Level 2 shuru! 🎉 Aaj ki trick ka naam hai Base Method. Jo numbers kisi round number (jaise 10) ke paas hon, unka guna pahaade (table) ke bina ho jaata hai: pehle dekho har number base se kitna kam ya kitna zyada hai, phir ek chhota ghatana (ya jod) aur ek chhota guna. 8 × 7 aur 12 × 13 se shuru karenge, aur tiles ke chitra se dekhenge ki yeh hamesha sahi kyun aata hai.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 8 × 7 matlab 7 ko 8 baar jodna (GUNA box). Running total (har baar ka naya jod) likho:
7, 14, 21, 28, 35, 42, 49, 56
Aath baar jodne pe 56. Jinko 8 ka pahaada yaad hai, unhe turant aa jaayega; jinko nahi, unhe aath jod lagaane padte hain. Aaj ki trick mein pahaade ki zaroorat nahi: bas 10 tak ki ginti, ek ghatana aur 2 × 3 jaisa chhota guna.
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
8 × 7 = 56
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
Aaj teen purani cheezein chahiye: 10 se ghatana (10 − 8 = 2), chhote numbers ka guna (2 × 3, GUNA box se), aur place value (5 dahai = 50). Aur do nayi cheezein: base aur deewar ( | ). Sab neeche ke boxes mein hai. Naye shabd:
📖 Shabd jo is post mein aayenge
- Base: paas wala round number (10, 100, 1000) jiske paas dono numbers hon. Aaj base 10 hai.
- Kitna kam: number base se kitna chhota hai: base − number. 8 → 10 − 8 = 2 kam.
- Kitna zyada: number base se kitna bada hai: number − base. 13 → 13 − 10 = 3 zyada.
- Tirchha (cross) ghatana: ek number mein se doosre number ka kitna kam ghatana. 8 × 7 mein: 8 − 3 (3 hai 7 ka kitna kam). Isse left hissa milta hai. “Tirchha” isliye kyunki copy pe yeh ek number se doosre ki line tak tedhi (tirchhi) lakeer jaisa hai.
- Left hissa | Right hissa: jawab ke do tukde, beech mein deewar ( | ). Base 10 mein left hissa dahai ginta hai, right hissa ikai. Right hisse ko hum “kona” bhi kahenge (chitra mein woh ek kona hai).
- Carry (haath ka): right hissa 10 ya zyada ho jaaye to uski dahai left hisse mein chali jaati hai. 3 | 12 → 4 | 2 = 42.
📏 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.
🔟 10 se guna = peeche ek 0 lagao
GUNA box mein dekha: 3 × 10 matlab 10 ko 3 baar jodo: 10 + 10 + 10 = 30. Isi tarah 46 × 10 matlab 46 ko 10 baar jodna. 46 mein 4 dahai aur 6 ikai hain. 10 baar lene pe 6 ikai ban jaati hain 6 dahai (60), aur 4 dahai ban jaati hain 4 saikde (400). Kul 400 + 60 = 460.
Aasaan niyam: kisi poore number ko 10 se guna karna ho to uske peeche (right mein) ek 0 likh do. Har digit ek jagah left khisak jaata hai, aur ikai ki khaali jagah mein 0 aa jaata hai.
| Number | × 10 | Kya hua |
|---|---|---|
| 7 | 70 | 7 ikai → 7 dahai |
| 46 | 460 | 4 dahai → 4 saikde, 6 ikai → 6 dahai |
| 128 | 1280 | har digit ek jagah left, peeche 0 |
| 365 | 3650 | har digit ek jagah left, peeche 0 |
🎯 Base kya hai? (Paas wala round number)
Round number woh hai jiske peeche (right mein) sirf zero hon: 10, 100, 1000. Aaj ki trick mein inhe base kehte hain. Base matlab “ghar” ya “nishaana”: woh round number jiske paas hamare dono numbers baithe hain.
- 8 aur 7: dono 10 ke paas hain (10 se thoda kam). Base = 10.
- 12 aur 13: dono 10 ke paas hain (10 se thoda zyada). Base = 10.
- 97 aur 96: dono 100 ke paas. Base = 100.
- 104 aur 107: dono 100 ke paas (thoda zyada). Base = 100.
- 997 aur 996: dono 1000 ke paas. Base = 1000.
Base kaise chunein? Number ko dekho aur socho: “Yeh 10, 100 ya 1000 mein se kiske sabse paas hai?” 8 to 10 se sirf 2 door hai, isliye 10. 97 to 100 se sirf 3 door, isliye 100. Dono numbers ka base ek hi hona chahiye.
| Base | Base mein kitne zero | Jawab ka left hissa kya ginta hai |
|---|---|---|
| 10 | 1 zero | kitne dahai (10 wale) |
| 100 | 2 zero | kitne saikde (100 wale) |
| 1000 | 3 zero | kitne hazaar (1000 wale) |
“Base mein kitne zero” wali baat yaad rakhna. Aage “right hissa kitne digit ka” isi se tay hoga.
