Chapter 16 ka last post! 🏆 Aaj 16.1–16.3 ka mix, soch wale sawaal: kaunsi trick kab (5, 25, 9, aur naya ÷ 50), remainder jaldi (poora divide kiye bina), reverse sawaal (□ ÷ 25 = 12), money divide karna, aur point wale (3.5 ÷ 5 = 0.7). Har sawaal ka check Chapter 5 aur 10 ke multiply se.
⏱ Before Timer: Pehle Purane Method Se
Pehle school wala “long division” (doosre number pe, taaki timer wale sawaal ka jawab pehle na dikhe). 1150 ÷ 25:
- 1 aur 11 mein 25 ek baar bhi nahi jaata, isliye pehle teen digit 115 lo. 115 mein 25 kitni baar? 25 × 4 = 100 (115 se chhota), 25 × 5 = 125 (bada). To 4. Bacha: 115 − 100 = 15.
- Agla digit 0 neeche utaaro: 150. 150 mein 25 kitni baar? 25 × 6 = 150. Bacha 0.
- Quotient ke digit 4 aur 6 → 46. Check: 25 × 46 = 1150 ✅
Tables, subtract karna, digit utaarna: kaafi kaam. 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
59
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 16 ke teeno post, aur check ke liye Chapter 5 (× 5, × 25) aur Chapter 10 (× 9). Yaad ke liye boxes neeche. Naye word:
📖 Word jo is post mein aayenge
- Divisor: jis number se divide karte hain, yaani ÷ ke baad wala number. 175 ÷ 25 mein divisor 25 hai.
- Reverse sawaal: jawab diya hai, number dhoondhna hai: □ ÷ 25 = 12 mein □ kya?
- Equal divide karna: sabko ek jitna dena; jo poora divide na ho, woh remainder.
- Remainder jaldi: poora divide kiye bina sirf remainder nikaalna.
- ÷ 50: 50 se divide; 50 × 2 = 100, isliye × 2 phir ÷ 100.
📏 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. 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 hundredths; 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”.
🔁 Chapter 10 yaad karo: × 9
Chapter 10: × 9 = pehle × 10 (peeche 0), phir wahi number ek baar subtract karo: 34 × 9 = 340 − 34 = 306. Kyunki 9, 10 se ek kam hai (9 = 10 − 1). Aaj isi “10 = 9 + 1” wali baat se 9 ka division karenge, aur jawab ka check isi Chapter 10 wale multiply se.
🔁 Chhota sa warm-up
- 25 × 4 = ?
- 5 × 2 = ?
- 50 × 2 = ?
Answers dekho
- 100
- 10
- 100
Yahi teen add kiye is post ki chaabi hain: 5 ka pair 2 (10 banta), 25 ka pair 4 (100), 50 ka pair 2 (100). Aur 9 ke liye 10 = 9 + 1.
— 📌 charumam.com
🎬 Story: Picnic Ka Bill
Class picnic ka expense ₹ 1475 aaya, aur 25 students the. Monitor Riya calculator dhoondh rahi thi. Kabir ne kaha: “Ruko! 25 se divide = 4 times, phir 100 se divide. 1475 ka double 2950, phir double 5900, do 0 remove karo: ₹ 59 har student!”
Phir sir ne kaha: “Bache hue ₹ 100 ke laddoo, 9 table pe equal divide kar do.” Riya muskurayi: “Ab meri baari: 1 | 1 → har table pe ₹ 11, aur remainder 1 + 0 + 0 = ₹ 1 bacha!” 🎒
Ek hi day mein ÷ 25 aur ÷ 9 dono. Aaj aise hi mix sawaal!
— 📌 charumam.com
🪄 Trick Step by Step: Pehle Identify karo, Phir Trick Chuno
💡 Is post ki ek badi baat: Pehle divisor (jisse divide karna hai, yaani ÷ ke baad wala number) dekho: 5 → × 2, phir ÷ 10. 25 → × 4, phir ÷ 100. 50 → × 2, phir ÷ 100. 9 → digit add karo (quotient aur remainder). Sirf remainder chahiye to aur bhi tez: ÷ 5 mein bas units, ÷ 25 mein bas last do digit, ÷ 9 mein digit add. Reverse sawaal mein multiply karo. Aakhir mein check.
