Chapter 16 shuru! 🎉 Ab tak multiply ki tricks seekhi; ab division (÷) ki baari. Aaj pehli trick: 5 se divide. Number ko double karo, phir 10 se divide (peeche ka 0 remove karo, ya point ek jagah left). 85 ÷ 5 = 17, do second mein! Saath mein ÷, quotient, remainder (jo bach jaaye) aur point wala jawab bilkul shuru se samjhenge. Yeh Chapter 5 (× 5) ka bilkul reverse hai.
⏱ Before Timer: Pehle Purane Method Se
Pehle school wala “long division” (ek doosre number pe, taaki timer wale sawaal ka jawab pehle na dikhe). 65 ÷ 5:
- Left se pehla digit 6. 6 mein 5 kitni baar? 1 baar (5 × 1 = 5). Upar 1 likho. 6 − 5 = 1 bacha.
- Agla digit 5 neeche utaaro, bache 1 ke saath: 15. 15 mein 5 kitni baar? 3 baar (5 × 3 = 15). Upar 3 likho. 15 − 15 = 0 bacha.
- Upar likha: 1 aur 3, yaani 13. To 65 ÷ 5 = 13 (check: 5 × 13 = 65).
Har step pe “kitni baar” sochna, multiply, subtract karna. Ab timer wala sawaal isi tarah kijiye.
Ab phone ya clock mein stopwatch (time measure karne wali clock) chalu kijiye. Neeche wala sawaal isi long division se kijiye (upar jaisa), copy-pencil ke saath. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
85 ÷ 5 = 17, kyunki 5 × 17 = 85
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki compare karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Chahiye: Chapter 5 ka × 5 (46 × 5 = 230) aur ÷ ka matlab, Chapter 2 ka addition (double karne ke liye). Naya: quotient, remainder, aur division mein point. Sab neeche ke boxes mein. Naye word:
📖 Word jo is post mein aayenge
- ÷ (divide ka sign): equal parts mein divide karna. 85 ÷ 5 padho “85 divided by 5” ya “85 ko 5 se divide”.
- Quotient: division ka jawab: har part mein kitna, ya kitne poore group. 85 ÷ 5 ka quotient 17.
- Remainder: jo bach jaaye, divide kiya na ja sake. 47 ÷ 5: 9 group, remainder 2.
- Reverse: kisi step ko wapas karna (undo). × 5 ka reverse ÷ 5: aaj ki trick Chapter 5 (× 5) ka reverse hai.
- Double: number ko usi mein add karna: 47 ka double 47 + 47 = 94.
- Decimal point: 9.4 ka point: 9 poore aur 4 tenths (box dekho).
- Tenth part: ek ke 10 equal pieces mein se ek piece: 0.1. Jaise ₹1 ke 10 money.
📏 Bade numbers padhna aur round number mein add karna
Har digit ki ek jagah (place) hoti hai. Right se count karo: pehli jagah Units (ones, 1 wale), uske left mein Tens (10 wale), phir Hundred (100 wale), phir Thousand (1000 wale).
10 ka bundle: 10 units = 1 ten (10). 10 tens = 1 hundred (100). 10 hundreds = 1 thousand (1000). Har jagah apne right wali jagah se 10 times badi hai.
| Number | Kaise padhein | Kis cheez se bana |
|---|---|---|
| 98 | attaanve | 9 tens (90) + 8 units |
| 165 | ek sau painsath | 1 hundred (100) + 6 tens (60) + 5 units |
| 999 | nau sau ninyaanve | 9 hundreds (900) + 9 tens (90) + 9 units |
| 1011 | ek hazaar gyaarah | 1 thousand (1000) + 0 hundred + 1 ten (10) + 1 unit |
Round number mein chhota number add karna (place box rule): chhote number ko right se likho, yaani units ke neeche units, tens ke neeche tens. Phir har box mein jo hai, woh jawab mein utaar do. Ek digit wala number sirf units ka zero badalta hai, do digit wala units aur tens dono.
- 100 + 65: 65 mein do digit, to 6 tens mein aur 5 units mein: 1|6|5 = 165.
