Chapter 12 ka aakhri post! 🏆 Aaj 12.1–12.3 ka mix: pehle kaunsa niyam lagana hai pehchano, phir ulte sawaal (□ × 7 = 238), jodi banao (6 × 37 + 6 × 63), aur dhokhe jaise × 60. Post 11.4 ki “andaaza + ikai check” wali soch yahan bhi chalegi, ek mazedaar badlaav ke saath.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. Dono guna alag karo, phir jodo.
- 6 × 37 = 37 × 6 = 222 (Post 12.1 ka niyam).
- 6 × 63 = 63 × 6 = 378.
- Jodo: 222 + 378 = 600.
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
6 × 37 + 6 × 63 = 600
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: 12.1–12.3 ke chaaron niyam aur Post 11.4 ka ulta sawaal (andaaza + ikai check). Chaaron niyam ek line mein:
📖 Shabd jo is post mein aayenge
- × 6: digit + aadha padosi, taaq pe 5.
- × 7: digit ka double + aadha padosi, taaq pe 5.
- × 9: ikai 10 se, baaki 9 se ghatao, padosi jodo, aakhir mein 1 kam.
- × 8: × 9 jaisa par baaki ka double, aakhir mein 2 kam.
- Ulta sawaal: □ × 7 = 238: jawab diya hai, number dhoondho.
- Dhokha: sawaal jo inme se kisi jaisa dikhe par seedha niyam na lage (× 60, × 16).
📏 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.
🔁 Chhota sa warm-up
- 34 × 7 = ?
- 30 × 7 = ?
- Taaq digit kaunse hain?
Answers dekho
- 238
- 210 (3 × 7 = 21, phir peeche 0)
- 1, 3, 5, 7, 9
Pehla wala hi aaj ka hook hai. Ulta karke dekhenge!
— 📌 charumam.com
🎬 Kahani: Syahi Phir Giri
Aarav ki copy pe phir syahi! Is baar dikh raha tha: □ × 7 = 238. “Post 11.4 jaisa,” Riya boli, “andaaza aur ikai.”
Andaaza: 30 × 7 = 210 aur 40 × 7 = 280. 238 beech mein, to number 30 aur 39 ke beech. Ikai: 238 ki ikai 8. × 7 mein kaunsi ikai 8 deti hai? 4 (double 8, 4 juft, to 5 nahi). To number 34.
Aarav hairaan: “Is baar to 2 option bhi nahi aaye, seedha ek!” CharuMam: “Yahi aaj ka raaz hai: × 7 aur × 9 mein ikai ek hi milti hai, × 6 aur × 8 mein do.” 🏆
— 📌 charumam.com
🪄 Trick Step by Step: Pehchano, Niyam Chuno, Andaaza, Ikai, Try
💡 Is post ki ek badi baat: Pehle pehchano: kaunsa number (6, 7, 8, 9)? Jodi ban sakti hai? Peeche 0 hai? Ulte sawaal mein: andaaze se number ki dahai, ikai table se number ki ikai (× 7, × 9 mein ek option, × 6, × 8 mein do), phir niyam se try karke pakka.
Step 1: Niyam chuno
× 6: aadha padosi + taaq pe 5. × 7: double + aadha padosi + taaq pe 5. × 9: baaki + padosi, aakhir 1 kam. × 8: baaki ka double + padosi, aakhir 2 kam.
Step 2: Ulta sawaal, kadam 1: andaaza
□ × 7 = 238. 30 × 7 = 210 (3 × 7 = 21, phir 0) aur 40 × 7 = 280. To □ 30 se 39: dahai 3.