Step 1: Divisor identify karo
Kis se divide hai: 5, 25, 50 ya 9? Har ek ki apni trick (diagram dekho).
Step 2: Trick lagao
÷ 5: double, phir point 1 jagah left. ÷ 25: do baar double, phir point 2 jagah left. ÷ 50: double, phir point 2 jagah left. ÷ 9: running sum aur digit add.
Step 3: Sirf remainder? Chhota path
÷ 5: units 0 se 4 ho to wahi remainder, 5 se 9 ho to units − 5. ÷ 25: last do digit mein se 25-25 remove karo. ÷ 9: digits add karo, 9-9 remove karo.
Step 4: Reverse sawaal: multiply karo
□ ÷ 25 = 12 → □ = 25 × 12 (Chapter 5: 12 × 100 ÷ 4 = 300). Remainder bhi ho to multiply ke baad remainder add karo (pehle multiply, phir add).
Step 5: Check karo
Divisor × quotient + remainder = number? 1475: 25 × 59 → 5900 ka half ka half (Chapter 5): 5900 → 2950 → 1475 ✅.
Type 1: Kaunsi trick kab?
| Sawaal | Trick | Jawab |
|---|---|---|
| 435 ÷ 5 | double 870, 0 remove karo | 87 |
| 1000 ÷ 25 | 4 times: 4000, do 0 remove karo | 40 |
| 350 ÷ 50 | double 700, do 0 remove karo | 7 |
| 52 ÷ 9 | pehla digit 5, add 5 + 2 = 7 | 5, remainder 7 |
Type 2: Remainder jaldi (poora divide kiye bina)
68 ÷ 5 ka remainder: units 8, jo 5 se 9 ke beech hai → 8 − 5 = 3. (Check: 5 × 13 = 65, 65 + 3 = 68 ✅)
240 ÷ 25 ka remainder: last do digit 40 → 40 − 25 = 15. (Check: 25 × 9 = 225, 225 + 15 = 240 ✅)
2023 ÷ 9 ka remainder: 2 + 0 + 2 + 3 = 7.
Type 3: Reverse sawaal
□ ÷ 25 = 12 → □ = 25 × 12 = 300. Check: 300 × 4 = 1200, do 0 remove karo → 12 ✅
Type 4: Money divide karna
435 ÷ 5: double: 435 + 435 = 870. 10 se divide: peeche ka 0 remove karo → 87.
Matlab ₹ 435, 5 dosto mein: har ek ko ₹ 87.
100 ÷ 9: quotient ke digit, left se “running sum”: pehla digit 1, phir 1 + 0 = 1 → 1 | 1 → 11. Remainder = saare digits ka sum: 1 + 0 + 0 = 1. Remainder 1, 9 se chhota, to theek. Jawab: quotient 11, remainder 1.
Matlab ₹ 100, 9 table pe: har table ₹ 11, ₹ 1 bacha.
Type 5: Point wale
3.5 ÷ 5: double: 3.5 + 3.5 = 7. 10 se divide: 7 → 0.7. To 3.5 ÷ 5 = 0.7. (Check: 5 × 0.7 = 3.5 ✅)
🆘 Atak gaye? Aise socho
- 5 → × 2, ÷ 10. 25 → × 4, ÷ 100. 50 → × 2, ÷ 100.
- 9 → running sum (quotient), digit add (remainder).
- Remainder jaldi: ÷ 5 units, ÷ 25 last do digit, ÷ 9 digit add.
- Reverse: □ = divisor × quotient (+ remainder). □ ÷ 25 = 12 → □ = 25 × 12 = 300.