- 100 + 2: 2 sirf units mein, tens ka 0 waise hi rehta hai: 1|0|2 = 102 (12 nahi, 120 nahi!).
- 200 + 6: 6 sirf units mein: 2|0|6 = 206.
- 1000 + 11: 11 mein do digit, to 1 tens mein aur 1 units mein: 1|0|1|1 = 1011.
➗ Division kya hai? ÷, quotient aur remainder
Chapter 5 mein dekha tha: ÷ (divide ka sign) matlab equal parts mein divide karna. “12 ÷ 4” padho “12 divided by 4” ya “12 ko 4 se divide”: 12 laddoo 4 students mein equal divide karo, har ek ko 3. Ise aise bhi soch sakte ho: 12 mein 4-4 ke kitne group bante hain? 3 group. Dono ka jawab ek hi: 12 ÷ 4 = 3, kyunki 4 × 3 = 12.
Quotient = division ka jawab: har ek ko kitna mila, ya kitne poore group bane. Remainder = jo aakhir mein bach gaya, jisse ek aur poora group nahi ban sakta. 47 laddoo, 5-5 ke boxes: 9 boxes bharte hain (5 × 9 = 45), aur 2 laddoo bach jaate hain. To quotient 9 (9 poore boxes) aur remainder 2 (2 bache laddoo). Hum likhenge: 47 ÷ 5 → quotient 9, remainder 2. (Remainder hamesha divide karne wale number se chhota hota hai: 5 se divide mein remainder 0, 1, 2, 3 ya 4.)
Check ka rule: divide karne wala × quotient + remainder = asli number. Is line mein pehle multiply, phir add: 47 = 5 × 9 + 2, kyunki 5 × 9 = 45 aur 45 + 2 = 47 ✅. (Agar pehle 9 + 2 = 11 add karte aur phir 5 × 11 = 55 karte, to galat hota.)
Poora divide: jab remainder 0 ho, to kehte hain number “poora divide” ho gaya: 45 ÷ 5 = 9, kuch nahi bacha.
🔸 10 aur 100 se divide, aur point (decimal)
10 se divide, jab peeche 0 ho: peeche ka ek 0 remove kar do. 170 ÷ 10 = 17 (170 = 17 tens, to 10-10 ke 17 group). 100 se divide: peeche ke do 0 remove karo: 700 ÷ 100 = 7.
Peeche 0 na ho to? Tab point (.) lagate hain, jise decimal point kehte hain (Post 14.3). Point ke left wala part poore number, right wala part “ek ke pieces”. 94 ÷ 10: har digit ek jagah right khisakta hai, yaani point ek jagah left: 9.4. (Har poore number ke aakhir mein ek chhupa point hota hai, bas likhte nahi: 94 matlab 94. Isi point ko ek jagah left khiskaate hain: 94. → 9.4.) Padho “nau point chaar”: 9 poore aur 4 tenth parts (ek ke 10 equal pieces mein se 4). Money mein: ₹94 ko 10 logon mein divide karo, har ek ko ₹9.40, yaani 9 rupees 40 money.
100 se divide: point do jagah left. 520 ÷ 100 = 5.20. Point ke baad aakhir ka 0 kuch nahi badalta (₹5.20 aur ₹5.2 ek hi: 5 rupees 20 money), to 5.2 likh sakte ho. 36 ÷ 100 = 0.36 (poore 0, aur 36 hundredth parts (hundredth = ek ke 100 pieces mein se ek, jaise 1 money); jaise 36 money = ₹0.36).
Point wale jawab ka check: 47 ÷ 5 = 9.4? 9.4 × 5: 9 × 5 = 45, aur 0.4 × 5 = 2 (4 tenths, 5 baar = 20 tenth = 2 poore). 45 + 2 = 47 ✅.
🔁 Chapter 5 yaad karo: × 5 aur × 25
Chapter 5: × 5 = pehle × 10 (peeche 0), phir half: 46 × 5: 460 ka half, yaani 230. Kyunki 5, 10 ka half hai. Aur × 25 = pehle × 100, phir half ka half: 36 × 25: 3600 → 1800 → 900. Kyunki 25, 100 ka quarter hai.
