Aaj do niyam ek saath, kyunki dono ek hi parivaar ke hain: × 9 aur × 8. Inme ek naya andaaz hai: digit ko 10 se ya 9 se ghatao (Chapter 3 wala “baaki”), padosi jodo, aur aakhri kadam pe 1 kam (× 9) ya 2 kam (× 8). Chapter 10 mein × 9 ek tareeke se kiya tha (470 − 47); aaj dekhenge ki Trachtenberg ka tareeka bina udhaar ke wahi jawab kaise deta hai.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle school wala tareeka (column method). 47 × 8, right se:
- Ikai: 8 × 7 = 56. Neeche 6 likho, 5 carry.
- Dahai: 8 × 4 = 32, carry 5 jodo: 32 + 5 = 37. Neeche 37 likho.
- Jawab: 376. 8 ka pahaada (8 × 7 = 56, 8 × 4 = 32) yaad hona chahiye.
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 × 8 = 376
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: Chapter 3 ki “baaki” (10 se ya 9 se kitna kam), Chapter 11 ka double, aur Trachtenberg ke shabd (aage 0, padosi, right se left, carry). Neeche ke boxes mein double aur baaki dobara. Naye shabd:
📖 Shabd jo is post mein aayenge
- 10 se baaki: 10 tak pahunchne mein kitna chahiye: 7 ke liye 10 − 7 = 3. (Chapter 3)
- 9 se baaki: 9 tak kitna chahiye: 4 ke liye 9 − 4 = 5.
- × 9 niyam: ikai: 10 se baaki. Baaki har digit: 9 se baaki + padosi. Aage wala 0: padosi − 1.
- × 8 niyam: ikai: 10 se baaki ka double. Baaki har digit: 9 se baaki ka double + padosi. Aage wala 0: padosi − 2.
- Aakhri kadam pe ghatana: aage wale 0 pe padosi mein se 1 (× 9) ya 2 (× 8) ghatao. Carry ho to pehle carry jodo, phir ghatao.
- Udhaar: Chapter 3 wala: ghatate waqt kam pade to left se 1 lena. Aaj ka niyam udhaar se bachata hai.
📏 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.
✌️ Double karna kya hai?
Double matlab number ko do baar lena, yaani number mein wahi number jodna. 7 ka double: 7 + 7 = 14. Yahi 2 × 7 bhi hai (GUNA box: 2 × 7 matlab 7 ko 2 baar jodo).
| Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Double | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |
(Table mein upar digit hai, neeche uska double. Jaise 6 ke neeche 12, kyunki 6 + 6 = 12.) Is chapter mein hum sirf ek digit (0 se 9) ka double karenge, to sabse bada double 18 hai.
🔟 10, 100, 1000 se “baaki” (Chapter 3 ki trick)
“Baaki” matlab: kitna aur chahiye taaki round number poora ho jaaye. Jaise 47 se 100 tak kitna? 53. Isse 100 se baaki kehte hain (100 − 47 = 53).
Post 3.1 aur 3.2 ki trick: aakhri digit ko 10 se poora karo, baaki har digit ko 9 se.
| Sawaal | Kaise | Baaki |
|---|---|---|
| 10 − 7 | 7 ko 10 se poora: 10 − 7 = 3 | 3 |
| 100 − 47 | 4 ko 9 se: 9 − 4 = 5; 7 ko 10 se: 10 − 7 = 3 | 53 |
| 100 − 8 | 8 ko 08 socho: 9 − 0 = 9; 10 − 8 = 2 | 92 |
| 1000 − 376 | 9 − 3 = 6, 9 − 7 = 2, 10 − 6 = 4 | 624 |
| 1000 − 47 | 047 socho: 9 − 0 = 9, 9 − 4 = 5, 10 − 7 = 3 | 953 |
Khaane (digit ki jagah) aur 0 bharna: 100 se baaki hamesha do khaane mein likhte hain, kyunki 100 mein do 0 hain. 100 − 99 = 1, par do khaane mein likho 01. Isi tarah 1000 se baaki teen khaane mein: 1000 − 995 = 5 → 005. Aage yeh bahut kaam aayega.