- Check: divisor × quotient + remainder.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Saari tricks ek hi soch se: 5 × 2 = 10, 25 × 4 = 100, 50 × 2 = 100. Jis number ko divide kar rahe ho (85) aur jisse divide kar rahe ho (5), dono ko ek jitna multiply karo to jawab nahi badalta: 85 ÷ 5 = 170 ÷ 10 = 17 (jaise 10 rotiyaan 5 mein, ya 20 rotiyaan 10 mein: dono mein 2-2). To ÷ 5 ko ÷ 10 bana diya, ÷ 25 aur ÷ 50 ko ÷ 100. Aur 10 aur 100 se divide sabse aasaan: point shift karo. ÷ 9 alag hai: wahan 10 = 9 + 1 kaam karta hai.
Remainder ke chhote raaste kyun chalte hain?
÷ 5: har tens (10) mein poore do 5 hain, kuch nahi bachta. To bachta sirf units mein se: 68 ka units digit 8 mein ek 5 aur 3 bache.
÷ 25: har hundred (100) mein poore chaar 25 hain. To sirf last do digit dekho: 240 ke 40 mein ek 25 aur 15 bache.
÷ 9: Post 16.3 wala: har 10 aur har 100 mein 1 bachta hai, to remainder = digits ka sum.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Method Se Check)
Example 1: ₹ 1000, 25 students mein equal. Har ek ko kitne?
1000 ÷ 25: double: 1000 + 1000 = 2000. Phir double: 2000 + 2000 = 4000 (yaani × 4). Do 0 remove karo → ₹ 40.
✔️ Normal method se check: 25 × 40 = 1000 ✅ (25 × 4 = 100, peeche ek 0)
Example 2: Kya 738, 9 se poora divide hota hai? Quotient kya?
Digit add 7 + 3 + 8 = 18: isme do 9, bacha 0 → haan, poora divide.
738 ÷ 9: quotient ke digit, left se “running sum”: pehla digit 7, phir 7 + 3 = 10 → 7 | 10 → carry (jaise Chapter 2): 10 ka 0 rakho, 1 left bhejo: 7 + 1 = 8 → 80. Remainder = saare digits ka sum: 7 + 3 + 8 = 18. 18, 9 se chhota nahi: usme 9 ke 2 group aur bane (9 + 9 = 18, bacha 0), to quotient 80 + 2 = 82, remainder 0.
✔️ Normal method se check: 9 × 82 = 820 − 82 = 738 ✅
Example 3: □ ÷ 25 → quotient 12, remainder 7. □ = ?
Reverse: □ = 25 × 12 + 7 (pehle multiply, phir add). 25 × 12: 12 × 100 = 1200, 1200 ÷ 4 = 300 (Chapter 5). Phir 300 + 7 = 307.
✔️ Normal method se check: 307: last do digit 07 → remainder 7; 300 ÷ 25 = 12 ✅
Example 4: 350 ÷ 50 = ? Aur 12.5 ÷ 25 = ?
350 ÷ 50: double: 350 + 350 = 700. Do 0 remove karo → 7.
12.5 ÷ 25: double: 12.5 + 12.5 = 25. Phir double: 25 + 25 = 50. 100 se divide: point do jagah left → 0.5.
✔️ Normal method se check: 50 × 7 = 350 ✅ aur 25 × 0.5 = 12.5 ✅ (25 ka half)
— 📌 charumam.com
💡 CharuMam Ki Smart Trick
CharuMam ki ek badi soch hai: “mushkil number ko aasaan base mein convert karo” (base = paas wala round number: 10, 100, 1000). 5, 25 aur 50 ko 10 aur 100 mein badla (jaise Chapter 5 mein × 5 aur × 25 ke liye kiya tha), aur 9 ko base 10 se “1 kam” maana (yaani base se distance dekhna: Chapter 3 aur 7). Ek baar soch samajh aa gayi, to har naye divisor ke liye khud trick bana sakte ho.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| ÷ 5 (435, 3.5) | ✅ × 2, ÷ 10 | Point 1 jagah left. |
| ÷ 25 (1475, 1000) | ✅ × 4, ÷ 100 | Do baar double. |
| ÷ 50 (350) | ✅ × 2, ÷ 100 | Ek double, point 2 jagah. |
| ÷ 9 (738, 100) | ✅ Digit add karo | Quotient aur remainder dono. |
| Sirf remainder (5, 25, 9) | ✅ Chhota path | Units / do digit / digit add. |
| ÷ 7, ÷ 13 | ❌ Nahi | Inke liye long division. |
— 📌 charumam.com
❌→✅ Common Mistakes
Mistake 1: ÷ 5 mein half kar diya
Sawaal: 85 ÷ 5
❌ Galat: “85 ka half 42.5.” (Woh ÷ 2 hai!)