Aaj hum reverse chalenge: multiply ki jagah division. Jo Chapter 5 mein “half” tha, woh aaj “double” banega; aur jo “× 10” tha, woh “÷ 10”.
🔁 Chhota sa warm-up
- 47 + 47 = ?
- 170 ÷ 10 = ?
- 5 × 9 + 2 = ?
Answers dekho
- 94 (40 + 40 = 80, 7 + 7 = 14, 80 + 14 = 94)
- 17 (peeche ka 0 remove karo)
- 47 (pehle 5 × 9 = 45, phir 45 + 2)
Pehle do mila do: 47 ka double 94, aur 10 se divide 9.4. Yahi 47 ÷ 5 hai!
— 📌 charumam.com
🎬 Story: Golu Ka Piggy Bank
Golu ke piggy bank mein sirf ₹5 ke coins the. Gin kar dekha to total ₹135. Mummy ne poocha: “Coins kitne hain?”
Golu ek-ek coin ginne laga… Didi Pihu boli: “Ruk! Har ₹10 mein do ₹5 ke coins hote hain. To 135 ka double karo: 270. Ab 10 se divide: peeche ka 0 remove karo: 27 coins!”
Golu ne count kiye: bilkul 27. 🪙 “Didi, yeh to Chapter 5 ka reverse hai!” Pihu: “Haan, aaj yahi trick!”
— 📌 charumam.com
🪄 Trick Step by Step: Double Karo, Phir 10 Se Divide
💡 Is post ki ek badi baat: Kisi number ÷ 5 = us number ka double, phir 10 se divide. Double: number mein wahi number add karo. 10 se divide: peeche 0 ho to remove karo, nahi to point ek jagah left. Kyunki har 10 mein do 5 hote hain (5 + 5 = 10). Remainder chahiye to: double ka last digit remove karo (= quotient), us digit ka half = remainder.
Step 1: Double karo
85 ÷ 5. Double: 85 + 85 = 170. (Pieces mein: 80 + 80 = 160, 5 + 5 = 10, 160 + 10 = 170.)
Step 2: 10 se divide
170 ke peeche 0 hai: remove karo → 17. To 85 ÷ 5 = 17.
Step 3: Peeche 0 nahi? Point ek jagah left
47 ÷ 5. Double: 47 + 47 = 94. Peeche 0 nahi, to point ek jagah left: 9.4 (9 poore aur 4 tenth). To 47 ÷ 5 = 9.4.
Point kahan tha? Har poore number ke aakhir mein ek chhupa point hota hai: 94 matlab 94. (bas likhte nahi). Wahi point ek jagah left shift kiya: 94. → 9.4.
Step 4: Remainder wala jawab
Kabhi sawaal kehta hai “quotient aur remainder batao”. 47 ÷ 5: double 94. Last digit 4 remove karo → quotient 9. Hataye digit ka half: 4 ÷ 2 = 2 → remainder 2. Matlab 9 poore group (5-5 ke) aur 2 bache.
Step 5: Check karo (Chapter 5 se)
Quotient × 5 + remainder = number? 9 × 5: 90 ka half, yaani 45 (Chapter 5). 45 + 2 = 47 ✅.
Aur examples, ek ke baad ek
340 ÷ 5: double: 340 + 340 = 680. 10 se divide: peeche ka 0 remove karo → 68.
1235 ÷ 5: double: 1235 + 1235 = 2470. 10 se divide: peeche ka 0 remove karo → 247.
72 ÷ 5: double: 72 + 72 = 144. 10 se divide: point ek jagah left → 14.4. Remainder wala jawab: 144 ka last digit 4 remove karo → quotient 14; hataye digit ka half 4 ÷ 2 = 2 → remainder 2. Check: 5 × 14 = 70, 70 + 2 = 72 ✅
3 ÷ 5: double: 3 + 3 = 6. 10 se divide: point ek jagah left → 0.6.
Dhyaan: double karte waqt carry bhoolna nahi (Chapter 2): 1235 + 1235 mein units 5 + 5 = 10, to 0 likho aur 1 aage.
🆘 Atak gaye? Aise socho
- Pehla step hamesha double (half nahi!).
- 10 se divide: peeche 0 → remove karo; nahi to point ek jagah left.
