a pe b

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, HCF ke liye prime factor yaad kar lijiye; ratio ke liye Post 2 — Ratio Kya Hai?.

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🎬 Kahani: Mummy Ke Laddoo Ki Recipe

Mummy ki diary mein: “450 g besan, 300 g cheeni.” Aaj sirf thode laddoo banane hain. 🍬

Mummy: “Asli baat yeh hai: har 3 katori besan pe 2 katori cheeni. Bas yaad rakho 3 : 2.”

450 : 300 se 3 : 2 kaise bana, aur kya kuch kho gaya? Aaj yahi samjhenge. 🤔

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📖 Concept: Simplest Form: Same Rishta, Sabse Chhote Whole Numbers

💡 Is post ki ek badi baat: Dono terms ko same number se guna/bhaag karo to ratio nahi badalta (rishta same). Jab terms ka common factor sirf 1 bache (HCF = 1), woh simplest form.

Step 1: Tareeka 1: HCF se ek baar

HCF(450, 300) = 150. 450 ÷ 150 = 3, 300 ÷ 150 = 2 → 3 : 2.

WHY kaam karta? 450 = 150 × 3, 300 = 150 × 2. Dono mein 150 “packet” common; ratio sirf packet ki ginti 3 aur 2 ka hai. Kab aasaan: jab HCF jaldi dikhe.

Step 2: Tareeka 2: Baar-baar chhota karo

450 : 300 → ÷10 → 45 : 30 → ÷5 → 9 : 6 → ÷3 → 3 : 2.

Kab aasaan: bade numbers, HCF turant na dikhe. Bas tab tak bhaag karo jab tak common factor na bache.

Step 3: Tareeka 3: Fraction ki tarah

450 : 300 = 450/300 = 3/2 → 3 : 2. Fraction simplify karne jaisa hi!

WHY? a : b = a/b, aur equivalent fractions = equivalent ratios.

Step 4: Decimal/fraction wale terms

1.2 : 0.8 → ×10 → 12 : 8 → 3 : 2.

2/3 : 1/2 → LCM 6 se guna → 4 : 3.

WHY guna? Guna bhi same factor hai, rishta nahi badalta. Pehle whole numbers banao, phir simplify.

Step 5: Check: wapas guna karo

3 : 2 × 150 = 450 : 300 ✅. Ya cross check: 450 × 2 = 300 × 3 = 900 ✅.

WHY cross? a/b = c/d ⇔ a × d = b × c (Post 4 — Proportion Kya Hai? (:: Ka Matlab) mein detail).

🪜 Atak Gaye? Aise Socho

  • Units same? Pehle karo.
  • Decimal/fraction? Whole banao (10, 100 ya LCM se guna).
  • Dono ko 2, 3, 5 se bhaag karte raho.
  • Common factor 1 bacha? Ruk jao.
  • Cross check karo.

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🔐 Deep Concept: Equivalent Ratios Ki Family: Ek Seedhi Line

3 : 2 ki family: 3 : 2, 6 : 4, 9 : 6, …, 450 : 300, 1.5 : 1. Sab mein pehla = doosra × 1.5.

Graph soch: (2, 3), (4, 6), (6, 9), (300, 450) ko plot karo → sab ek seedhi line pe jo (0, 0) se guzarti! Simplest form us line pe sabse paas wala whole-number point hai.

Kuch khoya? Haan: size. 3 : 2 se pata nahi ki 450 g tha ya 30 g. Simplest form rishta rakhta, maatra chhod deta. Isliye “kul” ya ek term pata ho to wapas maatra nikalte (Post 7 — Barabar Nahi, Ratio Mein Hissa).

Unifying idea: same factor se guna/bhaag = family mein ghoomna; rishta same rahta. 🎯

sirf charumam.com readers ke liye 🔐

✏️ Solved Examples

Example 1 (Easy): 84 : 126 simplest

HCF 42 → 2 : 3.

Check: 2 × 42 = 84, 3 × 42 = 126 ✅

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Example 2 (Medium): 0.25 : 1.5

× 100 → 25 : 150 → ÷ 25 → 1 : 6.

Check: 0.25 × 6 = 1.5 ✅

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Example 3 (NCERT style): 3/4 : 5/6

LCM 12 → 9 : 10.

Check: (3/4)/(5/6) = 18/20 = 9/10 ✅

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Mummy ki recipe: 450 : 300 = 3 : 2. Aaj 1 katori cheeni hai? To 1.5 katori besan. Laddoo ka swaad same! 🍬

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🏠 Simplest Ratio Kahaan Kaam Aata

  • 🍳 Recipe: “3 : 2” yaad rakhna aasaan, koi bhi size banao.
  • 🗺️ Map scale: 1 : 50000 jaise simplest roop.
  • 🎨 Rang mixing: 200 ml laal : 300 ml peela = 2 : 3.
  • 📊 Report: “paas : fail = 9 : 1” samajhna aasaan.
  • 📱 Photo crop: 1920 : 1080 = 16 : 9.