✅ Sahi: ÷ 5 = double, phir ÷ 10: 170 → 17.
Mistake 2: ÷ 25 mein ek hi baar double
Sawaal: 175 ÷ 25
❌ Galat: “350, do 0 ki jagah point → 3.5.”
✅ Sahi: × 4 ke liye do baar double: 350, phir 700 → 7.
Mistake 3: Point wale mein ÷ 10 bhool gaye
Sawaal: 3.5 ÷ 5
❌ Galat: “double 7, to jawab 7.”
✅ Sahi: phir 10 se divide: 0.7. (5 × 7 to 35 hota, 3.5 nahi.)
Mistake 4: ÷ 9 mein remainder 9 chhod diya
Sawaal: 54 ÷ 9
❌ Galat: “quotient 5, remainder 9.”
✅ Sahi: remainder 9 bhi ek poora group: quotient 6, remainder 0.
🧠 Rule of thumb: Divisor identify karo: 5, 25, 50 ko 10 ya 100 banao; 9 mein digit add karo; remainder ke chhote raaste; reverse mein multiply; aur check.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 mix sawaal. Target: 6 minute.
- 435 ÷ 5 = ?
- 1475 ÷ 25 = ?
- 350 ÷ 50 = ?
- 52 ÷ 9: quotient aur remainder?
- 3.5 ÷ 5 = ?
- 12.5 ÷ 25 = ?
- 68 ÷ 5: quotient aur remainder?
- 240 ÷ 25: quotient aur remainder?
- Kya 738, 9 se poora divide hota hai?
- Kya 748, 9 se poora divide hota hai?
- □ ÷ 25 = 12. □ = ?
- □ ÷ 5 = 23. □ = ?
- 100 ÷ 9: quotient aur remainder?
- 2023 ÷ 9 ka remainder?
- 900 ÷ 50 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 87
- 59
- 7
- 5, remainder 7
- 0.7
- 0.5
- 13, remainder 3
- 9, remainder 15
- Haan
- Nahi
- 300
- 115
- 11, remainder 1
- 7
- 18
Kaise kiya (kuch): 900 ÷ 50: double 1800, do 0 remove karo → 18. □ ÷ 5 = 23 → □ = 5 × 23: 230 ka half, yaani 115 (Chapter 5). 748: 7 + 4 + 8 = 19 → remainder 1, to poora divide nahi.
— 📌 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.
- 120 ÷ 5 = ?
- 300 ÷ 25 = ?
- 9 ÷ 5 = ?
- 450 ÷ 50 = ?
- 2.5 ÷ 5 = ?
- 1000 ÷ 25 = ?
- 65 ÷ 5 = ?
- 725 ÷ 25 = ?
- 400 ÷ 50 = ?
- 81 ÷ 9 = ?
| 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
- 24
- 12
- 1.8
- 9
- 0.5
- 40
- 13
- 29
- 8
- 9
Dhyaan: 9 ÷ 5: double 18, point 1 jagah → 1.8. 725 ÷ 25: × 4 = 2900 → 29. 81 ÷ 9: pehla digit 8, add 8 + 1 = 9 → ek aur 9 → quotient 9, remainder 0.
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. 1475 ÷ 25 = ?
Jawab aur reason dekho
Sahi jawab: (d) 59
- (a) galat ❌: 29.5: sirf ek baar double kiya (2950); × 4 ke liye do baar chahiye.
- (b) galat ❌: 5.9: point teen jagah left kar diya; 100 se divide mein sirf do jagah.
- (c) galat ❌: 590: 100 ki jagah sirf 10 se divide kiya.
- (d) sahi ✅: × 4 = 5900, do 0 remove karo → 59.
Q2. 3.5 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (c) 0.7
- (a) galat ❌: 0.07: point do jagah shift kar diya; ÷ 10 mein ek jagah.