- Remainder: double ka last digit remove karo; us digit ka half = remainder.
- Remainder 5 se chhota hi hoga (0, 1, 2, 3, 4).
- Check: quotient × 5 (Chapter 5: × 10 phir half) + remainder.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Har 10 mein do 5. Ek ₹10 ka note = do ₹5 ke coins. 47 = 4 tens (4 note) + 7. 4 note se 4 × 2 = 8 coins. Bache 7 mein ek aur 5 (5 + 2 = 7), to ek coin aur, aur 2 bache. Total 9 coins, remainder 2. Diagram dekho.
Double phir 10 se divide kyun? Division mein dono number double kar do, to jawab nahi badalta. 5 dost ₹47 divide karein, ya 10 dost ₹94 divide karein (double money, double dost): har ek ko utna hi milta hai. Jaise 30 ÷ 5 = 6 aur 60 ÷ 10 = 6, dono same. To 47 ÷ 5 ki jagah 94 ÷ 10 karo: 10 se divide sabse aasaan, point ek jagah left → 9.4. Jawab wahi.
Chapter 5 ka reverse
Chapter 5: × 5 = × 10, phir half (17 × 5: 170 ka half 85). Aaj: ÷ 5 = double, phir ÷ 10 (85 → 170 → 17). Half ↔ double aur × 10 ↔ ÷ 10, dono reverse ho gaye. Isliye jawab ka check Chapter 5 se itna aasaan hai.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Method Se Check)
Example 1: 135 ÷ 5 = ?
135 ÷ 5: double: 135 + 135 = 270. 10 se divide: peeche ka 0 remove karo → 27.
✔️ Normal method se check: 27 × 5: 270 ka half 135 (Chapter 5) ✅
Example 2: 72 ÷ 5 = ? (point wala aur remainder wala, dono)
72 ÷ 5: double: 72 + 72 = 144. 10 se divide: point ek jagah left → 14.4. Remainder wala jawab: 144 ka last digit 4 remove karo → quotient 14; hataye digit ka half 4 ÷ 2 = 2 → remainder 2. Check: 5 × 14 = 70, 70 + 2 = 72 ✅
✔️ Normal method se check: 14.4 × 5: 14 × 5 = 70 aur 0.4 × 5 = 2; 70 + 2 = 72 ✅
Example 3: 2045 ÷ 5 = ?
2045 ÷ 5: double: 2045 + 2045 = 4090. 10 se divide: peeche ka 0 remove karo → 409.
✔️ Normal method se check: 409 × 5: 4090 ka half 2045 ✅
Example 4: ₹385 ko 5 dosto mein equal divide karo. Har ek ko kitna?
385 ÷ 5: double: 385 + 385 = 770. 10 se divide: peeche ka 0 remove karo → 77.
Har dost ko ₹77.
✔️ Normal method se check: 77 × 5: 770 ka half 385 ✅
— 📌 charumam.com
💡 CharuMam Ki Smart Trick
CharuMam ki ek pyaari soch hai: mushkil number ki jagah uska aasaan relative lo. 5 ka relative 10 hai (5 = 10 ka half). 10 se divide sabse aasaan (bas 0 remove karo ya point shift karo), isliye 5 ka division 10 ke division mein badal diya, aur cost bas ek double ki. Yahi soch agle post mein 25 → 100 ke liye bhi.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Koi bhi number ÷ 5 (85, 1235) | ✅ Haan | Double, phir 10 se divide. |
| Remainder poocha (47 ÷ 5) | ✅ Haan | Last digit remove karo, uska half remainder. |
| ÷ 50 (350 ÷ 50) | ✅ Bahan trick | Double, phir 100 se divide (Challenge dekho). |
| Bahut chhota number (10 ÷ 5) | ⚠️ Table bhi theek | 5 × 2 = 10, seedha 2. |
| ÷ 6, ÷ 7 jaise | ❌ Nahi | Yeh trick sirf 5 (aur 50, 500) ke liye. |
— 📌 charumam.com
❌→✅ Common Mistakes
Mistake 1: 10 se divide bhool gaye
Sawaal: 85 ÷ 5
❌ Galat: “double kiya: 170. Jawab 170.”
