Naya chapter, nayi trick! Ab tak hamne 11, 5, 25, 50 se guna seekha, aur base method bhi. Aaj ka number hai 9. Pahaade mein 9 ki table sabse “darawni” lagti hai, par 9 asal mein 10 se bas 1 kam hai. Aur 10 se guna to sabse aasaan: peeche ek 0! Isliye aaj ki trick do chhote kadam ki hai: 10 guna karo, phir number ek baar ghatao.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle school wala tareeka (column method). 47 × 9 ko column mein karte hain:
- Ikai: 9 × 7 = 63. Neeche 3 likho, 6 dahai carry (haath mein).
- Dahai: 9 × 4 = 36, usme carry ke 6 jodo: 36 + 6 = 42. Neeche 42 likho.
- Jawab: 423. Isme 9 ki table yaad honi chahiye, aur carry ka dhyaan bhi.
Ab phone ya ghadi mein stopwatch (samay naapne wali ghadi) chalu kijiye. Neeche wala sawaal isi school wale tareeke (column method) se kijiye, copy-pencil ke saath. Column method na aata ho to ungliyon pe gin kar bhi kar sakte hain. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
47 × 9 = 423
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki tulna karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Chahiye: guna ka matlab, 10 se guna (peeche 0), aur ghatana (round karke ya udhaar se). Sab neeche ke boxes mein dobara samjhaaya hai. Naye shabd:
📖 Shabd jo is post mein aayenge
- 9 = 10 − 1: 9 hamesha 10 se ek kam hai. Yahi aaj ki poori trick ki jad hai.
- 10 guna: number ke peeche ek 0 lagana: 47 → 470.
- Ek baar ghatao: 10 guna wale number mein se wahi number (47) ek baar ghatana.
- 10 se baaki: 10 tak pahunchne mein kitna aur chahiye: 7 ke liye 10 − 7 = 3.
- Deewar ( | ): jawab ke do hisse alag dikhane wali khadi line, jaise 6 | 3 → 63. Chapter 7 mein bhi yahi thi.
📏 Bade numbers padhna aur round number mein jodna
Har digit ki ek jagah (place) hoti hai. Right se gino: pehli jagah Ikai (ones, 1 wale), uske left mein Dahai (tens, 10 wale), phir Saikda (hundreds, 100 wale), phir Hazaar (thousands, 1000 wale).
10 ka bundle: 10 ikai = 1 dahai (10). 10 dahai = 1 saikda (100). 10 saikde = 1 hazaar (1000). Har jagah apne right wali jagah se 10 guna badi hai.
| Number | Kaise padhein | Kis cheez se bana |
|---|---|---|
| 98 | attaanve | 9 dahai (90) + 8 ikai |
| 165 | ek sau painsath | 1 saikda (100) + 6 dahai (60) + 5 ikai |
| 999 | nau sau ninyaanve | 9 saikde (900) + 9 dahai (90) + 9 ikai |
| 1011 | ek hazaar gyaarah | 1 hazaar (1000) + 0 saikda + 1 dahai (10) + 1 ikai |
Round number mein chhota number jodna (place box niyam): chhote number ko right se likho, yaani ikai ke neeche ikai, dahai ke neeche dahai. Phir har dabbe mein jo hai, woh jawab mein utaar do. Ek digit wala number sirf ikai ka zero badalta hai, do digit wala ikai aur dahai dono.
- 100 + 65: 65 mein do digit, to 6 dahai mein aur 5 ikai mein: 1|6|5 = 165.
- 100 + 2: 2 sirf ikai mein, dahai ka 0 waise hi rehta hai: 1|0|2 = 102 (12 nahi, 120 nahi!).
- 200 + 6: 6 sirf ikai mein: 2|0|6 = 206.
- 1000 + 11: 11 mein do digit, to 1 dahai mein aur 1 ikai mein: 1|0|1|1 = 1011.