Ek aur dhyaan: agar aakhri digit 0 ho (jaise 100 − 40), to 9/10 wali trick seedhe mat lagao; 100 − 40 = 60 seedha karo.
🔁 Chhota sa warm-up
- 10 − 7 = ?
- 9 − 4 = ?
- 100 − 47 = ?
Answers dekho
- 3
- 5
- 53 (9 − 4 = 5, 10 − 7 = 3)
Teesra wala hi aaj ki chaabi hai: 47 ka “100 se baaki” 53!
— 📌 charumam.com
🎬 Kahani: Chapter 10 Se Ek Purani Mulaqaat
Riya ko Chapter 10 yaad tha: 47 × 9 = 470 − 47. “Par Mam, 470 − 47 mein udhaar lena padta hai, 0 mein se 7 nahi nikalta,” usne kaha.
CharuMam muskurayin: “Trachtenberg ne iska ilaaj nikaala. 47 ghatane ki jagah uska ‘100 se baaki’ 53 jodo, aur aakhir mein ek 100 wapas nikaal do. 470 + 53 = 523, aur 523 − 100 = 423. Koi udhaar nahi!”
Aarav: “Aur yahi digit-digit karke kare to?” Mam: “To ban jaata hai Trachtenberg ka × 9 niyam: 10 se, 9 se ghatao, padosi jodo, aakhir mein 1 kam.” 🔟
— 📌 charumam.com
🪄 Trick Step by Step: 10 Se, 9 Se Ghatao, Padosi Jodo, Aakhir Mein 1 (Ya 2) Kam
💡 Is post ki ek badi baat: × 9: aage 0. Ikai: 10 − digit. Baaki har digit: 9 − digit, phir padosi jodo. Aage wala 0: padosi − 1. × 8: wahi, bas har “baaki” ka double karo, aur aage wale 0 pe padosi − 2. Carry hamesha agle kadam mein (aakhri kadam pe pehle carry jodo, phir ghatao).
Step 1: × 9, kadam 1: aage 0 aur ikai
Sawaal: 47 × 9. Aage 0: 047. Ikai 7: 10 se baaki: 10 − 7 = 3. Ikai ka padosi nahi. Neeche 3 likho.
Step 2: × 9, kadam 2: beech ke digit
Dahai 4: 9 se baaki: 9 − 4 = 5. Padosi 7 jodo: 5 + 7 = 12 → 2 likho, 1 carry.
Step 3: × 9, kadam 3: aage wala 0
Aage wale 0 ka padosi 4. Carry 1 pehle jodo: 4 + 1 = 5. Phir 1 kam: 5 − 1 = 4.
Step 4: × 9: jawab aur check
4 | 2 | 3 = 423. Check (Chapter 10): 470 − 47 = 423 ✅
47 × 9: number ke aage 0 lagao → 047. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 7 | 10 se baaki: 10 − 7 = 3. Kul: 3 | 3 | 0 |
| 2 | Dahai | 4 | 9 se baaki: 9 − 4 = 5; padosi 7 jodo. Jod: 5 + 7 = 12 | 2 | 1 |
| 3 | Saikda | 0 (aage wala) | aage wala 0: padosi 4 mein se 1 ghatao; haath ka carry 1. Hisaab: 4 + 1 − 1 = 4 | 4 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 4 | 2 | 3 → 423.
Step 5: × 8: wahi, bas double aur 2 kam
Sawaal: 47 × 8. Har baaki ka double, aur aakhir mein 2 kam:
47 × 8: number ke aage 0 lagao → 047. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 7 | 10 se baaki: 10 − 7 = 3, uska double: 3 + 3 = 6. Kul: 6 | 6 | 0 |
| 2 | Dahai | 4 | 9 se baaki: 9 − 4 = 5, uska double: 5 + 5 = 10; padosi 7 jodo. Jod: 10 + 7 = 17 | 7 | 1 |
| 3 | Saikda | 0 (aage wala) | aage wala 0: padosi 4 mein se 2 ghatao; haath ka carry 1. Hisaab: 4 + 1 − 2 = 3 | 3 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 3 | 7 | 6 → 376.