✅ Sahi: phir 10 se divide: 17. Socho: 85 ko 5 parts mein divide karne se har part 85 se chhota hona chahiye, 170 to bada hai!
Mistake 2: Double ki jagah half
Sawaal: 85 ÷ 5
❌ Galat: “Chapter 5 jaisa half: 42.5.”
✅ Sahi: division mein reverse: double (170), phir 10 se divide → 17.
Mistake 3: Point galat jagah
Sawaal: 47 ÷ 5
❌ Galat: “94 → 0.94” (point do jagah shift kiya).
✅ Sahi: 10 se divide = point ek jagah: 9.4.
Mistake 4: Remainder mein half bhool gaye
Sawaal: 47 ÷ 5 ka remainder
❌ Galat: “94 ka last digit 4, to remainder 4.”
✅ Sahi: uska half: 4 ÷ 2 = 2. Check: 45 + 2 = 47 ✅ (45 + 4 to 49 hota).
🧠 Rule of thumb: ÷ 5 = double, phir 10 se divide. Remainder = double ke last digit ka half.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal: kuch point wale jawab, kuch remainder wale. Target: 3 minute.
- 85 ÷ 5 = ?
- 135 ÷ 5 = ?
- 240 ÷ 5 = ?
- 47 ÷ 5 = ?
- 72 ÷ 5 = ?
- 3 ÷ 5 = ?
- 1000 ÷ 5 = ?
- 465 ÷ 5 = ?
- 2045 ÷ 5 = ?
- 98 ÷ 5 = ?
- 11 ÷ 5 = ?
- 63 ÷ 5: quotient aur remainder?
- 29 ÷ 5: quotient aur remainder?
- 104 ÷ 5: quotient aur remainder?
- 3335 ÷ 5 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 17
- 27
- 48
- 9.4
- 14.4
- 0.6
- 200
- 93
- 409
- 19.6
- 2.2
- 12, remainder 3
- 5, remainder 4
- 20, remainder 4
- 667
Kaise kiya (kuch): 98 ÷ 5: 98 + 98 = 196 → point ek jagah left → 19.6. 63 ÷ 5: 126 → last 6 remove karo → quotient 12, 6 ka half 3 → remainder 3. 3335 ÷ 5: 6670 → 667.
— 📌 charumam.com
⏰ One-Minute Challenge
Sirf 1 minute (60 second). Timer lagao, aur jitne ho sakein utne sawaal mann mein (bina copy ke) karo. Sirf jawab likhna hai.
- 45 ÷ 5 = ?
- 60 ÷ 5 = ?
- 95 ÷ 5 = ?
- 120 ÷ 5 = ?
- 7 ÷ 5 = ?
- 35 ÷ 5 = ?
- 210 ÷ 5 = ?
- 55 ÷ 5 = ?
- 500 ÷ 5 = ?
- 23 ÷ 5 = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya start! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 9
- 12
- 19
- 24
- 1.4
- 7
- 42
- 11
- 100
- 4.6
Dhyaan: 7 ÷ 5: 14 → 1.4. 23 ÷ 5: 46 → 4.6. 500 ÷ 5: 1000 → 100.
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har day thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Reason)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 85 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (a) 17
- (a) sahi ✅: 85 + 85 = 170, 0 remove karo → 17.
- (b) galat ❌: 170: double kiya, par 10 se divide bhool gaye.
- (c) galat ❌: 42.5: double ki jagah half kar diya (Chapter 5 ki habit).
- (d) galat ❌: 1.7: point do jagah left shift kiya (100 se divide kar diya).
Q2. 47 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (d) 9.4
- (a) galat ❌: 94: double kiya, par 10 se divide bhool gaye.
- (b) galat ❌: 0.94: point do jagah left shift kiya.
- (c) galat ❌: 23.5: double ki jagah half kar diya.
- (d) sahi ✅: 47 + 47 = 94, point ek jagah left → 9.4.
Q3. 47 ÷ 5 → quotient 9. Remainder kitna?
Jawab aur reason dekho
Sahi jawab: (c) 2
- (a) galat ❌: 7: 47 ka units digit 7 hi remainder maan liya; par remainder 5 se chhota hota hai.
