2-digit × 11 aa gaya. Ab 3-digit: left digit, phir har padosi jodi ka jod, phir right digit. Carry step-by-step. Example hero: 312 × 11.
⏱ Before Timer: Pehle Purane Tareeke Se
Check pehle school/×10 tareeke se: 312 × 11 = 312 × 10 + 312:
Jawab 3432. Aaj padosi-jod trick yahi tez karti hai.
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
312 × 11 = 3432
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
4.1 yaad: beech = digits ka jod. 3-digit mein do beech — padosi pairs.
📖 Shabd jo is post mein aayenge
- Padosi digits ka jod: bagal wale digits ka jod: 312 mein 3+1 aur 1+2.
- Left se samajhna: pehle left digit, phir pairs, phir right — parts left se samjho.
- Carry ki chain: ek pair 10 ya zyada to next left place mein +1.
- 4-digit jawab: 3-digit × 11 ka jawab 4 digit ka hota hai (100 × 11 = 1100), aur bade numbers pe 5 digit bhi (999 × 11 = 10989).
- Check: number×10 + number = number×11. Jaise 312×10 + 312 = 312×11.
- Jagah (place): har jod apni jagah pe — ikai, dahai, saikda, hazaar.
📏 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.
🔁 Chhota sa warm-up
- 3 + 1 = ?
- 1 + 2 = ?
- 312 × 10 = ?
- 3120 + 312 = ?
Answers dekho
- 4
- 3
- 3120
- 3432
Padosi jod + check ready!
— 📌 charumam.com
🎬 Kahani: Ishan Ka Roll Number
Ishan ka roll 312. Teacher: “11 se guna, mental!”
Woh 4.1 wala sochne laga… teen digit?
CharuMam: “Left 3, phir 3+1, phir 1+2, phir 2 — 3432. Pairs left se right!” 🔢
— 📌 charumam.com
🪄 Trick Step by Step: Pairs Left Se Right
💡 Is post ki ek badi baat: 3-digit × 11: left digit | left+beech | beech+right | right digit, har sum pe carry left ki taraf sambhalo.
Step 1: Teen digits likho
312: left 3, beech 1, right 2.
Step 2: Left, do jod, right
3 | 3+1=4 | 1+2=3 | 2 → agar sab jod 10 se kam → 3432.
Direction: Parts left se samjho, par carry ho to likhna right se shuru karo.
Step 3: Carry rule
Koi sum 10 ya zyada: us place pe sum mein se 10 ghatakar likho, left place pe +1. Left-most pe carry ho to naya digit — jaise 999 × 11: aakhri left pe 9 + carry 1 = 10, isliye jawab 10 se shuru (10989).
Step 4: Check
312 × 10 + 312 = 3120 + 312 = 3432 ✅
Carry example: 456 × 11
Digits: left 4, beech 5, right 6.
- Right = 6
- Beech+right = 5+6 = 11 → likho 1, carry 1 left
- Left+beech = 4+5 = 9, + carry 1 = 10 → likho 0, carry 1 left
- Left = 4 + carry 1 = 5
Jawab: 5016. Check: 4560 + 456 = 5016 ✅
| Sawaal | Parts | Jawab |
|---|---|---|
| 312 × 11 | 3|4|3|2 | 3432 |
| 123 × 11 | 1|3|5|3 | 1353 |
| 278 × 11 | 2|9|15→ carry → 3058 | 3058 |
| 509 × 11 | 5|5|9|9 | 5599 |
| 999 × 11 | 9|18|18|9 → carries → 10989 | 10989 |
278 × 11 detail: 8; 7+8=15 → 5 carry1; 2+7+1=10 → 0 carry1; 2+1=3 → 3058.
🆘 Atak gaye? Aise socho
- Kaunse pairs? (left+beech) aur (beech+right) — beech dono mein.
- Right se carry asaan? Haan: pehle right, phir beech+right, phir left+beech, phir left — carry natural left jaaye.
- Check: ×10 + number.