✖️ Guna kya hai? (Multiplication)
Guna (nishaan ×) matlab ek hi number ko baar-baar jodna. “6 × 4” ko bolte hain “6 guna 4”, matlab 4 ko 6 baar jodo:
6 × 4 = 4 + 4 + 4 + 4 + 4 + 4 = 24
Isi tarah 6 × 7 matlab 7 ko 6 baar jodo. Running total (har baar ka naya jod) dekho: 7, 14, 21, 28, 35, 42. To 6 × 7 = 42.
10 dahai = 1 saikda: 10 dande (har danda 10) milkar 100 bante hain, yaani 1 saikda. Isliye 24 dahai = 20 dahai + 4 dahai = 2 saikde + 4 dahai = 240. (Aur 10 saikde milkar 1 hazaar, yaani 1000, bante hain.)
Tukdon mein guna kyun kar sakte hain? 47 = 4 dande (40) + 7 cube (7). 47 ko 6 baar lena matlab neeche jaisi 6 line. Dande alag gin lo, cube alag gin lo, kul utna hi rahega:
6 × 47: 6 baar 40 = 240, 6 baar 7 = 42, kul 240 + 42 = 282
Guna mein carry 1 se bada ho sakta hai: jod mein carry aksar 1 hota hai, par guna mein bada bhi aa sakta hai. Column mein 6 × 7 = 42 aaya, yaani 4 dahai aur 2 ikai. To ikai mein 2 likho aur 4 dahai carry karo (aage le jao). Phir dahai mein 6 × 4 = 24, usme carry ke 4 jodo: 24 + 4 = 28. Jawab 282.
Guna mein jagah badlo, jawab wahi: 16 × 4 aur 4 × 16 ek hi cheez hain. Neeche dots dekho: 4 line, har line mein 16 dots. Line se gino to 4 baar 16; khade column se gino to 16 baar 4. Dots wahi hain, to jawab bhi wahi: 64. Isliye jo aasaan lage, us tarah jodo.
Copy pe column mein (28 + 15 jaisa):
- Ikai: 6 × 7 = 42. Neeche ikai mein 2 likho. 42 ke 4 dahai carry hain: chhota 4 dahai wale digit (4) ke upar likho.
- Dahai: 6 × 4 = 24, usme upar likha carry 4 jodo: 24 + 4 = 28. Neeche 28 likho (8 dahai mein, 2 saikde mein).
- Jawab: 282.
10 se guna: 3 × 10 matlab 10 ko 3 baar jodna: 10 + 10 + 10 = 30. Kisi number ko 10 se guna karo to woh har digit ek jagah left khisak jaata hai aur ikai mein 0 aa jaata hai: 3 → 30, 30 → 300.
9️⃣ 9, 99 aur 999 kya hain? (Round number se 1 kam)
Pehle round number yaad karo: jiske peeche (right mein) sirf zero hon: 10, 100, 1000. Ab dekho:
| Number | Kis round number se 1 kam | Kitne 9 | Round number mein kitne 0 |
|---|---|---|---|
| 9 | 10 − 1 = 9 | ek 9 | 10 mein ek 0 |
| 99 | 100 − 1 = 99 | do 9 | 100 mein do 0 |
| 999 | 1000 − 1 = 999 | teen 9 | 1000 mein teen 0 |
Yaad rakho: jitne 9, utne 0. 99 mein do 9 hain, to uska “dost” round number 100 hai (do 0). Is poore chapter ki chaabi yahi hai: 9, 99, 999 se guna karna mushkil lagta hai, par 10, 100, 1000 se guna bahut aasaan hai.