- (b) galat ❌: 9: quotient ko hi remainder likh diya.
- (c) sahi ✅: 94 ka last digit 4, uska half 2. Check: 45 + 2 = 47.
- (d) galat ❌: 4: 94 ka last digit hi remainder maan liya; uska half lena tha.
Q4. 340 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (b) 68
- (a) galat ❌: 6.8: point do jagah left shift kiya.
- (b) sahi ✅: 340 + 340 = 680, 0 remove karo → 68.
- (c) galat ❌: 680: double kiya, 0 remove karna bhool gaye.
- (d) galat ❌: 170: double ki jagah half kar diya.
Q5. ÷ 5 ki trick kis baat pe tiki hai?
Jawab aur reason dekho
Sahi jawab: (a) Har 10 mein do 5 hote hain (5 + 5 = 10)
- (a) sahi ✅: Isliye “kitne 10” ka double = “kitne 5”.
- (b) galat ❌: Mistake: taaq hona yahan kaam nahi aata; 3 bhi taaq hai par 3 ki aisi trick nahi.
- (c) galat ❌: Mistake: 25 agle post (÷ 25) mein aata hai, yahan nahi.
- (d) galat ❌: Mistake: 5 mein 0 nahi hai; asli baat 10 = 5 + 5.
Q6. 3 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (d) 0.6
- (a) galat ❌: 6: point lagana bhool gaye.
- (b) galat ❌: 1.5: double ki jagah half kar diya (3 ka half).
- (c) galat ❌: 0.06: point do jagah left shift kiya.
- (d) sahi ✅: 3 + 3 = 6, point ek jagah left → 0.6.
Q7. 1235 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (c) 247
- (a) galat ❌: 617.5: double ki jagah half kar diya.
- (b) galat ❌: 24.7: point do jagah left shift kiya.
- (c) sahi ✅: 1235 + 1235 = 2470, 0 remove karo → 247.
- (d) galat ❌: 2470: double kiya, 0 remove karna bhool gaye.
Q8. Piggy bank mein ₹135, sab ₹5 ke coins. Kitne coins?
Jawab aur reason dekho
Sahi jawab: (b) 27
- (a) galat ❌: 13.5: seedha 10 se divide kar diya (135 ÷ 10), double bhool gaye.
- (b) sahi ✅: 135 + 135 = 270, 0 remove karo → 27.
- (c) galat ❌: 270: double kiya, 0 remove karna bhool gaye.
- (d) galat ❌: 67.5: double ki jagah half kar diya.
Q9. 72 ÷ 5 → quotient aur remainder?
Jawab aur reason dekho
Sahi jawab: (a) 14, remainder 2
- (a) sahi ✅: 144: last 4 remove karo → 14; 4 ka half 2. Check: 70 + 2 = 72.
- (b) galat ❌: 14, remainder 4: last digit hi remainder maan liya; half lena tha.
- (c) galat ❌: 14.4, remainder 0: point wala jawab aur remainder mila diye; remainder wale jawab mein quotient whole number hota hai.
- (d) galat ❌: 15, remainder 3: 72 ko upar 75 tak round kar diya (75 ÷ 5 = 15) aur upar ka difference 75 − 72 = 3 remainder likh diya. Par remainder hamesha bacha hua part hota hai, aur 5 × 15 = 75, jo 72 se bada hai.
Q10. Kaunsa number 5 se poora divide hota hai (remainder 0)?
Jawab aur reason dekho
Sahi jawab: (d) 235
- (a) galat ❌: Mistake: 238 ka units digit 8, remainder 3 (238 = 235 + 3).
- (b) galat ❌: Mistake: 241 ka units digit 1, remainder 1.
- (c) galat ❌: Mistake: 252 ka units digit 2, remainder 2.
- (d) sahi ✅: Units 5: 235 + 235 = 470, 0 remove karo → 47, remainder 0.
— 📌 charumam.com
🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda mind bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. 350 ÷ 50 = ? (÷ 5 ki bahan trick)
Solution dekho
100 mein do 50 hote hain (50 + 50 = 100). To ÷ 50 = double, phir 100 se divide. 350 + 350 = 700, 100 se divide (do 0 remove karo): 7.