- 2-digit se link: 42 ko 042 socho → 0|4|6|2 = 462 (4.1 wala jawab).
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Phir se 312×11 = 312×10 + 312. 312×10 = 3120. +312 place-wise:
- Ikai: 0+2=2
- Dahai: 2+1=3
- Saikda: 1+3=4
- Hazaar: 3
Dekho: ikai = right digit (2), dahai = beech+right (1+2), saikda = left+beech (3+1), hazaar = left (3). Yahi padosi-jod rule!
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 123 × 11 = ?
1 | 1+2=3 | 2+3=5 | 3 → 1353.
✔️ Normal tareeke se check: 1230+123=1353 ✅
Example 2: 509 × 11 = ?
5 | 5+0=5 | 0+9=9 | 9 → 5599.
✔️ Normal tareeke se check: 5090+509=5599 ✅
Example 3: 278 × 11 = ?
Right se: 8; 7+8=15 →5 c1; 2+7+1=10 →0 c1; 2+1=3 → 3058.
✔️ Normal tareeke se check: 2780+278=3058 ✅
Example 4: 456 × 11 = ?
→ 5016 (upar detail).
✔️ Normal tareeke se check: 4560+456=5016 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
4.1 jaisa hi — number×10 + number, digits se likha. Naam Vedic ho ya na ho, samajh zaroori hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| 3-digit × 11 | ✅ Haan | Pairs + carry. |
| 2-digit | ⚠️ 4.1 chhota post | Ya aage 0 laga kar isi rule se. |
| 4-digit × 11 | ⚠️ Post 4.3 | Zyada pairs. |
| Exam steps | ❌ Sheet column | Rough OK. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Galat pairs (left+right)
312 mein ❌ left+right (3+2) galat pair. ✅ Padosi = left+beech (3+1), beech+right (1+2).
Galti 2: Carry order
Right se process karo taaki carry clear rahe.
Galti 3: Chipka sums
15 ko do digit mat chipkao ek place pe.
🧠 Rule of thumb: Left digit | padosi jod | padosi jod | right digit; 10 ya zyada pe carry left. Check ×10+number.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
15 sawaal, 3-digit × 11. Target: 5 minute.
- 112 × 11 = ?
- 213 × 11 = ?
- 314 × 11 = ?
- 405 × 11 = ?
- 516 × 11 = ?
- 124 × 11 = ?
- 235 × 11 = ?
- 346 × 11 = ?
- 457 × 11 = ?
- 568 × 11 = ?
- 609 × 11 = ?
- 718 × 11 = ?
- 820 × 11 = ?
- 901 × 11 = ?
- 999 × 11 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 1232
- 2343
- 3454
- 4455
- 5676
- 1364
- 2585
- 3806
- 5027
- 6248
- 6699
- 7898
- 9020
- 9911
- 10989
— 📌 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.
- 101 × 11 = ?
- 202 × 11 = ?
- 303 × 11 = ?
- 414 × 11 = ?
- 525 × 11 = ?
- 636 × 11 = ?
- 147 × 11 = ?
- 258 × 11 = ?
- 369 × 11 = ?
- 480 × 11 = ?
| 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
- 1111
- 2222
- 3333
- 4554
- 5775
- 6996
- 1617
- 2838
- 4059
- 5280
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. 312 × 11 mein pehla beech jod (left+beech)?
Jawab aur kaaran dekho
Sahi jawab: (b) 4
- (a) galat ❌: 1 sirf beech digit hai, jod nahi.
- (b) sahi ✅: Left 3 + beech 1 = 4.
- (c) galat ❌: 5 = left+right (3+2) — galat pair; padosi left+beech chahiye.
- (d) galat ❌: 3 sirf left digit hai, jod nahi.
Q2. 312 × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 3432
- (a) sahi ✅: 3 | 3+1=4 | 1+2=3 | 2 → 3432.
- (b) galat ❌: 3312: pehla beech 3+1=4 ki jagah 3 likha (jaise 3+0) — pair galat.