Check: 47 × 8 = 470 − 47 − 47 = 470 − 94 = 376 ✅ (47 + 47 = 94; 470 − 94: 470 − 100 = 370, phir 6 wapas = 376.)
Lamba number × 9: 3412 × 9
Sirf ikai 10 se; baaki sab digit (sabse left wale 3 tak) 9 se. Phir aage wale 0 pe 1 kam.
3412 × 9: number ke aage 0 lagao → 03412. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 2 | 10 se baaki: 10 − 2 = 8. Kul: 8 | 8 | 0 |
| 2 | Dahai | 1 | 9 se baaki: 9 − 1 = 8; padosi 2 jodo. Jod: 8 + 2 = 10 | 0 | 1 |
| 3 | Saikda | 4 | 9 se baaki: 9 − 4 = 5; padosi 1 jodo; haath ka carry 1. Jod: 5 + 1 + 1 = 7 | 7 | 0 |
| 4 | Hazaar | 3 | 9 se baaki: 9 − 3 = 6; padosi 4 jodo. Jod: 6 + 4 = 10 | 0 | 1 |
| 5 | Das hazaar | 0 (aage wala) | aage wala 0: padosi 3 mein se 1 ghatao; haath ka carry 1. Hisaab: 3 + 1 − 1 = 3 | 3 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 3 | 0 | 7 | 0 | 8 → 30708.
× 8 mein carry 2: 625 × 8
625 × 8: number ke aage 0 lagao → 0625. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 5 | 10 se baaki: 10 − 5 = 5, uska double: 5 + 5 = 10. Kul: 10 | 0 | 1 |
| 2 | Dahai | 2 | 9 se baaki: 9 − 2 = 7, uska double: 7 + 7 = 14; padosi 5 jodo; haath ka carry 1. Jod: 14 + 5 + 1 = 20 | 0 | 2 |
| 3 | Saikda | 6 | 9 se baaki: 9 − 6 = 3, uska double: 3 + 3 = 6; padosi 2 jodo; haath ka carry 2. Jod: 6 + 2 + 2 = 10 | 0 | 1 |
| 4 | Hazaar | 0 (aage wala) | aage wala 0: padosi 6 mein se 2 ghatao; haath ka carry 1. Hisaab: 6 + 1 − 2 = 5 | 5 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 5 | 0 | 0 | 0 → 5000.
× 9 aur × 8 aamne-saamne
| Kadam | × 9 | × 8 |
|---|---|---|
| Ikai | 10 − digit | (10 − digit) ka double |
| Beech ke digit (sabse left digit tak) | (9 − digit) + padosi | (9 − digit) ka double + padosi |
| Aage wala 0 | padosi + carry − 1 | padosi + carry − 2 |
| Sabse bada carry | 1 | 2 |
| Example | 47 × 9 = 423 | 47 × 8 = 376 |
🆘 Atak gaye? Aise socho
- 10 se ya 9 se? Sirf ikai 10 se. Baaki sab 9 se.
- Padosi kab? Ikai ke baad har digit pe (ikai ka padosi nahi).
- Aakhri kadam: pehle carry jodo, phir 1 (× 9) ya 2 (× 8) ghatao. 0 aaye to likho mat.
- × 8 mein double kiska? Baaki ka (10 − digit ya 9 − digit), padosi ka nahi.
- Check: × 9 = × 10 − number (Chapter 10). × 8 = × 10 − number − number.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
× 9 kyun aisa? Chapter 10: 47 × 9 = 470 − 47. Ab ek chhoti chaal:
- 47 ghatane ki jagah “100 se baaki” jodo. 47 + 53 = 100, to 47 ghatana = 53 jodna aur 100 ghatana. 470 − 47 = 470 + 53 − 100.
- 470 ke digit kya hain? × 10 se har khaane mein padosi aa gaya (4, 7, 0).