Step 3: Ulta sawaal, kadam 2: ikai table
238 ki ikai 8. Neeche × 7 wali line mein 8 kahan hai? Ikai 4 ke neeche. To □ = 34.
| Number ki ikai | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| × 6: jawab ki ikai | 0 | 6 | 2 | 8 | 4 | 0 | 6 | 2 | 8 | 4 |
| × 7: jawab ki ikai | 0 | 7 | 4 | 1 | 8 | 5 | 2 | 9 | 6 | 3 |
| × 8: jawab ki ikai | 0 | 8 | 6 | 4 | 2 | 0 | 8 | 6 | 4 | 2 |
| × 9: jawab ki ikai | 0 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
(Har line niyam se hi bani: ikai ka padosi nahi hota, to sirf ikai pe niyam lagao aur aakhri digit dekho. Jaise × 7 mein ikai 4: double 8, 4 juft to 5 nahi → 8.)
Step 4: Ulta sawaal, kadam 3: try
34 × 7 niyam se:
34 × 7: number ke aage 0 lagao → 034. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 4 | 4 ka double: 4 + 4 = 8; 4 juft hai, to 5 nahi; padosi nahi (ikai ke right mein koi digit nahi). Kul: 8 | 8 | 0 |
| 2 | Dahai | 3 | 3 ka double: 3 + 3 = 6; 3 taaq hai, to 5 jodo; padosi 4 ka aadha 2. Jod: 6 + 5 + 2 = 13 | 3 | 1 |
| 3 | Saikda | 0 (aage wala) | aage wala 0: double 0 + 0 = 0; padosi 3 ka aadha 1 (aadha hissa chhod diya); haath ka carry 1. Jod: 0 + 1 + 1 = 2 | 2 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 2 | 3 | 8 → 238.
To □ = 34.
Step 5: Dhokha: × 60
60 = 6 × 10. To 47 × 60: pehle 47 × 6 = 282 (Post 12.1), phir peeche 0 → 2820.
Tricky sawaal ke type, ek nazar mein
| Type | Example | Kaise | Jawab |
|---|---|---|---|
| Jodi banao | 6 × 37 + 6 × 63 | 6 × 100 | 600 |
| Ulta (× 7) | □ × 7 = 238 | andaaza 30–39, ikai 4 | 34 |
| Ulta (× 8) | □ × 8 = 464 | andaaza 50–59, ikai 3 ya 8, try | 58 |
| Peeche 0 | 47 × 60 | 47 × 6 = 282, phir 0 | 2820 |
| Farak | 236 × 9 − 236 × 8 | ek baar 236 | 236 |
| “Ho sakta hai?” | □ × 6 = 745 | × 6 ka jawab hamesha juft | Nahi |
🆘 Atak gaye? Aise socho
- Niyam chuno: 6 aur 7 → aadha padosi + taaq pe 5. 8 aur 9 → baaki + padosi.
- Ulte mein ikai: × 7, × 9 → ek option. × 6, × 8 → do option, dono try karo.
- Taaq ikai? × 6 aur × 8 ka jawab hamesha juft. Taaq jawab ho to aisa number nahi.
- × 60, × 70, × 80, × 90: pehle 0 alag, phir niyam.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Ikai table kyun chalti hai? Ikai ka koi padosi nahi hota (Post 12.1). Isliye jawab ki ikai sirf number ki ikai se banti hai. Har niyam ko ikai 0 se 9 tak lagao, aur aakhri digit likho: wahi table hai.
× 7 aur × 9 mein ek hi option kyun? Table dekho: × 7 wali line mein 0 se 9 tak har digit ek-ek baar aata hai. × 9 mein bhi. Par × 6 aur × 8 ki line mein sirf juft digit, aur har ek do baar (jaise × 6 mein 2 do baar: ikai 2 aur 7 ke neeche). Isliye wahan do option.
Neeche tricky sawaal ka poora naksha hai.
34 × 7 ke khaane
Ulte sawaal ka jawab 34 chitra mein: ikai ke khaane mein sirf 4 ka double 8 (padosi nahi), isliye ikai check chala.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: □ × 9 = 423. □ = ?