0️⃣ 10, 100, 1000 se guna: peeche zero lagao
GUNA box mein dekha tha: kisi number ko 10 se guna karo to har digit ek jagah left khisak jaata hai aur ikai mein 0 aa jaata hai. Chapter 5 mein bhi yahi kiya tha (46 × 10 = 460, aur 36 × 100 = 3600).
| Guna | Kya karo | Example |
|---|---|---|
| 10 se guna | peeche ek 0 | 47 × 10 = 470 |
| 100 se guna | peeche do 0 | 47 × 100 = 4700 |
| 1000 se guna | peeche teen 0 | 47 × 1000 = 47000 |
Kyun? 47 × 10 matlab 47 ko 10 baar jodna. 4 dahai 10 baar = 40 dahai = 4 saikde, aur 7 ikai 10 baar = 70. Kul 400 + 70 = 470. Har tukda ek jagah upar (left) chala gaya, aur ikai khaali ho gayi, isliye 0.
➖ Bade round number mein se ghatana (do tareeke)
Is chapter mein hamesha ek ghatana aayega, jaise 470 − 47. Dono tareeke pehle seekh chuke ho:
Tareeka 1: round karke (Post 3.3). 47 ki jagah paas wala round number 50 ghatao, kyunki round number ghatana aasaan hai: 470 − 50 = 420. Par humne 3 zyada ghata diya (50 − 47 = 3), to woh 3 wapas jodo: 420 + 3 = 423.
Tareeka 2: column mein, udhaar ke saath (Chapter 3). Ikai mein 0 − 7 nahi ho sakta, to dahai se 1 dahai udhaar lo (1 dahai = 10 ikai). Ab 10 − 7 = 3. Dahai mein ab ek kam bacha. Phir dahai aur aage ki jagah normal ghatao.
Udhaar ka chhota yaad: right ki jagah mein kam pade to left wali jagah se 1 bundle lo; left wali jagah 1 kam ho jaati hai. Jo tareeka aasaan lage, wahi lo. Mann mein Tareeka 1 aksar tez hota hai.
🔁 Chhota sa warm-up
- 47 × 10 = ?
- 470 − 50 = ?
- 420 + 3 = ?
Answers dekho
- 470
- 420
- 423
Teeno aa gaye? Yahi milkar 47 × 9 = 423 banta hai!
— 📌 charumam.com
🎬 Kahani: Canteen Ka Hisaab: ₹9 Wala Samosa
School canteen mein samosa ₹9 ka hai. Aarav ki class ke 47 bachchon ne ek-ek samosa liya. Canteen wale bhaiya ne pencil uthayi: “9 saate… 9 chauke…”
Aarav bola: “Bhaiya, socho samosa ₹10 ka hota. To 47 samose ₹470 ke. Par har samosa ₹1 sasta hai, to 47 samose pe ₹47 kam: 470 − 47 = ₹423!”
Bhaiya ne column mein check kiya: ₹423. Bilkul sahi! 😄
Aaj yahi seekhenge: 9 ko “10 se 1 kam” socho, aur guna ek ghatane mein badal jaata hai. 9️⃣
— 📌 charumam.com
🪄 Trick Step by Step: 10 Guna Karo, Phir Number Ek Baar Ghatao
💡 Is post ki ek badi baat: Kisi bhi number × 9 = (number × 10) − number. Peeche 0 lagao, phir wahi number ek baar ghatao: 47 × 9 = 470 − 47 = 423.
Step 1: 9 ko “10 − 1” socho
Sawaal: 47 × 9. 9 = 10 − 1. To 47 × 9 matlab “47 ko 10 baar lo, phir 1 baar wapas nikaal do”.
Step 2: 10 guna: peeche 0
47 × 10 = 470. (Peeche ek 0.)
Step 3: Number ek baar ghatao
470 − 47. Round karke: 47 ki jagah 50 ghatao: 470 − 50 = 420. Par 3 zyada ghata diya (50 − 47 = 3), to 3 wapas: 420 + 3 = 423.
Step 4: Andaaze se check
Jawab 470 se thoda kam hona chahiye (sirf 47 kam). 423 ✅. Agar jawab 470 se bada aaye, ya bahut chhota (jaise 100 ke paas), to kahin galti hai.