- 53 ke digit kya hain? Chapter 3 ki trick: 47 ka 100 se baaki = 9 − 4 = 5 aur 10 − 7 = 3, yaani 53. Yaani ikai mein 10 se baaki, baaki digit 9 se baaki.
- Khaane-khaane jodo: padosi + baaki. Aur “− 100”? 100 sabse aage wale khaane (saikda) mein 1 hai, isliye aakhri kadam pe 1 kam.
470 + 53 = 523, 523 − 100 = 423. Neeche chitra mein yahi khaane hain. Koi udhaar nahi chahiye, kyunki humne ghatane ko jodne mein badal diya!
× 8 kyun? 8 = 10 − 2, to 47 × 8 = 470 − 47 − 47 = 470 + 53 + 53 − 200. Do baar baaki (yaani baaki ka double), aur aakhir mein 2 kam.
× 8 ke khaane: 47 × 8
Ab baaki ka double: ikai 3 → 6, dahai 5 → 10. Aakhri khaane se 2 kam.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 236 × 9 = ?
Aage 0: 0236. Ikai 6: 10 se baaki: 10 − 6 = 4 → 4 likho. Dahai 3: 9 se baaki: 9 − 3 = 6, padosi 6; 6 + 6 = 12 → 2 likho, carry 1. Saikda 2: 9 se baaki: 9 − 2 = 7, padosi 3, carry 1; 7 + 3 + 1 = 11 → 1 likho, carry 1. Aage wala 0: padosi mein se 1 ghatao, carry 1; 2 + 1 − 1 = 2 → 2 likho (aakhri kadam). Jawab: 2 | 1 | 2 | 4 → 2124.
✔️ Normal tareeke se check: Chapter 10: 2360 − 236 = 2124 (2360 − 200 = 2160, 2160 − 36 = 2124) ✅
Example 2: 58 × 8 = ?
Aage 0: 058. Ikai 8: 10 se baaki: 10 − 8 = 2, double: 2 + 2 = 4 → 4 likho. Dahai 5: 9 se baaki: 9 − 5 = 4, double: 4 + 4 = 8, padosi 8; 8 + 8 = 16 → 6 likho, carry 1. Aage wala 0: padosi mein se 2 ghatao, carry 1; 5 + 1 − 2 = 4 → 4 likho (aakhri kadam). Jawab: 4 | 6 | 4 → 464.
✔️ Normal tareeke se check: 580 − 58 − 58 = 580 − 116 = 464 ✅ (58 + 58 = 116)
Example 3: 405 × 9 = ? (beech mein 0)
Aage 0: 0405. Ikai 5: 10 se baaki: 10 − 5 = 5 → 5 likho. Dahai 0: 9 se baaki: 9 − 0 = 9, padosi 5; 9 + 5 = 14 → 4 likho, carry 1. Saikda 4: 9 se baaki: 9 − 4 = 5, padosi 0, carry 1; 5 + 0 + 1 = 6 → 6 likho. Aage wala 0: padosi mein se 1 ghatao; 4 − 1 = 3 → 3 likho (aakhri kadam). Jawab: 3 | 6 | 4 | 5 → 3645.
✔️ Normal tareeke se check: 4050 − 405 = 3645 (4050 − 400 = 3650, 3650 − 5 = 3645) ✅
Example 4: 236 × 8 = ?
Aage 0: 0236. Ikai 6: 10 se baaki: 10 − 6 = 4, double: 4 + 4 = 8 → 8 likho. Dahai 3: 9 se baaki: 9 − 3 = 6, double: 6 + 6 = 12, padosi 6; 12 + 6 = 18 → 8 likho, carry 1. Saikda 2: 9 se baaki: 9 − 2 = 7, double: 7 + 7 = 14, padosi 3, carry 1; 14 + 3 + 1 = 18 → 8 likho, carry 1. Aage wala 0: padosi mein se 2 ghatao, carry 1; 2 + 1 − 2 = 1 → 1 likho (aakhri kadam). Jawab: 1 | 8 | 8 | 8 → 1888.