📏 Base 10 se kitna kam, kitna zyada?
Har number ke liye ek chhota sawaal: “Base tak pahunchne mein kitna bacha?” ya “Base se kitna aage nikal gaya?”
- Kitna kam (number base se chhota ho) = base − number. Matlab number ko base banne ke liye kitna aur chahiye.
- Kitna zyada (number base se bada ho) = number − base. Matlab number base se kitna aage hai.
| Number | Base 10 se | Kaise nikala |
|---|---|---|
| 9 | 1 kam | 10 − 9 = 1 |
| 8 | 2 kam | 10 − 8 = 2 (8 se 9, 10: do kadam) |
| 7 | 3 kam | 10 − 7 = 3 |
| 6 | 4 kam | 10 − 6 = 4 |
| 12 | 2 zyada | 12 − 10 = 2 |
| 13 | 3 zyada | 13 − 10 = 3 |
| 15 | 5 zyada | 15 − 10 = 5 |
Chhota raasta: 10 se zyada wale (11 se 19) ka “kitna zyada” bas uska ikai digit hai: 13 → 3, 17 → 7. Kyunki 13 = 10 + 3.
🧱 Deewar ( | ), right hisse ke digit, aur carry
Is trick mein jawab do hisson mein banta hai: left hissa | right hissa. Beech ki khadi lakeer ( | ) ko “deewar” samjho. Yeh sirf hamare samjhne ke liye hai; asli jawab mein deewar nahi likhte, dono hisse saath-saath likh dete hain.
Base 10 mein 1 zero hai. Isliye right hisse ko jawab mein sirf 1 khaana (ikai) milta hai, aur left hissa dahai ginta hai.
- 5 | 6 matlab 5 dahai aur 6 ikai: 50 + 6 = 56.
- 15 | 6 matlab 15 dahai aur 6: 150 + 6 = 156.
Right hissa 10 ya usse bada aaye to? (Carry) Ikai ke khaane mein sirf ek digit baith sakta hai. Jaise 3 | 12: 12 mein ek poori dahai (10) aur 2 ikai hain. Woh ek dahai left wale dahai ke dher mein chali jaati hai: 3 + 1 = 4 dahai, aur ikai mein 2 bacha. Jawab 42. Place value se pakka: 3 dahai + 12 = 30 + 12 = 42 ✅. Yeh wahi “haath ka 1” (carry) hai jo jod mein seekha tha.
- 2 | 16 → 16 mein 1 dahai aur 6: 2 + 1 = 3 → 36 (20 + 16 = 36).
- 19 | 20 → 20 mein 2 dahai aur 0: 19 + 2 = 21 → 210 (190 + 20 = 210).
Pehle guna, phir jod (zaroori niyam): jab ek hi line mein × aur + dono hon, to pehle × (guna) karo, phir + (jod). Jaise 5 × 10 + 6: pehle 5 × 10 = 50, phir 50 + 6 = 56. (Agar pehle 10 + 6 = 16 karke 5 × 16 karte to 80 aata, jo galat hai.) Is post mein “left × base + right” isi niyam se padhna.
🔁 Chhota sa warm-up
- 10 − 7 = ?
- 2 × 3 = ?
- 50 + 6 = ?
Answers dekho
- 3
- 6
- 56
Teeno aa gaye? Yahi milkar 8 × 7 = 56 banta hai!
— 📌 charumam.com
🎬 Kahani: Pahaade Se Darne Wali Tara
Tara ko 2, 3, 4, 5 ke pahaade to yaad the, par 6, 7, 8, 9 ke pahaade sunke usse dar lagta tha. Test mein sawaal aaya: 8 × 7. Usne ungliyon pe 7, 14, 21… ginna shuru kiya, aur time nikalta gaya. 😟
Ghar aakar Didi ne kaha: “Pahaada bhoolo. Bas dekho, 8 aur 7, 10 se kitne door hain. 8 ko 10 banne ke liye 2 chahiye, 7 ko 3. Ab 8 − 3 = 5, aur 2 × 3 = 6. Jawab 56!”
Tara ne 7, 14, 21, 28, 35, 42, 49, 56 gin ke check kiya: “Sach mein 56!” Phir usne 9 × 6 try kiya: 1 kam, 4 kam → 9 − 4 = 5, 1 × 4 = 4 → 54. “Yeh to jaadu hai!”