- (c) galat ❌: 3123: digits ka order ulat diya (right wale hisse aage).
- (d) galat ❌: 3423: doosra beech 1+2=3 ki jagah 2 — ek jod galat.
Q3. 456 × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 5016
- (a) galat ❌: 4516 tab jab left+beech jodna bhool gaye (4+5=9 ki jagah sirf 5 likha) aur 5+6=11 ka sirf 1 likha, carry aage nahi badhaya.
- (b) galat ❌: 45611: number aur 11 chipka diye, guna nahi kiya.
- (c) galat ❌: 4916: ek carry liya par doosra nahi (4+5=9 bina +1) — galat.
- (d) sahi ✅: Right se: 6; 5+6=11→1 c1; 4+5+1=10→0 c1; 4+1=5 → 5016.
Q4. Padosi jod mein beech digit?
Jawab aur kaaran dekho
Sahi jawab: (c) Dono pairs mein aata
- (a) galat ❌: Sirf doosre mein nahi — dono mein.
- (b) galat ❌: Haan, beech digit aata hai.
- (c) sahi ✅: Beech digit dono pairs mein aata hai (3+1 aur 1+2).
- (d) galat ❌: Sirf pehle pair mein nahi — dono mein.
Q5. 123 × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 1353
- (a) galat ❌: 1123: left+beech 1+2=3 ki jagah 1 — galat.
- (b) sahi ✅: 1 | 1+2=3 | 2+3=5 | 3 → 1353.
- (c) galat ❌: 1323: doosra beech 2+3=5 ki jagah 2 — galat.
- (d) galat ❌: 1233: pairs skip karke digits chipka diye.
Q6. 278 × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 3058
- (a) sahi ✅: 8; 7+8=15→5; 2+7+1=10→0; 2+1=3 → 3058.
- (b) galat ❌: 2788: bina carry — 7+8=15 sambhala nahi.
- (c) galat ❌: 2918: left+beech 2+7=9, carry nahi liya (15 se +1 chahiye tha).
- (d) galat ❌: 2158 tab jab 7+8=15 ke 1 ko carry karne ki jagah alag digit likh diya (2 | 1 | 5 | 8) aur 2+7 wala hissa chhod diya.
Q7. Check kaise karein?
Jawab aur kaaran dekho
Sahi jawab: (d) number×10 + number
- (a) galat ❌: Minus se check nahi — ×11 = ×10 + ×1.
- (b) galat ❌: Sirf +11 galat; poora number ×11 chahiye.
- (c) galat ❌: Digits ka jod alag cheez; check ×10+number hai.
- (d) sahi ✅: 312×11 = 3120 + 312.
Q8. 999 × 11 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 10989
- (a) galat ❌: 10899 mein beech ke do digit ki jagah ulat gayi: sahi order 10 | 9 | 8 | 9 hai (9+9+1=19 se 9, 9+9=18 se 8), yahan 8 aur 9 aage-peeche likh diye.
- (b) galat ❌: 98901 sahi jawab 10989 ko ulta (peeche se) likhne se banta hai; likhte hain right se, par padhte left se.
- (c) sahi ✅: 9990 + 999 = 10989. Left pe 9+1=10 → jawab 10 se shuru.
- (d) galat ❌: 9999: jaise sirf ×10 + 9 — poora +999 nahi.
Q9. Kya 2-digit 42 ko 042 maan kar isi 3-digit rule se kar sakte hain?
Jawab aur kaaran dekho
Sahi jawab: (b) 0|4|6|2 = 462
- (a) galat ❌: Carry hamesha nahi — sirf jod 10 ya zyada pe.
- (b) sahi ✅: Haan: 042 × 11 rule se 0|4|6|2 = 462 — 4.1 jaisa jawab.
- (c) galat ❌: 042×11 alag nahi — wahi padosi-jod rule.
- (d) galat ❌: Kaam karta hai; “kaam nahi” galat.
Q10. Carry left kab?
Jawab aur kaaran dekho
Sahi jawab: (a) Pair sum 10 ya zyada
- (a) sahi ✅: Jab pair sum 10 ya zyada.