Check: 50 × 7 = 350 ✅
Q2. □ ÷ 5 = 17. □ = ?
Solution dekho
Reverse sawaal: 5 parts mein har part 17, to total = 17 × 5. Chapter 5: 170 ka half = 85.
Check: 85 + 85 = 170, 0 remove karo → 17 ✅
Q3. 123457 ÷ 5 ka remainder kitna? (Bina poora divide kiye)
Solution dekho
123457 = 123450 + 7. 123450 ke peeche 0 hai, to woh 10-10 ke groups mein poora divide ho jaata hai, aur har 10 mein do 5: koi remainder nahi. Bache 7 = 5 + 2 → remainder 2. Matlab 5 se divide ka remainder sirf units se: units 0–4 → wahi remainder; units 5–9 → units − 5.
Q4. 4.5 ÷ 5 = ?
Solution dekho
Double: 4.5 + 4.5 = 9 (4 + 4 = 8, aur 0.5 + 0.5 = 1, yaani do half milkar ek poora). 10 se divide: point ek jagah left → 0.9.
Check: 0.9 × 5 = 4.5 (9 tenth × 5 = 45 tenth = 4.5) ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Division, remainder, point wale jawab, money divide karne ke word problem. |
| Maths Olympiad | Remainder ke pattern (units se remainder), reverse sawaal. |
| NTSE / MAT | Tez Simplification, number series. |
| SSC / Bank (aage) | Percentage (yaani 100 mein se kitna) aur average mein ÷ 5, ÷ 50 daily aate hain. |
Shabdon ka matlab: Olympiad = school ke students ki maths competition. NTSE = Class 10 ke students ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ka exam (NTSE ka ek part). SSC / Bank exam = badon ke government job ke exam. Simplification = bade calculation ko chhota karke jawab nikaalna. Average = “equal divide karne pe har ek ke parts kitna”. Jaise 4 aur 6 ka average 5: dono ko add karo (10) aur equal 2 parts karo. Class 6–8 = school ki chhathi se aathvi class.
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👩🏫 CharuMam Ka Tip
Mantra: “double karo, zero remove karo.” Market mein ₹5 ke coins, 5 log, 5 kg: har jagah ÷ 5 milega. Daily 5 sawaal mann mein karo. Agle post mein isi ki badi bahan: ÷ 25 = double ka double, phir 100 se divide! ➗
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⏱ After Timer: Ab Trick Se!
Wahi sawaal jo shuru mein kiya tha. Stopwatch phir chalu kijiye, aur is baar aaj ki trick se kijiye:
Trick se kaise karein (dekho)
Double: 85 + 85 = 170. 10 se divide: peeche ka 0 remove karo → 17 ✅ (Koi “kitni baar” nahi!)
| Before time | After time | Kitna tez? |
|---|---|---|
| ____ second | ____ second | Before − After = ____ second bache! |
Pehli baar mein time zyada bhi lag sakta hai, ghabraiye nahi! Nayi trick ko 3 se 4 days ki practice chahiye. Phir yeh purane method se kaafi tez ho jaati hai. 🚀
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🤖 Aur Practice: AI Tutor Se Poochho
Neeche wali line copy kijiye aur CharuMam AI Tutor (tutor.charumam.com) mein paste kar dijiye. Tutor aapko naye sawaal dega aur mistake hone pe samjhayega:
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❓ FAQs (Students Ke Asli Sawaal)
1. Double hi kyun, half kyun nahi?
Division multiply ka reverse hai. Chapter 5 mein × 5 ke liye half kiya tha; ÷ 5 ke liye reverse, double.
2. Point wala jawab aur remainder wala jawab, dono sahi?
Haan, ek hi baat do tarah se: 47 ÷ 5 = 9.4, ya quotient 9 aur remainder 2 (0.4 × 5 = 2).
3. Remainder 5 ya zyada aa gaya to?
To mistake hai: 5 se divide mein remainder hamesha 0 se 4 tak.
4. ÷ 50 ki trick?
Double, phir 100 se divide: 350 → 700 → 7.
5. Agle post mein kya hai?
Post 16.2: ÷ 25: double ka double (× 4), phir 100 se divide: 175 ÷ 25 = 7.