✔️ Normal tareeke se check: 2360 − 236 − 236 = 2360 − 472 = 1888 ✅ (236 + 236 = 472)
— 📌 charumam.com
🕉️ Vedic Maths Connection
Yeh niyam seedha Vedic Maths ke Nikhilam sutra (“sab 9 se, aakhri 10 se”) se juda hai, jo Chapter 3 aur Chapter 10 mein dekha tha. Trachtenberg ne Nikhilam wale baaki ko padosi ke saath khaane-khaane jod diya, aur aakhri kadam pe 1 ya 2 kam karke round number (100, 1000) wapas nikaal diya. Do alag desh, do alag samay, ek hi soch!
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| × 9 (koi bhi number) | ✅ Haan | Baaki + padosi, aakhir mein 1 kam. Ya Chapter 10: × 10 − number. |
| × 8 (koi bhi number) | ✅ Haan | Baaki ka double + padosi, aakhir mein 2 kam. |
| Number 0 pe khatam (40 × 9) | ⚠️ Pehle 0 alag | 4 × 9 = 36, phir peeche 0 → 360. |
| × 99, × 999 | ➡️ Chapter 10 | Ek kam aur baaki wali trick wahan tez hai. |
| × 80, × 90 | ✅ Haan | × 8 ya × 9, phir peeche 0. |
| × 7, × 6 | ⬅️ Post 12.1–12.2 | Aadha padosi wale niyam. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Har digit 10 se ghata diya
Sawaal: 47 × 9
❌ Galat: dahai 4 ko bhi 10 se: 10 − 4 = 6, 6 + 7 = 13 → 3, carry 1; phir 4 + 1 − 1 = 4 → 433.
✅ Sahi: sirf ikai 10 se, baaki 9 se: 9 − 4 = 5, 5 + 7 = 12 → 423.
Galti 2: Aakhri kadam pe 1 kam karna bhool gaye
Sawaal: 47 × 9
❌ Galat: aage 0: 4 + 1 = 5 → 523.
✅ Sahi: 5 − 1 = 4 → 423. (Yaad: humne 100 extra joda tha, use wapas nikaalna hai.)
Galti 3: × 8 mein padosi ka double kar diya
Sawaal: 47 × 8
❌ Galat: dahai: baaki 5 + padosi 7, phir dono ka double: 24.
✅ Sahi: sirf baaki ka double: 10, phir padosi 7: 17 → 7, carry 1. Jawab 376.
Galti 4: × 8 mein 2 ki jagah 1 kam
Sawaal: 58 × 8
❌ Galat: aage 0: 5 + 1 − 1 = 5 → 564.
✅ Sahi: × 8 mein 2 kam: 5 + 1 − 2 = 4 → 464.
🧠 Rule of thumb: × 9: ikai 10 se, baaki 9 se, padosi jodo, aakhir mein 1 kam. × 8: baaki ka double, aakhir mein 2 kam.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, × 9 aur × 8 mix. Target: 8 minute. Pehle dekho 9 hai ya 8!
- 6 × 9 = ?
- 7 × 8 = ?
- 23 × 9 = ?
- 23 × 8 = ?
- 36 × 9 = ?
- 45 × 8 = ?
- 58 × 9 = ?
- 64 × 8 = ?
- 75 × 9 = ?
- 89 × 8 = ?
- 99 × 9 = ?
- 123 × 9 = ?
- 214 × 8 = ?
- 352 × 9 = ?
- 467 × 8 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 54
- 56
- 207
- 184
- 324
- 360
- 522
- 512
- 675
- 712
- 891
- 1107
- 1712
- 3168
- 3736
Kaise kiya (kuch):
Aage 0: 089. Ikai 9: 10 se baaki: 10 − 9 = 1, double: 1 + 1 = 2 → 2 likho. Dahai 8: 9 se baaki: 9 − 8 = 1, double: 1 + 1 = 2, padosi 9; 2 + 9 = 11 → 1 likho, carry 1. Aage wala 0: padosi mein se 2 ghatao, carry 1; 8 + 1 − 2 = 7 → 7 likho (aakhri kadam). Jawab: 7 | 1 | 2 → 712.