CharuMam: “Jaadu nahi, Base Method hai. Aaj seekhenge kaise karte hain, aur chitra se dekhenge kyun sahi aata hai.” 🎯
— 📌 charumam.com
🪄 Trick Step by Step: Base 10: Kitna Kam, Tirchha Ghatao, Chhota Guna
💡 Is post ki ek badi baat: Do numbers jo 10 ke paas hon (dono thode kam): left hissa = ek number − doosre ka kitna kam, right hissa = dono ke “kitna kam” ka guna. Jawab = left dahai + right. 8 × 7: 8 − 3 = 5, 2 × 3 = 6 → 56.
Step 1: Base chuno
Sawaal: 8 × 7. Dono numbers 10 ke paas hain (10 se thode kam). To base = 10. Base 10 mein 1 zero hai, to right hissa 1 digit ka hoga.
Step 2: Har number ka “kitna kam” nikaalo
8 → 10 − 8 = 2 kam. 7 → 10 − 7 = 3 kam. Copy pe aise likho:
Step 3: Left hissa: tirchha ghatao
Ek number mein se doosre number ka kitna kam ghatao: 8 − 3 = 5. (3 to 7 ka kitna kam tha.) Doosri taraf se bhi kar sakte ho: 7 − 2 = 5. Dono baar same aata hai, hamesha! Kyun? 8 − 3 aur 7 − 2 dono asal mein “10 mein se 2 bhi kam, 3 bhi kam” hain: 10 − 2 − 3 = 5.
Step 4: Right hissa: dono “kitna kam” ka guna
2 × 3 = 6 (3 + 3 = 6). Base 10 mein right hisse ko 1 khaana milta hai, aur 6 ek hi digit hai, to theek.
Step 5: Dono hisse saath likho
5 | 6: left hissa 5 matlab 5 dahai (50), right hissa 6 ikai. 5 × 10 + 6 = 50 + 6 = 56 (pehle guna, phir jod). To 8 × 7 = 56 ✅
10 se kam wale jode (pahaade ki zaroorat nahi!)
| Sawaal | Base se doori | Left (tirchha) | Kona (right) | Jawab |
|---|---|---|---|---|
| 9 × 9 | 1 kam, 1 kam | 9 − 1 = 8 | 1 × 1 = 1 | 8 | 1 → 81 |
| 9 × 8 | 1 kam, 2 kam | 9 − 2 = 7 | 1 × 2 = 2 | 7 | 2 → 72 |
| 9 × 7 | 1 kam, 3 kam | 9 − 3 = 6 | 1 × 3 = 3 | 6 | 3 → 63 |
| 8 × 8 | 2 kam, 2 kam | 8 − 2 = 6 | 2 × 2 = 4 | 6 | 4 → 64 |
| 8 × 7 | 2 kam, 3 kam | 8 − 3 = 5 | 2 × 3 = 6 | 5 | 6 → 56 |
| 9 × 6 | 1 kam, 4 kam | 9 − 4 = 5 | 1 × 4 = 4 | 5 | 4 → 54 |
| 7 × 7 | 3 kam, 3 kam | 7 − 3 = 4 | 3 × 3 = 9 | 4 | 9 → 49 |
| 8 × 6 | 2 kam, 4 kam | 8 − 4 = 4 | 2 × 4 = 8 | 4 | 8 → 48 |
| 7 × 6 | 3 kam, 4 kam | 7 − 4 = 3 | 3 × 4 = 12 | 3 | 12 → 4 | 2 → 42 |
| 6 × 6 | 4 kam, 4 kam | 6 − 4 = 2 | 4 × 4 = 16 | 2 | 16 → 3 | 6 → 36 |
Right hissa 10 ya zyada? Carry karo
7 × 6: 7 → 3 kam, 6 → 4 kam. Left: 7 − 4 = 3 (ya 6 − 3 = 3). Right: 3 × 4 = 12. Par base 10 mein right ko sirf 1 khaana milta hai, aur 12 mein do digit hain! 12 = 1 dahai + 2. Woh 1 dahai left mein jodo: 3 + 1 = 4. Right mein 2 bacha. Jawab 4 | 2 = 42.
Place value se pakka: 3 dahai + 12 = 30 + 12 = 42 ✅. Ginti se: 6, 12, 18, 24, 30, 36, 42 (6 ko 7 baar) ✅.
10 se zyada wale: 12 × 13
Ab dono numbers 10 se thode zyada. Same trick, bas left mein ghatane ki jagah jodna:
- 12 → 12 − 10 = 2 zyada. 13 → 13 − 10 = 3 zyada.
- Left: ek number mein doosre ka kitna zyada jodo: 12 + 3 = 15 (ya 13 + 2 = 15, same).
- Right: 2 × 3 = 6.
- Jawab: 15 | 6 → 15 dahai + 6 = 150 + 6 = 156.