- (b) galat ❌: 1.75: half kar diya; woh ÷ 2 hai, ÷ 5 nahi.
- (c) sahi ✅: Double 7, phir ÷ 10 → 0.7.
- (d) galat ❌: 7: double kiya par 10 se divide bhool gaye.
Q3. 350 ÷ 50 = ?
Jawab aur reason dekho
Sahi jawab: (b) 7
- (a) galat ❌: 1.75: double ki jagah half kar diya (350 ka half 175), phir 100 se divide (point do jagah left) → 1.75. ÷ 50 mein double karna tha.
- (b) sahi ✅: Double 700, do 0 remove karo → 7.
- (c) galat ❌: 70: 100 ki jagah sirf 10 se divide kiya.
- (d) galat ❌: 0.7: point teen jagah shift kar diya.
Q4. □ ÷ 25 = 12. □ = ?
Jawab aur reason dekho
Sahi jawab: (a) 300
- (a) sahi ✅: □ = 25 × 12 = 300.
- (b) galat ❌: 37: multiply ki jagah add diya (25 + 12).
- (c) galat ❌: 0.48: reverse divide kar diya (12 ÷ 25).
- (d) galat ❌: 48: 12 ko 4 se multiply kiya; 25 se multiply karna tha.
Q5. 68 ÷ 5 ka remainder?
Jawab aur reason dekho
Sahi jawab: (d) 3
- (a) galat ❌: 8: units ko seedha remainder maan liya; usme abhi ek 5 hai.
- (b) galat ❌: 6: point wala jawab 13.6 nikaala aur point ke baad wala 6 hi remainder maan liya; par 0.6 ka matlab 5 ka 0.6 part (0.6 × 5 = 3).
- (c) galat ❌: 13: quotient 13 ko hi remainder likh diya.
- (d) sahi ✅: Units 8 → 8 − 5 = 3.
Q6. 240 ÷ 25 ka remainder?
Jawab aur reason dekho
Sahi jawab: (c) 15
- (a) galat ❌: 9: quotient 9 ko hi remainder likh diya.
- (b) galat ❌: 6: point wala jawab 9.6 nikaala aur point ke baad wala 6 hi remainder maan liya; par 0.6 ka matlab 25 ka 0.6 part (0.6 × 25 = 15).
- (c) sahi ✅: Last do digit 40 → 40 − 25 = 15.
- (d) galat ❌: 40: last do digit seedhe remainder maan liye; 40 mein ek 25 hai.
Q7. Kaunsa number 9 se poora divide hota hai?
Jawab aur reason dekho
Sahi jawab: (b) 738
- (a) galat ❌: 768: digit add 21 → remainder 3.
- (b) sahi ✅: 7 + 3 + 8 = 18 → remainder 0.
- (c) galat ❌: 748: digit add 19 → remainder 1.
- (d) galat ❌: 758: digit add 20 → remainder 2.
Q8. ₹ 100, 9 dosto mein equal (poore rupees). Har ek ko kitne, kitne bache?
Jawab aur reason dekho
Sahi jawab: (a) ₹ 11, ₹ 1 bacha
- (a) sahi ✅: Running sum 1 | 1 → 11; remainder 1 + 0 + 0 = 1.
- (b) galat ❌: ₹ 10, ₹ 10 bache: har dost ko ₹ 10 de diye (9 × 10 = 90) aur bache 100 − 90 = 10 ko remainder maan liya. Par bache ₹ 10 mein ek aur 9 hai, to har ek ko ₹ 11.
- (c) galat ❌: ₹ 11, kuch nahi: remainder nikaalna bhool gaye.
- (d) galat ❌: ₹ 1, ₹ 1: 3-digit mein quotient sirf pehla digit liya.
Q9. ÷ 25 ka sabse tez method?
Jawab aur reason dekho
Sahi jawab: (d) × 4, phir ÷ 100
- (a) galat ❌: × 2 phir ÷ 10: yeh ÷ 5 ki trick hai.
- (b) galat ❌: Digit add karo: yeh ÷ 9 ki trick hai.