Aage 0: 0352. Ikai 2: 10 se baaki: 10 − 2 = 8 → 8 likho. Dahai 5: 9 se baaki: 9 − 5 = 4, padosi 2; 4 + 2 = 6 → 6 likho. Saikda 3: 9 se baaki: 9 − 3 = 6, padosi 5; 6 + 5 = 11 → 1 likho, carry 1. Aage wala 0: padosi mein se 1 ghatao, carry 1; 3 + 1 − 1 = 3 → 3 likho (aakhri kadam). Jawab: 3 | 1 | 6 | 8 → 3168.
— 📌 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 = ?
- 4 × 8 = ?
- 9 × 9 = ?
- 9 × 8 = ?
- 12 × 9 = ?
- 25 × 8 = ?
- 33 × 9 = ?
- 50 × 8 = ?
- 62 × 9 = ?
- 71 × 8 = ?
| 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
- 32
- 81
- 72
- 108
- 200
- 297
- 400
- 558
- 568
Dhyaan:
Aage 0: 025. Ikai 5: 10 se baaki: 10 − 5 = 5, double: 5 + 5 = 10 → 0 likho, carry 1. Dahai 2: 9 se baaki: 9 − 2 = 7, double: 7 + 7 = 14, padosi 5, carry 1; 14 + 5 + 1 = 20 → 0 likho, carry 2. Aage wala 0: padosi mein se 2 ghatao, carry 2; 2 + 2 − 2 = 2 → 2 likho (aakhri kadam). Jawab: 2 | 0 | 0 → 200.
50 × 8: 5 × 8 = 40, peeche 0 → 400.
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: (c) 423
- (a) galat ❌: 433: dahai 4 ko bhi 10 se ghata diya (10 − 4 = 6).
- (b) galat ❌: 323: dahai ka carry 1 aakhri kadam mein nahi joda (4 − 1 = 3).
- (c) sahi ✅: 047: 10 − 7 = 3; 9 − 4 = 5, 5 + 7 = 12 (2, c1); 4 + 1 − 1 = 4 → 423.
- (d) galat ❌: 523: aakhri kadam pe 1 kam karna bhool gaye.
Q2. × 9 niyam mein 10 se kaun ghatta hai?
Jawab aur kaaran dekho
Sahi jawab: (b) Sirf ikai
- (a) galat ❌: Ikai 10 se ghatti hai: 47 mein 10 − 7 = 3.
- (b) sahi ✅: Sirf ikai 10 se (jaise 100 se baaki mein aakhri digit), baaki 9 se.
- (c) galat ❌: Har digit 10 se ghatane se 47 × 9 → 433 aata hai, galat.
- (d) galat ❌: Sabse left digit bhi 9 se ghatta hai; aakhri kadam (aage 0) pe padosi − 1.
Q3. 47 × 8 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 376
- (a) sahi ✅: 047: (10 − 7) ka double 6; (9 − 4) ka double 10, 10 + 7 = 17 (7, c1); 4 + 1 − 2 = 3 → 376.
- (b) galat ❌: 576: aakhri kadam pe 2 kam karna bhool gaye.
- (c) galat ❌: 374: ikai ko bhi 9 se ghata diya (9 − 7 = 2, double 4).
- (d) galat ❌: 276: dahai ka carry 1 nahi joda (4 − 2 = 2).
Q4. × 9 mein aakhri kadam pe “1 kam” kyun?
Jawab aur kaaran dekho
Sahi jawab: (d) Humne 100 (ya 1000) extra joda tha
- (a) galat ❌: Ikai ke liye 10 se baaki lete hain; 1 kam aakhri khaane ka hai, ikai ka nahi.
- (b) galat ❌: Yeh aadat nahi, hisaab hai: 100 ka 1 aakhri khaane mein hai.
- (c) galat ❌: Taaq digit ka 5 × 6 aur × 7 ka niyam hai, × 9 ka nahi.
- (d) sahi ✅: 470 − 47 = 470 + 53 − 100: baaki jodne mein 100 extra aaya, aakhri khaane se 1 kam karke wapas.