Check: 12 ko 13 baar = 12 ko 10 baar + 12 ko 3 baar = 120 + 36 = 156 ✅.
| Sawaal | Base se doori | Left (tirchha) | Kona (right) | Jawab |
|---|---|---|---|---|
| 11 × 12 | 1 zyada, 2 zyada | 11 + 2 = 13 | 1 × 2 = 2 | 13 | 2 → 132 |
| 12 × 12 | 2 zyada, 2 zyada | 12 + 2 = 14 | 2 × 2 = 4 | 14 | 4 → 144 |
| 11 × 15 | 1 zyada, 5 zyada | 11 + 5 = 16 | 1 × 5 = 5 | 16 | 5 → 165 |
| 13 × 13 | 3 zyada, 3 zyada | 13 + 3 = 16 | 3 × 3 = 9 | 16 | 9 → 169 |
| 12 × 14 | 2 zyada, 4 zyada | 12 + 4 = 16 | 2 × 4 = 8 | 16 | 8 → 168 |
| 11 × 19 | 1 zyada, 9 zyada | 11 + 9 = 20 | 1 × 9 = 9 | 20 | 9 → 209 |
| 13 × 14 | 3 zyada, 4 zyada | 13 + 4 = 17 | 3 × 4 = 12 | 17 | 12 → 18 | 2 → 182 |
| 14 × 15 | 4 zyada, 5 zyada | 14 + 5 = 19 | 4 × 5 = 20 | 19 | 20 → 21 | 0 → 210 |
| 15 × 15 | 5 zyada, 5 zyada | 15 + 5 = 20 | 5 × 5 = 25 | 20 | 25 → 22 | 5 → 225 |
Dekho: 15 × 15 = 225 aata hai, bilkul Post 6.1 jaisa (1 × 2 = 2, peeche 25)! Do alag tricks, ek hi jawab.
Yaad rakhne ka tareeka: numbers base se kam hain to left mein ghatao; base se zyada hain to left mein jodo. Right mein hamesha guna.
Ek number 10 se kam aur ek zyada (jaise 12 × 8)? Uske liye thoda alag niyam hai; woh Chapter 8 mein. Aaj sirf dono kam, ya dono zyada.
🆘 Atak gaye? Aise socho
- Kitna kam yaad nahi? Number se 10 tak aage gino: 7 se 8, 9, 10 → 3 kadam = 3 kam.
- Left mein kiska ghatau? Hamesha doosre number ka kam (tirchha). 8 × 7 mein 8 − 3, ya 7 − 2. Apna hi mat ghatao (8 − 2 galat).
- Right 10 ya zyada aaya? Uski dahai left mein jodo: 3 | 12 → 4 | 2.
- Check: chhota number utni baar jodo (7, 14, 21, …), ya andaaza: 8 × 7 to 10 × 7 = 70 se thoda kam hona chahiye.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Tiles se samjho. 8 × 7 matlab 8 column, har column mein 7 tile (chhote chaukor dabbe). Kul tile = 56. Ab dekho base method ke 5 aur 6 kahan se aate hain (chitra):
- 7 tile wale column ko 10 ka banana hai, to har column ko 3 tile aur chahiye (3 hai 7 ka kitna kam).
- Isliye 8 column mein se right ke 3 column (naarangi) kaat lo. Left mein 8 − 3 = 5 neele column bache. Yahi tirchha ghatana hai!
- Kaati hui naarangi patti (3 column, har ek mein 7 tile) ko ghuma kar neele column ke upar laga do. Ab woh 7 tile lambi aur 3 line oonchi hai. Har neele column ke upar 3 naarangi tile aa gaye: har column ab 7 + 3 = 10 ka. To 5 column × 10 = 50 (5 dahai).
- Par patti 7 lambi thi aur neela hissa sirf 5 chauda. To patti ka 7 − 5 = 2 chauda aur 3 ooncha tukda (gulaabi) baahar nikla rehta hai: 2 × 3 = 6 tile. Dhyaan do: yeh 2 to 8 ka kitna kam hai, aur 3, 7 ka. Yahi right hissa hai!
Kul: 50 + 6 = 56. Koi tile na bani, na miti; bas jagah badli. Isliye trick hamesha sahi.
Aur 10 se zyada wale (12 × 13) kyun?
12 × 13 ke tiles ko 4 hisson mein baanto (neeche ka chitra, Post 6.3 jaisa): neela 10 × 10 = 100, naarangi patti 2 column × 10 = 20, hari patti 3 line × 10 = 30, aur gulaabi kona 2 × 3 = 6. Neela + naarangi milkar 12 column, har ek mein 10 tile = 12 dahai. Hari patti 3 dahai aur. To 12 + 3 = 15 dahai = 150: yahi left hissa (12 + 3)! Gulaabi kona 2 × 3 = 6: right hissa. Kul 150 + 6 = 156.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 9 × 7 = ?