Ek-digit × 9: ek aur tez raasta (“ek kam | 10 se baaki”)
Jab number ek hi digit ka ho (2 se 9), to jawab seedha likh sakte ho: left mein number se 1 kam, right mein 10 se baaki. 7 × 9: left 7 − 1 = 6, right 10 − 7 = 3 → 6 | 3 = 63.
| Sawaal | Left: number se 1 kam | Right: 10 se baaki | Jawab | Check (× 10 − number) |
|---|---|---|---|---|
| 2 × 9 | 2 − 1 = 1 | 10 − 2 = 8 | 18 | 20 − 2 = 18 |
| 3 × 9 | 3 − 1 = 2 | 10 − 3 = 7 | 27 | 30 − 3 = 27 |
| 4 × 9 | 4 − 1 = 3 | 10 − 4 = 6 | 36 | 40 − 4 = 36 |
| 5 × 9 | 5 − 1 = 4 | 10 − 5 = 5 | 45 | 50 − 5 = 45 |
| 6 × 9 | 6 − 1 = 5 | 10 − 6 = 4 | 54 | 60 − 6 = 54 |
| 7 × 9 | 7 − 1 = 6 | 10 − 7 = 3 | 63 | 70 − 7 = 63 |
| 8 × 9 | 8 − 1 = 7 | 10 − 8 = 2 | 72 | 80 − 8 = 72 |
| 9 × 9 | 9 − 1 = 8 | 10 − 9 = 1 | 81 | 90 − 9 = 81 |
Yeh kyun? 7 × 9 = 70 − 7. 70 mein se 7 ghatane ke liye pehle poora 10 ghatao: 70 − 10 = 60 (dahai 1 kam: 7 se 6). Par 3 zyada ghataya (10 − 7 = 3), to 3 wapas: 60 + 3 = 63. Wahi 6 | 3!
Bonus: table mein har jawab ke dono digit jodo: 6 + 3 = 9, 7 + 2 = 9, 4 + 5 = 9. Hamesha 9! Kyunki (number − 1) + (10 − number) = 9.
Bada number? Wahi niyam
123 × 9: peeche 0 → 1230. 123 ghatao: 1230 − 123. Round karke: 1230 − 100 = 1130, phir 1130 − 23 = 1107. (Tukdon mein ghatana bhi round karne jaisa hi hai.)
🆘 Atak gaye? Aise socho
- Pehla kadam bhool gaye? Hamesha pehle peeche 0 lagao: 47 → 470.
- Kya ghataun? Wahi number jo 9 se guna ho raha hai (47), 9 nahi!
- Ghatana mushkil lag raha? Round karke ghatao (470 − 50 = 420, phir 3 wapas), ya column mein udhaar se.
- Check: jawab hamesha “number × 10” se thoda kam. 47 × 9 → 470 se kam: 423 ✅
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Dabbon se samjho. 6 × 9 matlab 6 line, har line mein 9 dabbe. (Neeche chitra.)
- Har line mein 10 ki jagah banao. 9 dabbe bhare hain, aur 1 jagah khaali (dotted).
- Agar sab jagah bhari hoti, to 6 line × 10 = 60 dabbe hote. Yeh “peeche 0 lagao” wala kadam hai.
- Par har line mein 1 khaali hai, aur line 6 hain. To kul 6 jagah khaali.
- Asli dabbe: 60 − 6 = 54. Isliye 6 × 9 = 54. Jitni line, utni khaali jagah: isliye wahi number ghatate hain!
Bade number ke liye: patti se socho
47 × 9 ke liye 47 line banana lamba hai. To ek lambi patti socho jo 47 × 10 = 470 ki hai. Har line ka 1 khaali dabba, kul 47, patti ke aakhir mein ek tukda bana do. Use kaato: 470 − 47 = 423.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 8 × 9 = ?
Ek digit: left 8 − 1 = 7, right 10 − 8 = 2 → 7 | 2 = 72. Ya: 80 − 8 = 72.
✔️ Normal tareeke se check: 9 ko 8 baar jodo: 9, 18, 27, 36, 45, 54, 63, 72 ✅
Example 2: 23 × 9 = ?