1920 : 1080 → HCF 120 → 16 : 9. Har TV, phone ka “16 : 9” yahi hai!

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🧭 Kab Use Karein, Kab Nahi

SituationKya kareinKyun
HCF jaldi dikhe✅ HCF ek baar450 : 300 → 150
Bade numbers✅ Baar-baar bhaag÷10, ÷5, ÷3
Decimal terms✅ 10/100 se guna1.2 : 0.8
Fraction terms✅ LCM se guna2/3 : 1/2
Pakka karna✅ Cross checka × d = b × c

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❌→✅ Worked Mistake

Sawaal: 12 : 18 simplest?

❌ Galat: “Dono mein se 6 ghatao” → 6 : 12 = 1 : 2.

✅ Sahi: ÷ 6 → 2 : 3. Check: 2 × 6 = 12, 3 × 6 = 18 ✅; jabki 1 : 2 se 12 pe 24 aata ❌

Doosri galti: 6 : 4 pe ruk jaana (abhi 2 common hai) → 3 : 2.

🧠 Rule of thumb: Ratio mein sirf guna/bhaag, kabhi jod/ghatao nahi. HCF 1 tak bhaag karo.

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📝 10 MCQs

Q1. 450 : 300 simplest?

(a) 3 : 2
(b) 45 : 30
(c) 2 : 3
(d) 150 : 1
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Bilkul sahi jawab: HCF 150 ✅
  • (b) galat: Abhi 15 common hai, isliye yeh galat.
  • (c) galat: Order ulta ho gaya, isliye yeh galat.
  • (d) galat: HCF ko hi ratio bana diya.

Q2. 1.2 : 0.8 = ?

(a) 3 : 2
(b) 12 : 8
(c) 2 : 3
(d) 1 : 1
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Bilkul sahi jawab: ×10, ÷4 ✅
  • (b) galat: Simplify adhoora hai, isliye yeh galat.
  • (c) galat: Order ulta ho gaya, isliye yeh galat.
  • (d) galat: Ghatao wali galat soch.

Q3. 12 : 18 se 6 ghataya: kya galat?

(a) Ratio badal gaya
(b) Kuch nahi
(c) Units
(d) Order
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 1 : 2 ≠ 2 : 3 ✅
  • (b) galat: Ghatane se ratio badalta.
  • (c) galat: Units ki baat nahi yahan.
  • (d) galat: Order theek tha, isliye yeh galat.

Q4. 2/3 : 1/2 = ?

(a) 4 : 3
(b) 2 : 1
(c) 3 : 4
(d) 1 : 3
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Bilkul sahi jawab: ×6 ✅
  • (b) galat: Sirf numerators le liye.
  • (c) galat: Order ulta ho gaya, isliye yeh galat.
  • (d) galat: Yeh galat hisaab hai, isliye yeh option sahi nahi.

Q5. Simplest kab?

(a) HCF = 1
(b) Dono odd
(c) Pehla chhota
(d) Dono < 10
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Koi common factor nahi ✅
  • (b) galat: 9 : 15 dono odd, par 3 common.
  • (c) galat: Size se farak nahi padta.
  • (d) galat: 8 : 6 abhi simplify hoga.

Q6. 1920 : 1080 = ?

(a) 16 : 9
(b) 4 : 3
(c) 19 : 10
(d) 32 : 18
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Bilkul sahi jawab: HCF 120 ✅
  • (b) galat: 4 : 3 purani screen thi.
  • (c) galat: Kaat ke round kiya, galat.
  • (d) galat: Abhi 2 common hai, isliye yeh galat.

Q7. Kaunsa 3 : 2 ki family mein nahi?

(a) 8 : 6
(b) 9 : 6
(c) 1.5 : 1
(d) 30 : 20
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 8/6 = 4/3 ✅
  • (b) galat: 9/6 = 1.5, family mein hai.
  • (c) galat: 1.5 = 1.5, family mein.
  • (d) galat: 30/20 = 1.5, family mein.

Q8. 0.25 : 1.5?

(a) 1 : 6
(b) 25 : 15
(c) 6 : 1
(d) 1 : 5
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: × 100, ÷ 25 ✅
  • (b) galat: 150 ko 15 likh diya, isliye yeh galat.
  • (c) galat: Order ulta ho gaya, isliye yeh galat.
  • (d) galat: 0.25 × 6 = 1.5, 5 nahi.

Q9. 3 : 2 se kya pata nahi chalta?

(a) Asli maatra
(b) Rishta
(c) Kaun bada
(d) Order
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: Size kho jaata ✅
  • (b) galat: Rishta to pata hai, isliye yeh galat.
  • (c) galat: Pehla bada, pata hai, isliye yeh galat.
  • (d) galat: Order to diya hai, isliye yeh galat.