Base 10. 9 → 1 kam, 7 → 3 kam. Left: 9 − 3 = 6 (ya 7 − 1 = 6). Right: 1 × 3 = 3. 6 | 3 → 63.
✔️ Normal tareeke se check: 7 ko 9 baar: 7 ko 10 baar = 70, usme se ek 7 kam: 70 − 7 = 63 ✅
Example 2: 6 × 7 = ? (carry wala)
6 → 4 kam, 7 → 3 kam. Left: 6 − 3 = 3 (ya 7 − 4 = 3). Right: 4 × 3 = 12. Right mein sirf 1 khaana, to 12 ki 1 dahai left mein: 3 + 1 = 4, right mein 2. 4 | 2 → 42.
✔️ Normal tareeke se check: 7 ko 6 baar, running total: 7, 14, 21, 28, 35, 42 ✅
Example 3: 13 × 14 = ? (10 se zyada, carry ke saath)
13 → 3 zyada, 14 → 4 zyada. Left: 13 + 4 = 17 (ya 14 + 3 = 17). Right: 3 × 4 = 12 → carry: 17 + 1 = 18, right mein 2. 18 | 2 → 182.
✔️ Normal tareeke se check: 13 ko 14 baar = 13 ko 10 baar + 13 ko 4 baar = 130 + 52 = 182 ✅ (13 ko 4 baar: 13, 26, 39, 52)
Example 4: 11 × 17 = ?
11 → 1 zyada, 17 → 7 zyada. Left: 11 + 7 = 18. Right: 1 × 7 = 7. 18 | 7 → 187.
✔️ Normal tareeke se check: Chapter 4 ki × 11 trick: 17 × 11 → 1, phir 1 + 7 = 8, phir 7 → 187 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabon mein is tareeke ko Nikhilam se joda jaata hai. Sutra ka poora naam “Nikhilam Navatashcaramam Dashatah” hai, mota-mota matlab: “sab 9 se, aur aakhri 10 se”. Yaad hai? Chapter 3 mein isi soch se 100 − 37 jaise sawaal kiye the: har digit ko 9 se poora, aakhri ko 10 se. Wahi “poora karna” yahan kitna kam nikaalne ka kaam karta hai (base 10 ke liye bas 10 − digit). Kitabein is guna wale tareeke ko “Nikhilam guna” bhi kehti hain. Hum naam se zyada tiles wali wajah yaad rakhenge: 3 column kaato, upar rakho, kona bacha.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Dono numbers 10 se thode kam (9 × 7, 8 × 6) | ✅ Haan | Pahaade ki zaroorat nahi: ek ghatana, ek chhota guna. |
| Dono 10 se thode zyada (12 × 13, 11 × 18) | ✅ Haan | Left mein jodo, right mein guna. |
| Ek 10 se kam, ek zyada (12 × 8) | ⚠️ Chapter 8 | Right hissa ghatana padta hai; Ch 8 mein seekhenge. |
| 10 se bahut door (3 × 4, 2 × 9) | ❌ Nahi | Kitna kam bahut bada (7, 8); seedha pahaada aasaan. |
| Pahaada pakka yaad hai (9 × 9) | ⚠️ Jo tez lage | Yaad hai to seedha bolo; trick check ke liye kaam aayegi. |
| Teacher ne steps maange | ❌ Answer sheet pe nahi | Answer sheet pe seedha tareeka likho; kachchi copy (rough) mein trick se check karo. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Apna hi “kitna kam” ghata diya
Sawaal: 8 × 7
❌ Galat: 8 − 2 = 6 (2 to 8 ka hi kam hai), right 6 → 66.
✅ Sahi: tirchha: 8 − 3 = 5 (3 hai 7 ka kam) → 56. Check: 7 ko 8 baar: 7, 14, 21, 28, 35, 42, 49, 56. 66 nahi aata.
Galti 2: Right mein jod kar diya
Sawaal: 8 × 7
❌ Galat: right 2 + 3 = 5 → 55.
✅ Sahi: right mein guna: 2 × 3 = 6 → 56.
Galti 3: Carry bhool gaye
Sawaal: 7 × 6
❌ Galat: 3 | 12 ko seedha “312” likh diya.
✅ Sahi: right ko 1 hi khaana: 12 ki 1 dahai left mein → 4 | 2 = 42. Andaaza: 7 aur 6 dono 10 se chhote hain, isliye 7 × 6 to 10 × 10 = 100 se bhi chhota hai, 312 ho hi nahi sakta.
Galti 4: 10 se zyada pe ghata diya
Sawaal: 12 × 13
❌ Galat: 12 − 3 = 9, right 6 → 96.