Peeche 0: 230. Ghatao 23: 230 − 30 = 200, aur 7 zyada ghataya (30 − 23 = 7), wapas: 200 + 7 = 207.
✔️ Normal tareeke se check: Column: 9 × 3 = 27 (7 likho, 2 carry), 9 × 2 = 18, 18 + 2 = 20 → 207 ✅
Example 3: 56 × 9 = ?
Peeche 0: 560. Ghatao 56: 560 − 60 = 500, aur 4 wapas (60 − 56 = 4): 500 + 4 = 504.
✔️ Normal tareeke se check: Tukdon mein: 50 × 9 = 450, 6 × 9 = 54, 450 + 54 = 504 ✅
Example 4: 125 × 9 = ?
Peeche 0: 1250. Ghatao 125 tukdon mein: 1250 − 100 = 1150, phir 1150 − 25 = 1125.
✔️ Normal tareeke se check: Tukdon mein: 100 × 9 = 900, 25 × 9 = 225, 900 + 225 = 1125 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths mein 9, 99, 999 se guna ke liye ek sutra (yaani chhota niyam) hai: “Ekanyunena Purvena”, matlab “pichhle se ek kam”. Aaj ki “ek kam | 10 se baaki” (7 × 9 → 6 | 3) bilkul wahi hai: left mein number se ek kam, right mein 10 se baaki (jo Chapter 3 ka Nikhilam hai). Humne chitra aur “10 guna − number” se dekha ki yeh kyun sahi hai, to yeh ratta nahi, samajh hai. Agle post mein yahi sutra 99 ke saath poori taakat se kaam karega.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Koi bhi number × 9 (23 × 9, 56 × 9) | ✅ Haan | Peeche 0, phir number ghatao. |
| Ek-digit × 9 (7 × 9) | ✅ Bahut tez | Ek kam | 10 se baaki: 6 | 3. |
| Bada number × 9 (125 × 9) | ✅ Chalega | 1250 − 125, tukdon mein ghatao. |
| × 8 ya × 7 (38 × 7) | ⚠️ Soch ke | 7 = 10 − 3, to 38 ko 3 baar ghatana padega: 38 + 38 + 38 = 114, phir 380 − 114 = 266. Kai baar seedha tod aasaan. |
| × 5 (38 × 5) | ➡️ Chapter 5 | Peeche 0, phir aadha: 190. |
| × 11 (38 × 11) | ➡️ Chapter 4 | Beech mein digits ka jod: 418. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Number ghatana bhool gaye
Sawaal: 47 × 9
❌ Galat: 470 (sirf peeche 0 lagaya).
✅ Sahi: 470 to 47 × 10 hai. Ek 47 nikaalo: 470 − 47 = 423.
Galti 2: 9 ghata diya
Sawaal: 47 × 9
❌ Galat: 470 − 9 = 461.
✅ Sahi: chitra yaad karo: har line ka 1 khaali dabba, line 47, to 47 ghatao: 423.
Galti 3: Udhaar nahi liya
Sawaal: 470 − 47
❌ Galat: ikai mein 0 − 7 ki jagah 7 − 0 = 7 likh diya → 437.
✅ Sahi: 0 mein se 7 nahi nikalta, to 1 dahai udhaar: 10 − 7 = 3, dahai 7 − 1 = 6, 6 − 4 = 2 → 423. Ya round karke: 470 − 50 + 3 = 423.
Galti 4: Ek-digit mein dono hisse ulte
Sawaal: 7 × 9
❌ Galat: 3 | 6 → 36.
✅ Sahi: left mein ek kam (6), right mein baaki (3): 63. Check: 70 se thoda kam hona chahiye; 36 to bahut chhota.
🧠 Rule of thumb: × 9 = peeche 0 lagao, phir WAHI number ek baar ghatao. Jawab “× 10” se thoda kam.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, sab × 9. Target: 4 minute.
- 7 × 9 = ?
- 6 × 9 = ?