Andaaza: 40 × 9 = 360, 50 × 9 = 450 → □ 40 se 49. Ikai: 423 ki ikai 3 → × 9 table mein 3 ikai 7 ke neeche. To □ = 47. Try: 047 → 10 − 7 = 3; 9 − 4 = 5, 5 + 7 = 12 (2, carry 1); 4 + 1 − 1 = 4 → 423 ✅. □ = 47.
✔️ Normal tareeke se check: 470 − 47 = 423 ✅
Example 2: □ × 8 = 464. □ = ?
Andaaza: 50 × 8 = 400, 60 × 8 = 480 → □ 50 se 59. Ikai: 464 ki ikai 4 → × 8 table mein 4 do jagah: ikai 3 aur 8. Try 53: 53 × 8 = 424 ❌. Try 58: 058 → (10 − 8) = 2, double 4; (9 − 5) = 4, double 8, 8 + 8 = 16 (6, carry 1); 5 + 1 − 2 = 4 → 464 ✅. □ = 58.
✔️ Normal tareeke se check: 580 − 58 − 58 = 580 − 116 = 464 ✅
Example 3: 236 × 9 − 236 × 8 = ?
236 nau baar mein se 236 aath baar hata do: bacha ek baar 236. Jawab 236. (Lamba tareeka: 2124 − 1888 = 236.)
✔️ Normal tareeke se check: 2124 − 1888 = 236 ✅ (1888 + 236 = 2124)
Example 4: 125 × 8 = ? (ek box mein 8 pencil, 125 box)
Aage 0: 0125. 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. Saikda 1: 9 se baaki: 9 − 1 = 8, double: 8 + 8 = 16, padosi 2, carry 2; 16 + 2 + 2 = 20 → 0 likho, carry 2. Aage wala 0: padosi mein se 2 ghatao, carry 2; 1 + 2 − 2 = 1 → 1 likho (aakhri kadam). Jawab: 1 | 0 | 0 | 0 → 1000.
✔️ Normal tareeke se check: 1250 − 125 − 125 = 1250 − 250 = 1000 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Ulte sawaal mein jawab ko dekh kar number pehchanna Vedic Maths ki “Vilokanam” (observation) wali soch hai, jo Post 11.4 mein dekhi thi. Aur ikai table mein jo “har digit ek-ek baar” wala pattern hai, woh aage division (bhaag) aur check ki tricks mein bahut kaam aata hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| × 6, × 7 (koi number) | ✅ Aadha padosi | Taaq pe 5; × 7 mein double bhi. |
| × 8, × 9 (koi number) | ✅ Baaki + padosi | Aakhir mein 2 ya 1 kam. |
| × 60, × 70, × 80, × 90 | ✅ Pehle 0 alag | Phir niyam, phir peeche 0. |
| □ × 7 = 238 | ✅ Ulta | Andaaza + ikai table (ek option). |
| □ × 6 = 745 (taaq) | ❌ Aisa number nahi | × 6 aur × 8 ka jawab hamesha juft. |
| × 16, × 67 | ⚠️ Dhokha | Yeh 6 ya 7 ka seedha niyam nahi. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Ulte mein ikai seedhi utha li
Sawaal: □ × 7 = 238
❌ Galat: “238 ki ikai 8, to number 38.” Par 38 × 7 = 266.
✅ Sahi: × 7 table: jawab ki ikai 8 → number ki ikai 4. □ = 34.
Galti 2: × 60 mein peeche ka 0 bhool gaye
Sawaal: 47 × 60
❌ Galat: 282.
✅ Sahi: 47 × 6 = 282, phir peeche 0: 2820.
Galti 3: × 7 pe × 6 ka niyam
Sawaal: 34 × 7
❌ Galat: double bhool gaye (× 6 jaisa kiya): 204, jo asal mein 34 × 6 hai.
✅ Sahi: × 7 mein double + aadha padosi: 238.
Galti 4: Jodi mein sab jod diya
Sawaal: 6 × 37 + 6 × 63
❌ Galat: 6 + 37 + 6 + 63 = 112.