✅ Sahi: base se zyada hain to jodo: 12 + 3 = 15 → 156. Andaaza: 12 × 13 to 10 × 10 = 100 se bada hona chahiye; 96 chhota hai.
🧠 Rule of thumb: Kam hain to tirchha ghatao, zyada hain to tirchha jodo; right mein hamesha guna; base 10 mein right ko 1 khaana, zyada ho to carry.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal: pehle 10 se kam wale, phir 10 se zyada wale. Target: 3 minute.
- 9 × 9 = ?
- 9 × 8 = ?
- 8 × 8 = ?
- 9 × 7 = ?
- 8 × 7 = ?
- 7 × 7 = ?
- 9 × 6 = ?
- 8 × 6 = ?
- 7 × 6 = ?
- 6 × 6 = ?
- 11 × 12 = ?
- 12 × 13 = ?
- 13 × 13 = ?
- 14 × 12 = ?
- 15 × 13 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 81
- 72
- 64
- 63
- 56
- 49
- 54
- 48
- 42
- 36
- 132
- 156
- 169
- 168
- 195
Kaise kiya (kuch): 6 × 6: 4 kam, 4 kam → 6 − 4 = 2 | 4 × 4 = 16 → carry: 3 | 6 → 36. 14 × 12: 14 + 2 = 16 | 4 × 2 = 8 → 168. 15 × 13: 15 + 3 = 18 | 5 × 3 = 15 → carry: 19 | 5 → 195.
— 📌 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.
- 9 × 8 = ?
- 7 × 8 = ?
- 6 × 9 = ?
- 7 × 7 = ?
- 6 × 8 = ?
- 11 × 13 = ?
- 12 × 12 = ?
- 14 × 13 = ?
- 11 × 18 = ?
- 15 × 14 = ?
| 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
- 72
- 56
- 54
- 49
- 48
- 143
- 144
- 182
- 198
- 210
Dhyaan: 15 × 14: 15 + 4 = 19 | 5 × 4 = 20 → 20 ki 2 dahai left mein: 21 | 0 → 210.
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. 8 × 7 base method se: left hissa kya hai?
Jawab aur kaaran dekho
Sahi jawab: (a) 5
- (a) sahi ✅: 8 − 3 = 5 (ya 7 − 2 = 5): ek number mein se doosre number ka kitna kam.
- (b) galat ❌: 6: 8 mein se apna hi kitna kam ghata diya: 8 − 2 = 6. (6 to right hissa bhi hai: 2 × 3 = 6.)
- (c) galat ❌: 15: dono numbers jod diye: 8 + 7 = 15. Left mein jodna nahi, tirchha ghatana hai.
- (d) galat ❌: 1: dono numbers ka farq le liya: 8 − 7 = 1. Farq nahi, doosre ka kitna kam ghatana hai.
Q2. 9 × 6 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 54
- (a) galat ❌: 45: left aur right ulte likh diye: 4 | 5 → 45. Left 5 hai, right 4.
- (b) galat ❌: 84: 9 mein se apna hi kitna kam ghata diya: 9 − 1 = 8 | 4 → 84.
- (c) galat ❌: 55: right mein guna ki jagah jod: 1 + 4 = 5 → 5 | 5 → 55.
- (d) sahi ✅: 1 kam, 4 kam: 9 − 4 = 5 | 1 × 4 = 4 → 54.
Q3. 7 ka base 10 se “kitna kam” kya hai?
Jawab aur kaaran dekho
Sahi jawab: (c) 3
- (a) galat ❌: 17: ghatane ki jagah jod diya: 10 + 7 = 17.
- (b) galat ❌: 10: base hi likh diya. Base 10 hai; kitna kam = 10 − 7.
- (c) sahi ✅: 10 − 7 = 3: 7 se 8, 9, 10 tak teen kadam.
- (d) galat ❌: 7: sawaal ka number hi likh diya. Kitna kam matlab 10 tak pahunchne mein kitna bacha.
Q4. 7 × 6 mein right hissa 12 aaya. Ab kya karein?
Jawab aur kaaran dekho
Sahi jawab: (b) 12 ki 1 dahai left mein jodo: 4 | 2 → 42
- (a) galat ❌: 15: poora 12 left mein daal diya: 3 + 12 = 15. Sirf 12 ki 1 dahai left mein jaati hai, 2 right mein rehta hai.
- (b) sahi ✅: Base 10 mein right ko 1 khaana. 12 ki 1 dahai left mein: 3 + 1 = 4 | 2 → 42. Check: 6 ko 7 baar: 6, 12, 18, 24, 30, 36, 42 ✅
- (c) galat ❌: 312: carry bhool kar 3 | 12 ko seedha saath likh diya: 3 | 12 → 312. Par 7 aur 6 dono 10 se chhote hain, isliye 7 × 6 to 10 × 10 = 100 se bhi chhota hai.