- 4 × 9 = ?
- 12 × 9 = ?
- 15 × 9 = ?
- 23 × 9 = ?
- 34 × 9 = ?
- 45 × 9 = ?
- 56 × 9 = ?
- 67 × 9 = ?
- 78 × 9 = ?
- 89 × 9 = ?
- 99 × 9 = ?
- 105 × 9 = ?
- 250 × 9 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 63
- 54
- 36
- 108
- 135
- 207
- 306
- 405
- 504
- 603
- 702
- 801
- 891
- 945
- 2250
Kaise kiya (kuch): 78 × 9: 780 − 80 = 700, phir 2 wapas → 702. 99 × 9: 990 − 100 = 890, phir 1 wapas → 891. 250 × 9: 2500 − 250 = 2250.
— 📌 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.
- 3 × 9 = ?
- 9 × 9 = ?
- 11 × 9 = ?
- 13 × 9 = ?
- 21 × 9 = ?
- 25 × 9 = ?
- 38 × 9 = ?
- 44 × 9 = ?
- 62 × 9 = ?
- 90 × 9 = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya shuruaat! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 27
- 81
- 99
- 117
- 189
- 225
- 342
- 396
- 558
- 810
Dhyaan: 38 × 9: 380 − 40 = 340, 2 wapas → 342. 90 × 9: 900 − 90 = 810.
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har din thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Kaaran)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 47 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 423
- (a) sahi ✅: 470 − 47 = 423 (470 − 50 = 420, phir 3 wapas).
- (b) galat ❌: 470: sirf peeche 0 lagaya (47 × 10), 47 ghatana bhool gaye.
- (c) galat ❌: 461: 47 ki jagah 9 ghata diya: 470 − 9 = 461.
- (d) galat ❌: 437: 470 − 47 mein ikai pe udhaar nahi liya (0 − 7 ki jagah 7 − 0 = 7 likha), dahai 7 − 4 = 3, saikda 4.
Q2. 9 ko kaise socho to guna aasaan ho?
Jawab aur kaaran dekho
Sahi jawab: (d) 10 − 1
- (a) galat ❌: 10 + 1 = 11 hai, 9 nahi. Yeh Chapter 4 wala number hai.
- (b) galat ❌: 9 + 1 = 10 hai, 9 nahi.
- (c) galat ❌: 100 − 1 = 99 hai: yeh agle post ka number hai.
- (d) sahi ✅: 9 = 10 − 1, isliye × 9 = × 10, phir ek baar ghatao.
Q3. 8 × 9 ka “ek kam | 10 se baaki” roop?
Jawab aur kaaran dekho
Sahi jawab: (c) 7 | 2 → 72
- (a) galat ❌: 27: dono hisse ulte likh diye.
- (b) galat ❌: 71: right mein 10 − 8 ki jagah 9 − 8 = 1 kar diya.
- (c) sahi ✅: Left 8 − 1 = 7, right 10 − 8 = 2 → 72.
- (d) galat ❌: 82: left mein 1 kam karna bhool gaye (8 hi rakha).
Q4. 56 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 504
- (a) galat ❌: 551: 56 ki jagah 9 ghata diya: 560 − 9 = 551.
- (b) sahi ✅: 560 − 60 = 500, phir 4 wapas (60 − 56 = 4): 504.
- (c) galat ❌: 560: sirf 56 × 10, ghatana bhool gaye.
- (d) galat ❌: 496: 560 − 60 = 500 ke baad 4 jodne ki jagah ghata diya: 500 − 4 = 496.
Q5. 23 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 207
- (a) sahi ✅: 230 − 30 = 200, phir 7 wapas (30 − 23 = 7): 207.
- (b) galat ❌: 230: sirf 23 × 10.
- (c) galat ❌: 197: 230 − 30 = 200 ke baad 7 jodne ki jagah 3 ghata diya: 200 − 3 = 197.
- (d) galat ❌: 221: 23 ki jagah 9 ghata diya: 230 − 9 = 221.