✅ Sahi: 6 × (37 + 63) = 6 × 100 = 600 (bracket ke andar wala pehle jodo: kul 37 + 63 baar 6).
🧠 Rule of thumb: Pehchano, niyam chuno, ulte mein andaaza + ikai table + try, aur hamesha check.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 mix sawaal, kuch ulte. Target: 8 minute.
- 36 × 6 = ?
- 36 × 7 = ?
- 36 × 8 = ?
- 36 × 9 = ?
- 125 × 8 = ?
- 143 × 7 = ?
- 222 × 6 = ?
- 47 × 60 = ?
- 23 × 90 = ?
- 6 × 37 + 6 × 63 = ?
- □ × 7 = 238. □ = ?
- □ × 9 = 423. □ = ?
- □ × 6 = 282. □ = ?
- □ × 8 = 464. □ = ?
- □ × 7 = 161. □ = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 216
- 252
- 288
- 324
- 1000
- 1001
- 1332
- 2820
- 2070
- 600
- 34
- 47
- 47
- 58
- 23
Kaise kiya (kuch):
Aage 0: 0143. Ikai 3: double 3 + 3 = 6, 3 taaq → +5; 6 + 5 = 11 → 1 likho, carry 1. Dahai 4: double 4 + 4 = 8, 4 juft, padosi 3 ka aadha 1, carry 1; 8 + 1 + 1 = 10 → 0 likho, carry 1. Saikda 1: double 1 + 1 = 2, 1 taaq → +5, padosi 4 ka aadha 2, carry 1; 2 + 5 + 2 + 1 = 10 → 0 likho, carry 1. Aage wala 0: padosi 1 ka aadha 0, carry 1; 0 + 0 + 1 = 1 → 1 likho (aakhri kadam). Jawab: 1 | 0 | 0 | 1 → 1001.
□ × 6 = 282: andaaza 40 × 6 = 240, 50 × 6 = 300 → 40 se 49; ikai 2 → × 6 table mein ikai 2 ya 7 → 42 ya 47; 42 × 6 = 252, to 47. 23 × 90: 23 × 9 = 207, phir 0 → 2070.
— 📌 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.
- 5 × 6 = ?
- 5 × 7 = ?
- 8 × 8 = ?
- 9 × 6 = ?
- 11 × 7 = ?
- 20 × 9 = ?
- 25 × 6 = ?
- 50 × 7 = ?
- 7 × 9 + 9 = ?
- 6 × 8 + 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
- 30
- 35
- 64
- 54
- 77
- 180
- 150
- 350
- 72
- 56
Dhyaan: 7 × 9 + 9: 7 baar 9 aur ek 9 aur, yaani 8 baar 9 = 72. 6 × 8 + 8: yeh 7 baar 8, yaani 56. 50 × 7: 5 × 7 = 35, phir 0 → 350.
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. □ × 7 = 238. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 34
- (a) galat ❌: 38: jawab ki ikai 8 seedhi utha li; 38 × 7 = 266.
- (b) galat ❌: 24: andaaza galat; 24 × 7 = 168.
- (c) galat ❌: 44: andaaza galat; 44 × 7 = 308.
- (d) sahi ✅: Andaaza 30–39, × 7 table mein ikai 8 → 4: 34 × 7 = 238 ✅.
Q2. □ × 9 = 423. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 47
- (a) galat ❌: 37: andaaza galat; 37 × 9 = 333.
- (b) galat ❌: 57: andaaza galat; 57 × 9 = 513.
- (c) sahi ✅: Andaaza 40–49, × 9 table mein ikai 3 → 7: 47 × 9 = 423 ✅.
- (d) galat ❌: 43: ikai 3 seedhi utha li; 43 × 9 = 387.
Q3. Kaunse niyam mein “double” nahi hota, sirf digit + aadha padosi (taaq pe 5)?
Jawab aur kaaran dekho
Sahi jawab: (b) × 6
- (a) galat ❌: × 9 mein baaki + padosi; na double, na aadha.