- (d) galat ❌: 12 chhodne se sirf 3 bachta, par 7 × 6 = 42 hai. 12 jawab ka hissa hai, chhoda nahi ja sakta.
Q5. 12 × 13 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 156
- (a) sahi ✅: 2 zyada, 3 zyada: 12 + 3 = 15 | 2 × 3 = 6 → 156.
- (b) galat ❌: 96: zyada wale mein bhi ghata diya: 12 − 3 = 9 | 6 → 96.
- (c) galat ❌: 126: left mein 12 hi utaar liya, 3 jodna bhool gaye: 12 | 6 → 126.
- (d) galat ❌: 166: 13 mein apna hi kitna zyada jod diya: 13 + 3 = 16 | 6 → 166.
Q6. Base method mein right hissa kaise nikalta hai?
Jawab aur kaaran dekho
Sahi jawab: (d) Dono “kitna kam/zyada” ka guna
- (a) galat ❌: Dono numbers ka guna (8 × 7) to poora sawaal hi hai; right hissa sirf chhota kona hai: 2 × 3 = 6.
- (b) galat ❌: Jod karne se 2 + 3 = 5 aata, aur 5 | 5 → 55 galat jawab banta (sahi 56).
- (c) galat ❌: Dono numbers jodne se 8 + 7 = 15 aata; yeh na left hai, na right.
- (d) sahi ✅: Jaise 8 × 7 mein 2 kam aur 3 kam: 2 × 3 = 6, yahi right hissa.
Q7. Kis sawaal pe base 10 trick SEEDHI (aaj wali) lagegi?
Jawab aur kaaran dekho
Sahi jawab: (c) 9 × 8
- (a) galat ❌: 3 aur 4, 10 se bahut door (7 kam, 6 kam). Seedha: 3 × 4 = 4 + 4 + 4 = 12, aasaan.
- (b) galat ❌: 23 aur 27, 10 se bahut door (13 aur 17 zyada). Inki apni trick Post 6.3 mein hai (dahai same, ikai ka jod 3 + 7 = 10).
- (c) sahi ✅: Dono 10 se thode kam: 1 kam, 2 kam → 9 − 2 = 7 | 1 × 2 = 2 → 72.
- (d) galat ❌: 12 upar (2 zyada), 8 neeche (2 kam): ek upar ek neeche, yeh Chapter 8 ka type hai.
Q8. 14 × 15 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 210
- (a) galat ❌: 200: left mein sirf 1 joda: 19 + 1 = 20 | 0 → 200. Par 20 mein 2 dahai hain: 19 + 2 = 21.
- (b) sahi ✅: 4 zyada, 5 zyada: 14 + 5 = 19 | 4 × 5 = 20 → 20 ki 2 dahai left mein: 21 | 0 → 210.
- (c) galat ❌: 1920: carry bhool kar 19 | 20 ko seedha saath likh diya: 19 | 20 → 1920.
- (d) galat ❌: 190: 20 ka sirf 0 likha, uski 2 dahai left mein le jaana bhool gaye: 19 | 0 → 190.
Q9. Chitra mein 8 × 7 ke 3 naarangi column kyun kaate?
Jawab aur kaaran dekho
Sahi jawab: (a) Taaki 7 tile wale column 10 ke ban jaayein (7 ka kitna kam 3 hai)
- (a) sahi ✅: Patti ghuma kar upar rakhne se har column 7 + 3 = 10 tile ka ho gaya.
- (b) galat ❌: 3 chhota hai, par chitra mein wajah yeh hai ki har 7 tile wale column ko 10 banane ke liye 3 tile chahiye.
- (c) galat ❌: 8 − 5 = 3 sach hai, par 5 to kaatne ke baad bacha. 3 column isliye kaate kyunki 7 ko 10 banne mein 3 chahiye.
- (d) galat ❌: Sundar dikhna wajah nahi; wajah hai 7 + 3 = 10.
Q10. 6 × 6 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 36
- (a) galat ❌: 216: carry bhool kar 2 | 16 ko seedha saath likh diya: 2 | 16 → 216.
- (b) galat ❌: 26: 16 ka sirf 6 likha, uski 1 dahai left mein jodna bhool gaye: 2 | 6 → 26.
- (c) galat ❌: 46: left mein 2 dahai jod di: 2 + 2 = 4 | 6 → 46. 16 mein sirf 1 dahai hai.
- (d) sahi ✅: 4 kam, 4 kam: 6 − 4 = 2 | 4 × 4 = 16 → 16 ki 1 dahai left mein: 3 | 6 → 36.