- (c) galat ❌: × 5 phir ÷ 100: yeh ÷ 20 ban jaata hai (20 × 5 = 100).
- (d) sahi ✅: 25 × 4 = 100.
Q10. 9 ÷ 5 = ?
Jawab aur reason dekho
Sahi jawab: (c) 1.8
- (a) galat ❌: 18: double kiya, 10 se divide bhool gaye.
- (b) galat ❌: 0.18: point do jagah shift kar diya.
- (c) sahi ✅: Double 18, point 1 jagah left → 1.8.
- (d) galat ❌: 4.5: half kar diya (÷ 2).
— 📌 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. 0.75 ÷ 25 = ?
Solution dekho
Double: 0.75 + 0.75 = 1.5. Phir double: 1.5 + 1.5 = 3 (yaani × 4). 100 se divide: point do jagah left → 0.03.
Check: 25 × 0.03 = 0.75 ✅ (25 × 3 = 75, aur point do jagah)
Q2. 50 se chhota ek number: 9 se poora divide hota hai, aur 5 se divide karne pe remainder 3. Number?
Solution dekho
9 se poora divide: 9, 18, 27, 36, 45. Ab ÷ 5 ka remainder (units se): 9 → 4, 18 → 3, 27 → 2, 36 → 1, 45 → 0. Sirf 18.
Check: 18 = 5 × 3 + 3 ✅, aur 1 + 8 = 9 ✅
Q3. 1000 ko 5, 25 aur 9 teeno se divide kar do.
Solution dekho
1000 ÷ 5: double 2000, 0 remove karo → 200. 1000 ÷ 25: × 4 = 4000 → 40. 1000 ÷ 9: running sum 1 | 1 | 1 → 111, remainder 1 + 0 + 0 + 0 = 1 → 111, remainder 1.
Check: 9 × 111 = 1110 − 111 = 999, aur 999 + 1 = 1000 ✅
Q4. Bina poora divide kiye: 123457 ka 5, 25 aur 9 se remainder?
Solution dekho
÷ 5: units 7 → 7 − 5 = 2. ÷ 25: last do digit 57 → 57 − 50 = 7 (50 mein do 25). ÷ 9: 1 + 2 + 3 + 4 + 5 + 7 = 22 → 22 − 18 = 4.
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🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Division, remainder, money divide karna, point wale division. |
| Maths Olympiad | Remainder wale puzzle, “kaunsa number” wale sawaal. |
| NTSE / MAT | Divisibility (bina divide kiye pehchanna ki poora divide hoga ya nahi), number puzzle, tez Simplification. |
| SSC / Bank (aage) | Simplification mein ÷ 25, ÷ 50 aur remainder ke chhote raaste. |
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. Class 6–8 = school ki chhathi se aathvi class.
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👩🏫 CharuMam Ka Tip
Mantra: “5 ka pair 2, 25 ka pair 4, 50 ka pair 2, aur 9 mein add karo.” Shop ka bill ya cricket ka run-rate (har over mein kitne run) dekho, aur mann mein divide karo. Agla chapter: Divisibility Shortcuts, jahan bina divide kiye pata chalega ki poora divide hoga ya nahi. ➗
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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)
÷ 25 matlab × 4, phir ÷ 100. Double: 1475 + 1475 = 2950. Phir double: 2950 + 2950 = 5900. Do 0 remove karo → 59 ✅
| 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. Kaunsi trick kab, kaise yaad rakhein?
Divisor dekho: 5 → × 2, ÷ 10; 25 → × 4, ÷ 100; 50 → × 2, ÷ 100; 9 → digit add.
2. ÷ 5 ka remainder sirf units se kyun?
Har 10 mein poore do 5 hain, to bachta sirf units mein se.
3. ÷ 25 ka remainder last do digit se kyun?
Har 100 mein poore chaar 25 hain.
4. Reverse sawaal kaise?
□ = divisor × quotient: □ ÷ 25 = 12 ho to □ = 25 × 12 = 300. Remainder bhi ho to multiply ke baad add karo (quotient 12, remainder 7 → 300 + 7 = 307).
5. Agla chapter kya hai?
Chapter 17: Divisibility Shortcuts, jald aa raha hai.