- (b) sahi ✅: × 6 = × 1 + × 5: digit khud + aadha padosi.
- (c) galat ❌: × 7 mein digit ka double hota hai (7 = 2 + 5).
- (d) galat ❌: × 8 mein baaki ka double aur padosi; aadha padosi nahi.
Q4. 47 × 60 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 2820
- (a) sahi ✅: 47 × 6 = 282, phir peeche 0 → 2820.
- (b) galat ❌: 282: peeche ka 0 bhool gaye.
- (c) galat ❌: 28200: do 0 laga diye; 60 mein ek hi 0.
- (d) galat ❌: 3290: × 70 kar diya (47 × 7 = 329).
Q5. Kya □ × 6 = 745 ho sakta hai (□ poora number)?
Jawab aur kaaran dekho
Sahi jawab: (d) Nahi, × 6 ka jawab hamesha juft
- (a) galat ❌: 124 × 6 = 744, 745 nahi.
- (b) galat ❌: 125 × 6 = 750, 745 nahi.
- (c) galat ❌: 745 to jawab hai; 745 × 6 bahut bada.
- (d) sahi ✅: × 6 table ki line mein sirf juft ikai (0, 2, 4, 6, 8). 745 taaq pe khatam, to nahi.
Q6. 6 × 37 + 6 × 63 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 600
- (a) galat ❌: 700: 37 + 63 = 100 ke baad 7 se guna kar diya.
- (b) galat ❌: 378: sirf 6 × 63 kiya, 6 × 37 bhool gaye.
- (c) sahi ✅: 6 × (37 + 63) = 6 × 100 = 600 (bracket ke andar wala pehle jodo: kul 37 + 63 baar 6).
- (d) galat ❌: 112: guna ki jagah sab jod diya (6 + 37 + 6 + 63).
Q7. □ × 8 = 464. □ = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 58
- (a) galat ❌: 68: andaaza galat; 68 × 8 = 544.
- (b) sahi ✅: Andaaza 50–59, ikai 3 ya 8; 53 × 8 = 424, 58 × 8 = 464 ✅.
- (c) galat ❌: 53: ikai ka doosra option, par 53 × 8 = 424.
- (d) galat ❌: 54: ikai 4 seedhi utha li; 54 × 8 = 432.
Q8. Kin niyamon mein jawab ki ikai se number ki ikai sirf ek milti hai?
Jawab aur kaaran dekho
Sahi jawab: (a) × 7 aur × 9
- (a) sahi ✅: × 7 aur × 9 ki line mein har digit ek-ek baar aata hai.
- (b) galat ❌: × 6 aur × 8 mein har juft digit do baar, to do option.
- (c) galat ❌: × 6 mein do option aate hain (jaise 2 → ikai 2 ya 7).
- (d) galat ❌: × 7 aur × 9 mein ek hi milta hai, table dekho.
Q9. 143 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 1001
- (a) galat ❌: 991: carry nahi jode.
- (b) galat ❌: 496: taaq digit pe 5 jodna bhool gaye.
- (c) galat ❌: 2221: padosi ka aadha nahi, poora joda.
- (d) sahi ✅: 0143: 6 + 0 + 5 = 11 (1, c1); 8 + 1 + 1 = 10 (0, c1); 2 + 2 + 5 + 1 = 10 (0, c1); 0 + 0 + 1 = 1 → 1001.
Q10. 236 × 9 − 236 × 8 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 236
- (a) galat ❌: 2124: sirf 236 × 9 kiya, ghatana bhool gaye.
- (b) galat ❌: 472: 236 do baar le liya (236 + 236).
- (c) sahi ✅: 9 baar mein se 8 baar hataya, bacha ek baar 236.
- (d) galat ❌: 1: sirf 9 − 8 kiya, 236 bhool gaye.
— 📌 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. Ek box mein 8 pencil. 125 box mein kitni pencil? Aur 250 box mein?