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🟢 Recap: Aaj Kya Seekha
- ÷ matlab equal divide karna; quotient = har part, remainder = bacha hua.
- ÷ 5 = double, phir 10 se divide: 85 → 170 → 17.
- Peeche 0 nahi to point ek jagah left: 47 → 94 → 9.4.
- Remainder: double ka last digit remove karo, uska half: 47 → 9, remainder 2.
- Check: quotient × 5 + remainder (pehle multiply, phir add).
- Kyun: har 10 mein do 5.
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👉 Aage Kya?
Ab Post 16.2: ÷ 25. 100 mein chaar 25 hote hain, to double ka double (× 4), phir 100 se divide: 175 ÷ 25 = 7, 130 ÷ 25 = 5.2!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
Har option pe tap karo, turant pata chalega sahi ya galat.
Q1. 95 ÷ 5 = ?
(a) 190
❌ Galat: Double karke 10 se divide karna tha, par sirf double kiya (95 × 2 = 190) aur ruk gaye.
(b) 38
❌ Galat: Double ke baad 5 se divide kar diya. Double ke baad hamesha 10 se divide: 190 ÷ 10 = 19.
(c) 19
✅ Sahi! Double: 95 + 95 = 190. 10 se divide: peeche ka 0 remove karo → 19. Check: 5 × 19 = 95.
(d) 9.5
❌ Galat: Sirf 10 se divide kiya, pehle double karna bhool gaye. Double 190, phir ÷ 10 = 19.
Q2. 63 ÷ 5 = ?
(a) 126
❌ Galat: Double kiya (63 × 2 = 126) par 10 se divide nahi kiya.
(b) 12.6
✅ Sahi! Double 126, phir 10 se divide: point ek jagah left → 12.6. Check: 12.6 × 5 = 63.
(c) 1.26
❌ Galat: Point do jagah left kar diya. 10 se divide mein point sirf ek jagah left: 12.6.
(d) 6.3
❌ Galat: Double bhool gaye, seedha 10 se divide kar diya. Pehle 63 × 2 = 126, phir ÷ 10.
Q3. 58 ÷ 5 → quotient aur remainder?
(a) quotient 11, remainder 6
❌ Galat: Hataya hua digit 6 hi remainder likh diya. Remainder = uska half: 6 ÷ 2 = 3.
(b) quotient 12, remainder 3
❌ Galat: 58 ÷ 5 = 11.6 nikaala aur use paas wale poore number 12 tak bada kar diya (round kiya). Par quotient sirf poore groups hain, to 11.
(c) quotient 11, remainder 12
❌ Galat: Remainder ke liye hataye digit ka half lena tha, par double kar diya. 6 ÷ 2 = 3.
(d) quotient 11, remainder 3
✅ Sahi! Double 116. Last digit 6 remove karo → quotient 11. 6 ka half 3 → remainder 3. Check: 5 × 11 + 3 = 58.
Q4. 240 stickers 5 students mein equal divide karne hain. Har students ko kitne stickers milenge?
(a) 48
✅ Sahi! Double: 240 × 2 = 480. 10 se divide: 0 remove karo → 48. Check: 48 × 5 = 240.
(b) 480
❌ Galat: Double kiya par 10 se divide bhool gaye: 240 × 2 = 480.
(c) 24
❌ Galat: Double bhool gaye, seedha 10 se divide kar diya. Pehle 240 × 2 = 480.
(d) 1200
❌ Galat: Divide ki jagah multiply kar diya. 5 students mein divide karne se har ek ko kam milenge.
Q5. Kaunsa number 5 se divide karne par 14 deta hai?
(a) 2.8
❌ Galat: Reverse sawaal mein multiply karna tha, par divide kar diya. Number = 14 × 5.
(b) 19
❌ Galat: 5 add kar diya. Number = 14 × 5, yaani 140 ka half.
(c) 140
❌ Galat: 14 × 10 = 140 tak kiya, half karna bhool gaye. 140 ka half = 70.
(d) 70
✅ Sahi! 14 × 10 = 140, aur uska half 70. To 14 × 5 = 70. Check: 70 ÷ 5 = 14.
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