— 📌 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. 19 × 19 = ? (right hissa bahut bada)
Solution dekho
19 → 9 zyada. Left: 19 + 9 = 28. Right: 9 × 9 = 81. Base 10 mein right ko 1 khaana, aur 81 mein 8 dahai hain. 8 dahai left mein: 28 + 8 = 36, right mein 1. 36 | 1 → 361.
Check: 19 ko 19 baar = 19 ko 20 baar se ek 19 kam = 380 − 19 = 361 ✅ (19 ko 2 baar = 38, peeche 0 lagao to 380)
Q2. 8 × 7 aur 12 × 13, dono ka right hissa 6 kyun hai?
Solution dekho
8 × 7 mein: 2 kam aur 3 kam → 2 × 3 = 6. 12 × 13 mein: 2 zyada aur 3 zyada → 2 × 3 = 6. Dono mein 10 se doori 2 aur 3 hai, isliye kona (2 × 3) same! Bas left alag: 8 − 3 = 5, aur 12 + 3 = 15. Jawab 56 aur 156.
Check: 7 ko 8 baar = 56 ✅, 12 ko 13 baar = 120 + 36 = 156 ✅
Q3. Bagiche mein 16 qataar (line) hain, har qataar mein 12 paudhe. Kul paudhe?
Solution dekho
16 × 12: 6 zyada, 2 zyada. Left: 16 + 2 = 18. Right: 6 × 2 = 12 → carry: 18 + 1 = 19, right 2. 19 | 2 → 192 paudhe.
Check: 16 ko 12 baar = 16 ko 10 baar + 16 ko 2 baar = 160 + 32 = 192 ✅
Q4. Riya ne 4 × 3 pe base 10 trick lagani chaahi. Kya hoga?
Solution dekho
4 → 6 kam, 3 → 7 kam. Left: 4 − 7. Par 4 mein se 7 nikal hi nahi sakte (4 to 7 se chhota hai)! Right: 6 × 7 = 42, woh bhi bada. Trick yahan kaam ki nahi. Seedha: 4 × 3 = 3 + 3 + 3 + 3 = 12.
Seekh: trick tabhi jab numbers base ke paas hon (kitna kam chhota ho).
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Guna, pahaade aur area (lambai × chaudai) ke sawaal mein jaldi check. |
| Maths Olympiad | Pattern aur “kyun” wale sawaal: 8 × 7 aur 12 × 13 ka kona same kyun? |
| NTSE / MAT | Mental calculation: bina copy ke tez guna. |
| SSC / Bank (aage) | Simplification mein 9 × 8, 13 × 14 jaise guna seconds mein. |
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. Mental calculation = bina copy-pencil ke, mann mein hisaab karna. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Roz 6 se 9 tak ke jode (9 × 9, 8 × 7, 7 × 6, …) base method se bolo: “do kam, teen kam, paanch, chhe: chhappan!” Ek hafte mein pahaade ka dar khatam. Aur yeh soch (base se kitna door) agle post mein 97 × 96 jaise bade numbers ka darwaaza kholegi! 🎯
— 📌 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)
Base 10. 8 → 2 kam, 7 → 3 kam. Left: 8 − 3 = 5. Right: 2 × 3 = 6. Jawab 5 | 6 = 56 ✅
| 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 pahaade yaad karna ab zaroori nahi?
Pahaade bahut kaam ke hain, unhe yaad rakhna achha hai! Yeh trick unhe pakka karne aur bhool jaane pe jaldi nikaalne ka raasta hai.
2. Left hissa dono taraf se same kyun aata hai?
Kyunki 8 − 3 aur 7 − 2 dono “10 − 2 − 3” hi hain. Chitra mein bhi: kaate gaye column hamesha doosre number ke kitna kam jitne.
3. Kya 5 × 5 pe chalegi?
Chalegi: 5 kam, 5 kam → 5 − 5 = 0 | 5 × 5 = 25 → carry: 2 | 5 → 25. Sahi! Par itne door numbers pe seedha pahaada hi aasaan.
4. Agle post mein kya hai?
Post 7.2: base 100: 97 × 96 jaise bade guna, jahan right hisse ko 2 khaane milte hain.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Base = paas wala round number; aaj base 10.
- Kitna kam = 10 − number; kitna zyada = number − 10.
- Left: tirchha ghatao (kam wale) ya tirchha jodo (zyada wale).
- Right: dono kam/zyada ka guna; base 10 mein 1 khaana.
- Right 10 ya zyada → uski dahai left mein (7 × 6 = 42).
- 8 × 7 = 56, 12 × 13 = 156; check baar-baar jod se.
— charumam.com 🎯
👉 Aage Kya?
Ab base 100: Post 7.2 mein 97 × 96 jaise guna, jahan kitna kam Chapter 3 ki trick se nikalega, aur right hisse ko 2 khaane milenge!
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