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🟢 Recap: Aaj Kya Seekha
- 5 → × 2, ÷ 10. 25 → × 4, ÷ 100. 50 → × 2, ÷ 100.
- 9 → running sum (quotient), digit add (remainder).
- Remainder jaldi: ÷ 5 units, ÷ 25 last do digit, ÷ 9 digit add.
- Reverse: □ = divisor × quotient + remainder.
- Point wale: 3.5 ÷ 5 = 0.7.
- Check: Chapter 5 aur 10 ke multiply se.
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👉 Aage Kya?
Chapter 16 poora! 🎉 Agla Chapter 17: Divisibility Shortcuts (bina divide kiye pata karo ki poora divide hoga ya nahi) jald aa raha hai.
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
Har option pe tap karo, turant pata chalega sahi ya galat.
Q1. 650 ÷ 50 = ?
(a) 130
❌ Galat: Sirf ek 0 hataya. ÷ 50 = × 2, phir ÷ 100: 1300 → 13.
(b) 13
✅ Sahi! ÷ 50 = × 2, phir ÷ 100. 650 × 2 = 1300 → 13. Check: 50 × 13 = 650.
(c) 1300
❌ Galat: 650 × 2 = 1300 tak kiya, 100 se divide bhool gaye.
(d) 32500
❌ Galat: Divide ki jagah multiply kar diya. 650 ÷ 50 chhota number dega.
Q2. 4.5 ÷ 5 = ?
(a) 9
❌ Galat: Double kiya (4.5 × 2 = 9) par 10 se divide bhool gaye.
(b) 0.09
❌ Galat: Point do jagah left kar diya. 10 se divide mein ek jagah: 9 → 0.9.
(c) 22.5
❌ Galat: Divide ki jagah 5 se multiply kar diya. ÷ 5 = double, phir ÷ 10.
(d) 0.9
✅ Sahi! Double: 4.5 × 2 = 9. 10 se divide → 0.9. Check: 0.9 × 5 = 4.5.
Q3. Ek number ko 25 se divide kiya to 18 mila. Number kya hai?
(a) 0.72
❌ Galat: Reverse sawaal mein multiply karna tha, par divide kar diya. Number = 18 × 25.
(b) 72
❌ Galat: Sirf × 4 kiya, × 100 bhool gaye. 18 × 25 = 1800 ÷ 4.
(c) 450
✅ Sahi! 18 × 25 = 18 × 100 ÷ 4 = 1800 ÷ 4 = 450. Check: 450 ÷ 25 = 18.
(d) 43
❌ Galat: 25 add kar diya. Number = 18 × 25.
Q4. ₹200 ko 9 doston mein equal divide karna hai (sirf poore rupees). Har ek ko kitne milenge, aur kitne bachenge?
(a) ₹22 har ek ko, ₹2 bache
✅ Sahi! Running sum: 2, 2 + 0 = 2 → quotient 22. Remainder = 2 + 0 + 0 = 2. Check: 9 × 22 + 2 = 200.
(b) ₹20 har ek ko, ₹2 bache
❌ Galat: Quotient mein running sum ki jagah pehle do digit 20 likh diye. Running sum 2, 2 → 22.
(c) ₹22 har ek ko, ₹0 bache
❌ Galat: Remainder mein sirf last digit 0 liya. Remainder = 2 + 0 + 0 = 2.
(d) ₹20 har ek ko, ₹0 bache
❌ Galat: 9 ki jagah 10 doston mein divide kar diya. Dost 9 hain.
Q5. 47 ÷ 25 = ?
(a) 18.8
❌ Galat: Point sirf ek jagah left kiya. 100 se divide mein do jagah: 188 → 1.88.
(b) 188
❌ Galat: 47 × 4 = 188 tak kiya, 100 se divide bhool gaye.
(c) 0.47
❌ Galat: × 4 bhool gaye, seedha 100 se divide. Pehle 47 × 4 = 188.
(d) 1.88
✅ Sahi! 47 × 4 = 188. 100 se divide: point do jagah left → 1.88. Check: 1.88 × 25 = 47.
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