- (b) galat ❌: Hamesha nahi — sirf jod 10 ya zyada pe.
- (c) galat ❌: Odd digit se carry nahi banta; jod se banta hai.
- (d) galat ❌: Zero pe automatic carry nahi; jod 10 ya zyada chahiye.
— 📌 charumam.com
🧠 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. Kaunsa 3-digit × 11 = 3432?
Solution dekho
Jawab 3432 se peeche: right digit = 2 (number ka right). Left digit = 3 (jawab ka pehla, bina extra carry). Beech: left+beech = 4 → 3+beech=4 → beech=1; beech+right = 3 → 1+2=3 ✅. To number 312. Check: 312 × 11 = 3432 ✅
Q2. 100 × 11 aur 99 × 11 ka farq?
Solution dekho
1100 − 1089 = 11. Farq 1 × 11, kyunki 100−99=1.
Q3. 214 × 11 + 301 × 11 = ?
Solution dekho
Pehle 214+301=515. Phir 515×11: 5 | 5+1=6 | 1+5=6 | 5 → 5665. Check: 2354+3311=5665 ✅
Q4. Sabse chhota 3-digit jisme ×11 pe dono pairs pe carry?
Solution dekho
Dono pairs ka jod 10 ya zyada hona chahiye. Try chhote numbers: 191 → 1+9=10 aur 9+1=10, dono carry. 191×11 = 2101. Check: 1910+191=2101 ✅. 190 mein doosra pair 9+0=9 (carry nahi). To sabse chhota 191.
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School | Teen digit number ×11 mann mein. |
| Olympiad | Padosi digits ke jod se sochna. |
| NTSE | Mann mein tez ×11. |
| SSC | Simplification ×11. |
Shabdon ka matlab: Olympiad = school ke bachchon ki maths pratiyogita (competition). NTSE = Class 10 ke bachchon ka ek national scholarship (vazifa) exam. SSC / Bank exam = badon ke sarkari naukri ke exam. Simplification = lambe hisaab ko chhota karke jawab nikaalna.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
3-digit pe right se likho: pehle right, phir beech+right, phir left+beech, phir left — carry natural. Bolkar practice: “teen, chaar, teen, do!” 🔢
— 📌 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)
3 | 3+1=4 | 1+2=3 | 2 → 3432. Check: 3120 + 312 = 3432 ✅
| 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. 4-digit number × 11?
Agla post 4.3 mein lamba number pe same padosi-jod seekhenge.
2. Kya jawab hamesha 4-digit hota hai?
3-digit × 11 ka jawab 4 digit ka hota hai (100 × 11 = 1100), aur bade numbers pe 5 digit bhi (999 × 11 = 10989).
3. Left se likhun ya right se?
Jawab same. Parts left se samjho; carry ho to likhna right se shuru karo — carry sambhalna aasaan.
4. Pairs bhool jaun to?
Beech wala digit dono jodon mein aata hai — jaise 312 mein 1 dono pairs mein. Yaad rakho.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- 3-digit ×11: left | left+beech | beech+right | right.
- 312 × 11 = 3432.
- Sum 10 ya zyada → carry.
- Check: ×10 + number.
- Likho right se — carry asaan.
- 2-digit = aage 0 laga kar wahi rule.
— charumam.com 🎯
👉 Aage Kya?
Post 4.3: lamba ×11, ulta check, kab NA use karein!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
💛 Post Achha Laga? Like, Share, Subscribe, Follow!
Agar aaj kuch naya samajh aaya, to post ko like kijiye, apne doston aur class ke group mein share kijiye, aur roz nayi trick ke liye humein subscribe aur follow kijiye! 🙏
- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
- ▶️ YouTube (subscribe): @charumamofficial
- 📸 Instagram (follow): @charumamofficial
- ✈️ Telegram: t.me/charumam
- 💬 WhatsApp Channel: CharuMam WhatsApp Channel
— 📌 charumam.com