Q6. Chitra mein 6 × 9: kul kitne dabbe khaali?
Jawab aur kaaran dekho
Sahi jawab: (d) 6
- (a) galat ❌: 9 to har line mein bhare dabbe hain.
- (b) galat ❌: 10 har line ki poori jagah hai.
- (c) galat ❌: 54 to bhare dabbe hain (60 − 6).
- (d) sahi ✅: 6 line, har line mein 1 khaali → 6.
Q7. 125 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 1125
- (a) galat ❌: 1241: 125 ki jagah 9 ghata diya: 1250 − 9 = 1241.
- (b) galat ❌: 1135: 1250 − 125 mein ikai pe udhaar nahi liya (5 − 0 = 5 likha), phir 5 − 2 = 3, 2 − 1 = 1, aur 1.
- (c) sahi ✅: 1250 − 125: 1250 − 100 = 1150, 1150 − 25 = 1125.
- (d) galat ❌: 1250: sirf 125 × 10.
Q8. Kis sawaal mein “× 10, phir ek baar ghatao” sabse seedha lagta hai?
Jawab aur kaaran dekho
Sahi jawab: (b) 38 × 9
- (a) galat ❌: × 5 ke liye Chapter 5 ki trick (peeche 0, phir aadha) aasaan: 380 ka aadha 190.
- (b) sahi ✅: 9 = 10 − 1: 380 − 38 = 342, sirf ek baar ghatana.
- (c) galat ❌: 7 = 10 − 3: 38 ko 3 baar ghatana padega. Teen baar 38 jodo: 38 + 38 + 38 = 114, phir 380 − 114 = 266. Lamba.
- (d) galat ❌: 6 = 10 − 4: 38 ko 4 baar ghatana. Chaar baar 38: 38 × 4 = 152 (38 + 38 = 76, 76 + 76 = 152), phir 380 − 152 = 228. Aur lamba.
Q9. 9 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 81
- (a) sahi ✅: Left 9 − 1 = 8, right 10 − 9 = 1 → 81. (90 − 9 = 81.)
- (b) galat ❌: 91: left mein 1 kam karna bhool gaye: 9 | 1.
- (c) galat ❌: 18: dono hisse ulte: 1 | 8.
- (d) galat ❌: 72 to 8 × 9 hai, 9 × 9 nahi.
Q10. □ × 9 = 360. □ = ? (□ = woh number jo humein dhoondhna hai, yaani khaali dabba)
Jawab aur kaaran dekho
Sahi jawab: (d) 40
- (a) galat ❌: 36: 360 ka 0 hata diya, par 36 × 9 = 324, 360 nahi.
- (b) galat ❌: 351: 360 − 9 kar diya; yeh □ nahi, aur 351 × 9 to bahut bada.
- (c) galat ❌: 369: 360 + 9 kar diya; 369 × 9 bhi bahut bada.
- (d) sahi ✅: Kaise: 360 ka aakhri 0 hata do to 36 bacha, aur 36 = 4 × 9. To 360 = 40 × 9, yaani □ = 40. Check: 40 × 9 = 400 − 40 = 360 ✅.
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🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda dimaag bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. Pattern dekho: 1 × 9 + 2 = 11, 12 × 9 + 3 = 111, 123 × 9 + 4 = 1111. Agli line kya hogi?
Solution dekho
Agli line: 1234 × 9 + 5 = 11111.
Check aaj ki trick se: 1234 × 9 = 12340 − 1234 = 11106. Phir 11106 + 5 = 11111 ✅
Q2. 9 ki table (9 × 2 se 9 × 10) ke har jawab ke digits jodo. Kya milta hai, aur kyun?
Solution dekho
18 → 1 + 8 = 9, 27 → 9, 63 → 6 + 3 = 9, 90 → 9 + 0 = 9. Hamesha 9!