Solution dekho
125 × 8 = 1000 (upar Example 4). 250 box = 125 box ke do guna: 1000 + 1000 = 2000.
Check: 250 × 8: 25 × 8 = 200, phir 0 → 2000 ✅
Q2. 143 × 7 = 1001. To 143 × 7 × 3 = ? Aur 143 × 7 × 5 = ?
Solution dekho
1001 × 3 = 3003 (1000 × 3 = 3000, 1 × 3 = 3). 1001 × 5 = 5005. Mazedaar pattern!
Check: 3003 = 3000 + 3 ✅
Q3. Riya: “□ × 6 = 282, to □ = 42.” Aarav: “Nahi, 47.” Kaun sahi?
Solution dekho
Andaaza: 40–49. Ikai: 282 ki ikai 2 → × 6 table mein 2 ya 7. 42 × 6: 042 → 2; 4 + 1 = 5; 0 + 2 = 2 → 252. 47 × 6 = 282 (Post 12.1). Aarav sahi: □ = 47.
Check: 47 × 6 = 47 × 5 + 47 = 235 + 47 = 282 ✅ (47 × 5: 470 ka aadha, yaani 235)
Q4. Ek 2-digit number × 9 ka jawab 3-digit hai aur 1 pe khatam hota hai. Sabse chhota aisa number?
Solution dekho
× 9 table: jawab ki ikai 1 → number ki ikai 9. Sabse chhota 2-digit jo 9 pe khatam: 19. 19 × 9: 019 → 10 − 9 = 1; 9 − 1 = 8, 8 + 9 = 17 (7, carry 1); 1 + 1 − 1 = 1 → 171 (3-digit ✅). Jawab 19.
Check: 190 − 19 = 171 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Guna, word problem (box, hafte, ghante), jodi wale sawaal. |
| Maths Olympiad | Ulte sawaal, “kya aisa ho sakta hai?”, ikai pattern. |
| NTSE / MAT | Mental maths, number pattern (143 × 7 = 1001). |
| SSC / Bank (aage) | Simplification aur fast multiplication. |
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: “pehchano, niyam chuno, andaaza, ikai, try.” Ikai table ek baar khud bana lo (niyam se, 0 se 9), phir ulte sawaal khel ban jaayenge. Chapter 12 poora: ab aap 6, 7, 8, 9, 11 aur 12 se bina pahaade guna kar sakte ho! 🏆
— 📌 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)
Dono mein 6. 37 baar 6 aur 63 baar 6, yaani kul (37 + 63) baar 6 = 100 baar 6 = 600 ✅ (Jodi banao, Post 11.4 jaisa!)
| 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. Ikai table yaad karni padegi?
Nahi. Niyam se 1 minute mein ban jaati hai: har digit pe niyam lagao, aakhri digit likho.
2. Ulte mein dono option galat aaye to?
Andaaza dobara dekho. Ya jawab ki ikai taaq hai aur sawaal × 6 ya × 8 ka hai, to aisa number nahi.
3. × 16 ya × 67 jaise sawaal?
Yeh in niyamon ka seedha kaam nahi; inhe tod kar (× 10 + × 6) karo.
4. Ab aage kya?
Chapter 12 poora! Agla chapter jald aa raha hai.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Niyam chuno: 6/7 aadha padosi + taaq pe 5; 8/9 baaki + padosi.
- Ulta: andaaze se dahai, ikai table se ikai, try.
- × 7, × 9: ikai ka ek option; × 6, × 8: do.
- × 6, × 8 ka jawab hamesha juft.
- × 60 jaise: pehle 0 alag.
- Jodi: 6 × 37 + 6 × 63 = 6 × 100.
— charumam.com 🎯
👉 Aage Kya?
Chapter 12 poora! 🎉 Ab aap 6, 7, 8, 9, 11 aur 12 se bina pahaade guna kar sakte ho. Agla chapter jald aa raha hai, tab tak drill aur ikai table practice karo.
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
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— 📌 charumam.com