Q5. 58 × 8 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 464
- (a) galat ❌: 664: aakhri kadam pe kuch kam nahi kiya.
- (b) galat ❌: 462: ikai ko 9 se ghata diya (9 − 8 = 1, double 2).
- (c) sahi ✅: 058: (10 − 8) = 2, double 4; (9 − 5) = 4, double 8, 8 + 8 = 16 (6, c1); 5 + 1 − 2 = 4 → 464.
- (d) galat ❌: 564: aakhri kadam pe 2 ki jagah 1 kam kiya.
Q6. 3412 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 30708
- (a) galat ❌: 30707: ikai ko 9 se ghata diya (9 − 2 = 7).
- (b) sahi ✅: 03412: 8; 8 + 2 = 10 (0, c1); 5 + 1 + 1 = 7; 6 + 4 = 10 (0, c1); 3 + 1 − 1 = 3 → 30708.
- (c) galat ❌: 40708: aakhri kadam pe 1 kam bhool gaye.
- (d) galat ❌: 20608: carry nahi jode.
Q7. 625 × 8 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 5000
- (a) sahi ✅: 0625: 10 (0, c1); 14 + 5 + 1 = 20 (0, c2); 6 + 2 + 2 = 10 (0, c1); 6 + 1 − 2 = 5 → 5000.
- (b) galat ❌: 7000: aakhri kadam pe 2 kam nahi kiya.
- (c) galat ❌: 4998: ikai ko 9 se ghata diya.
- (d) galat ❌: 4890: carry nahi jode.
Q8. 12 × 9 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 108
- (a) galat ❌: 208: aakhri kadam pe 1 kam bhool gaye.
- (b) galat ❌: 8: carry aur aakhri kadam dono chhoot gaye (sirf ikai likhi).
- (c) galat ❌: 107: ikai ko 9 se ghata diya (9 − 2 = 7).
- (d) sahi ✅: 012: 10 − 2 = 8; 9 − 1 = 8, 8 + 2 = 10 (0, c1); 1 + 1 − 1 = 1 → 108.
Q9. Kis sawaal mein pehle peeche ka 0 alag karna achha hai?
Jawab aur kaaran dekho
Sahi jawab: (c) 40 × 9
- (a) galat ❌: 41 × 9 = 369, seedha niyam.
- (b) galat ❌: 49 × 9 = 441, seedha niyam.
- (c) sahi ✅: 40 ki ikai 0: 4 × 9 = 36, phir peeche 0 → 360. (Niyam bhi chalega: 10 − 0 = 10, par 0 alag karna aasaan.)
- (d) galat ❌: 47 × 9 = 423, seedha niyam.
Q10. 99 × 8 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 792
- (a) galat ❌: 891: × 9 kar diya; yeh 99 × 9 hai.
- (b) sahi ✅: 099: (10 − 9) = 1, double 2; (9 − 9) = 0, double 0, 0 + 9 = 9; 9 − 2 = 7 → 792.
- (c) galat ❌: 992: aakhri kadam pe 2 kam bhool gaye.
- (d) galat ❌: 790: ikai ko 9 se ghata diya (0, double 0).
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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. 47 × 9 = 423 aur 47 × 8 = 376. Dono mein farak kitna, aur kyun?
Solution dekho
423 − 376 = 47. Kyunki 47 × 9 mein 47 ek baar zyada hai (9 = 8 + 1). Check: 376 + 47 = 423 ✅
Q2. Ek din mein 9 ghante school. 236 din mein kitne ghante?
Solution dekho
236 × 9: 0236 → 10 − 6 = 4; 9 − 3 = 6, 6 + 6 = 12 (2, carry 1); 9 − 2 = 7, 7 + 3 + 1 = 11 (1, carry 1); aage 0: 2 + 1 − 1 = 2. Jawab 2124 ghante.
Check: 2360 − 236 = 2124 ✅
Q3. × 9 ka jawab: number ke digits ka jod dekho. 47 × 9 = 423 → 4 + 2 + 3 = 9. 236 × 9 = 2124 → 2 + 1 + 2 + 4 = 9. 3412 × 9 = 30708 → ?