Q10. Cross check 450 : 300 = 3 : 2?

(a) 450 × 2 = 300 × 3
(b) 450 × 3 = 300 × 2
(c) 450 + 2 = 300 + 3
(d) Koi nahi
Solution dekho

Sahi jawab: (a)

  • (a) sahi: Sahi jawab: 900 = 900 ✅
  • (b) galat: Galat jodi ka guna, isliye yeh option sahi nahi.
  • (c) galat: Jod se check nahi hota.
  • (d) galat: Cross check hota hai, isliye yeh galat.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Simplest form mein decimal?

Nahi, dono whole numbers aur HCF 1.

2. 3 : 2 ko 1.5 : 1 likh sakte?

Haan, “unit ratio” kehte; tulna mein kaam aata (Post 5 — Ratio Se Tulna: Strong Ya Light?).

3. Teen terms?

Teeno ka HCF: 6 : 9 : 15 → 2 : 3 : 5.

4. Units alag?

Pehle same: 2 kg : 500 g = 4 : 1.

5. Kya simplest form unique?

Haan, har ratio family ka ek hi.

6. Aage?

Do ratios barabar kab? Post 4 — Proportion Kya Hai? (:: Ka Matlab).

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy 36 : 48?

Solution dekho

3 : 4. Check: 3 × 12 = 36 ✅

Q2. Easy 75 : 125?

Solution dekho

3 : 5. Check ✅

Q3. Easy 0.6 : 0.9?

Solution dekho

2 : 3. Check ✅

Q4. Easy 2 kg : 500 g?

Solution dekho

4 : 1. Check ✅

Q5. Medium 1/4 : 1/6?

Solution dekho

× 12 → 3 : 2. Check ✅

Q6. Medium 252 : 336?

Solution dekho

HCF 84 → 3 : 4. Check ✅

Q7. Medium 2.5 : 0.75?

Solution dekho

250 : 75 → 10 : 3. Check ✅

Q8. Medium 18 : 27 : 45?

Solution dekho

HCF 9 → 2 : 3 : 5. Check ✅

Q9. NCERT style 4 : 7 ki family ka term jiska jod 66?

Solution dekho

k = 6 → 24 : 42. Check: 66 ✅

Q10. NCERT style 1 1/2 : 2 1/4?

Solution dekho

3/2 : 9/4 → × 4 → 2 : 3. Check ✅

Q11. NCERT style 45 min : 2 ghante?

Solution dekho

45 : 120 → 3 : 8. Check ✅

Q12. NCERT style x : 35 = 4 : 7. x?

Solution dekho

20. Check: 20/35 = 4/7 ✅

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🧠 HOTS (Sochne Wale Sawaal)

Q1. a : b = 5 : 8 aur a ka 3 guna = b ka 2 guna? Sach?

Solution dekho

3a = 15k, 2b = 16k → nahi. Check ✅

Q2. Ratio 7 : 9 mein dono mein x jodne pe 4 : 5. x?

Solution dekho

5(7+x) = 4(9+x) → x = 1. Check: 8 : 10 ✅

Q3. Do numbers 3 : 5, HCF 12. Numbers?

Solution dekho

36, 60. Check ✅

Q4. Kya do alag simplest ratios same family mein?

Solution dekho

Nahi: family ka ek hi simplest. Check ✅

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🏆 Olympiad Corner

Q1. 0.04 : 0.6?

Solution dekho

1 : 15.

Q2. 3/5 : 9/10?

Solution dekho

2 : 3.

Q3. a : b = 2 : 3, b : c = 4 : 5. a : b : c?

Solution dekho

8 : 12 : 15.

Q4. Ratio 5 : 7, LCM 140. Numbers?

Solution dekho

20, 28.

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💗 CharuMam Motivation

Mummy ki tarah, aap bhi badi recipe ko “3 : 2” jaisi chhoti yaad mein badal sakte ho. Chhota form, poora rishta! ✂️

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🟢 Master Recap

  • 💡 Chaabi: Dono terms ko same number se guna/bhaag karo to ratio nahi badalta (rishta same). Jab terms ka common factor sirf 1 bache (HCF = 1), woh simplest form.
  • Same factor se guna/bhaag → ratio same.
  • Simplest: HCF 1.
  • HCF / baar-baar / fraction: teen tareeke.
  • Decimal: ×10, 100; fraction: ×LCM.
  • Jod/ghatao nahi!
  • Cross check.

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👉 Aage Kya?

4 glass mein 6 chammach vs 10 glass mein 15: same swaad? Post 4 — Proportion Kya Hai? (:: Ka Matlab).

← Pichla: Post 2 — Ratio Kya Hai?📚 Chapter 7 ke saare postsAgla: Post 4 — Proportion Kya Hai? (:: Ka Matlab) →

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