Kyun: ek-digit × 9 ka left = number − 1, right = 10 − number. Dono jodo: (number − 1) + (10 − number). Isme number ek baar ghatta hai aur ek baar judta hai, to woh kat jaata hai; bachte hain sirf −1 aur +10, yaani 10 − 1 = 9.
Example, 6 ke saath: 6 − 1 + 10 − 6. Pehle +6 aur −6 ek doosre ko kaat dete hain (6 − 6 = 0). Bache −1 aur +10: 10 − 1 = 9. Seedha bhi: 6 − 1 = 5, 10 − 6 = 4, aur 5 + 4 = 9 ✅ (6 × 9 = 54 → 5 + 4 = 9).
Q3. Ek pen ₹48 ka. 9 pen ka daam?
Solution dekho
48 × 9 = 480 − 48. 480 − 50 = 430, 2 wapas: ₹432.
Check: 40 × 9 = 360, 8 × 9 = 72, 360 + 72 = 432 ✅
Q4. □ × 9 = 288. □ = ?
Solution dekho
Socho: 30 × 9 = 270. 288 − 270 = 18, aur 18 = 2 × 9. To □ = 30 + 2 = 32.
Check aaj ki trick se: 32 × 9 = 320 − 32 = 288 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Guna ke sawaal, dukaan/cost (9 cheezein × daam), aur pahaade ki check. |
| Maths Olympiad | Pattern (1 × 9 + 2 = 11 …) aur digits ka jod 9. |
| NTSE / MAT | Mental maths aur number series. |
| SSC / Bank (aage) | Simplification mein × 9 ka tez hisaab. |
Shabdon ka matlab: Olympiad = school ke bachchon ki maths pratiyogita (competition). NTSE = Class 10 ke bachchon ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ki pariksha (NTSE ka ek hissa). SSC / Bank exam = badon ke sarkari naukri ke exam. Simplification = lambe hisaab ko chhota karke jawab nikaalna. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “0 lagao, number ghatao.” Roz 5 sawaal 2-digit × 9 ke mann mein, aur 9 ki table “ek kam | 10 se baaki” se bolo. Agle post mein yahi trick 99 ke saath, aur ek bahut tez shortcut: 47 × 99 seedha 4653! 9️⃣
— 📌 charumam.com
⏱ 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)
47 ke peeche 0: 470. Ab 47 ek baar ghatao: 470 − 50 = 420, aur 3 zyada ghataya tha, wapas jodo: 420 + 3 = 423 ✅
| 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 din ki practice chahiye. Phir yeh purane tareeke se kaafi tez ho jaati hai. 🚀
— 📌 charumam.com
🤖 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 galti hone pe samjhayega:
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Kya 9 ki table ratni padegi?
Nahi. “Ek kam | 10 se baaki” se koi bhi 9 × (2 se 9) turant: 6 × 9 → 5 | 4 = 54.
2. Ghatate waqt 9 kyun nahi ghatate?
Kyunki 9 ki jagah 10 liya tha, to har baar 1 extra liya. Number jitni baar (47 baar), utne 1 extra: 47 ghatao.
3. Udhaar zaroori hai?
Nahi. Round karke ghatao (470 − 50 + 3) to udhaar ki zaroorat nahi padti.
4. Agle post mein kya hai?
Post 10.2: × 99. 47 × 99 = 4700 − 47 = 4653, aur shortcut 46 | 53.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- 9 = 10 − 1.
- × 9: peeche 0 lagao, phir wahi number ghatao (470 − 47 = 423).
- Ghatana: round karke (470 − 50 + 3) ya udhaar se.
- Ek-digit: ek kam | 10 se baaki (7 × 9 → 6 | 3 = 63).
- Chitra: har line ka 1 khaali dabba.
- Check: jawab “× 10” se thoda kam.
— charumam.com 🎯
👉 Aage Kya?
Ab 99 ki baari: Post 10.2 mein 47 × 99 = 4700 − 47, aur ek aur tez raasta: left mein 46, right mein 100 se baaki 53 → 4653!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
- ▶️ YouTube (subscribe): @charumamofficial
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