Solution dekho
3 + 0 + 7 + 0 + 8 = 18, aur 1 + 8 = 9! × 9 ke har jawab ke digits jodte jao to aakhir mein 9 hi aata hai. (9 ki table mein bhi yahi dikhta hai: 18 → 1 + 8 = 9, 27 → 2 + 7 = 9, 36 → 3 + 6 = 9.) Yeh aage aane wale “9 se check” (casting out nines: digits jodkar 9 se check karna) ki jhalak hai.
Q4. 12 × 8 karo. Aakhri kadam pe kya hota hai?
Solution dekho
012: ikai 2: 10 − 2 = 8, double 16 → 6, carry 1. Dahai 1: 9 − 1 = 8, double 16, padosi 2, carry 1: 16 + 2 + 1 = 19 → 9, carry 1. Aage 0: padosi 1 + carry 1 = 2, phir 2 kam: 2 − 2 = 0, to likhte nahi. Jawab 96.
Check: 120 − 12 − 12 = 96 ✅. Isliye “pehle carry jodo, phir ghatao”.
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🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Guna, pahaada check, ghante/din ke word problem. |
| Maths Olympiad | Digits ka jod 9 wala pattern, × 8 aur × 9 ka farak. |
| NTSE / MAT | Mental maths aur number series. |
| SSC / Bank (aage) | Simplification mein × 8, × 9. |
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.
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👩🏫 CharuMam Ka Tip
Mantra: “ikai 10 se, baaki 9 se, padosi jodo, aakhir mein kam.” × 9 pe 1 kam, × 8 pe 2 kam (aur double). Ek din × 9, agle din × 8, phir mix. Agle post mein 6, 7, 8, 9 ke tricky sawaal! 🔟
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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)
Aage 0: 047. Ikai 7: 10 se baaki 3, double 6 → 6. Dahai 4: 9 se baaki 5, double 10, padosi 7: 10 + 7 = 17 → 7, carry 1. Aage 0: padosi 4, carry 1, phir 2 kam: 4 + 1 − 2 = 3. Jawab 376 ✅
| 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. 🚀
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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 galti hone pe samjhayega:
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❓ FAQs (Bachchon Ke Asli Sawaal)
1. Chapter 10 ka × 9 aur yeh, kaunsa behtar?
Dono sahi. 2-digit ke liye Chapter 10 (470 − 47) bhi tez hai. Lambe number pe Trachtenberg mein udhaar nahi lagta, to galti kam.
2. Aakhri kadam pe ghatane se pehle number chhota ho (12 × 8 mein 1 − 2)?
Pehle carry jodo: 1 + 1 = 2, phir 2 − 2 = 0. Carry hamesha itna aata hai ki ghatana ho jaaye.
3. Number 0 pe khatam ho to?
Niyam chalega (10 − 0 = 10 → 0 likho, 1 carry), par aasaan hai pehle 0 alag karna: 40 × 9 mein 4 × 9 = 36, phir peeche 0 → 360.
4. Agle post mein kya hai?
Post 12.4: 6, 7, 8, 9 ke tricky sawaal: kaunsa niyam, ulte sawaal, dhokhe.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- × 9: ikai 10 − digit; baaki (9 − digit) + padosi; aage 0: padosi − 1.
- × 8: wahi, par baaki ka double; aage 0: padosi − 2.
- Kyun: ghatane ko “baaki jodo, round number nikaalo” mein badla.
- Aakhri kadam: pehle carry jodo, phir ghatao; 0 aaye to mat likho.
- Carry: × 9 mein 1 tak, × 8 mein 2 tak.
- Check: × 10 − number (× 9), × 10 − 2 baar number (× 8).
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👉 Aage Kya?
Chapter 12 ka aakhri post: Post 12.4 mein 6, 7, 8, 9 ke tricky sawaal: kaunsa niyam kab, ulte sawaal (□ × 7 = 238), aur dhokhe!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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