Post 8.1 mein 12 × 8 jaise guna kiye: ek 10 se upar, ek neeche, aur kona minus. Aaj wahi 100 ke paas: 103 × 97, 104 × 98, 108 × 95. Teen purani cheezein milengi: 2 khaane (Post 7.2), minus kona (8.1) aur 100 se ghatana (Chapter 3). Jawab 4 ya 5 digit ka, phir bhi mann mein!
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 103 × 97: 97 ko 103 baar = 97 ko 100 baar + 97 ko 3 baar = 9700 + 291 = 9991. (97 ko 3 baar: 97, 194, 291.)
Chal jaata hai, par 97 × 3 aur 4-digit jod. Base method mein sirf 103 − 3 aur 3 × 3.
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
103 × 97 = 9991
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: 100 se doori (kitna kam/zyada), 2 khaane wala niyam, minus kona aur 1 saikde ka udhaar. Sab neeche ke boxes mein; laal box “Minus wala right hissa (base 100)” zaroor dekho. Naye shabd:
📖 Shabd jo is post mein aayenge
- Saikda udhaar: base 100 mein left hissa saikde ginta hai. Minus kona ghatane ke liye left se 1 saikda (100) udhaar lo.
- 100 − kona: udhaar ke baad right hissa: 100 mein se kona ghatao. Chapter 3 ki trick: dahai 9 se poori, ikai 10 se. 100 − 09 = 91.
- Left − 1: udhaar dene ke baad left 1 kam ho jaata hai: 100 → 99.
- Do saikde udhaar: kona 100 se bada ho (jaise 120) to 2 saikde (200) udhaar: left − 2, right 200 − kona.
📏 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.
💯 100 se guna = peeche do 0 lagao
100 = 10 × 10 (10 ko 10 baar jodo: 10, 20, 30, … 100). Isliye 100 se guna karna matlab do baar 10 se guna. Har baar 10 se guna pe peeche ek 0 lagta hai (upar wala box), to 100 se guna pe do 0:
36 → (× 10) 360 → (× 10) 3600
Place value se: 36 × 100 matlab 36 saikde (36 sau). 36 sau = 3600 (padho: teen hazaar chhe sau).
| Number | × 100 |
|---|---|
| 7 | 700 |
| 36 | 3600 |
| 37 | 3700 |
| 124 | 12400 (padho: barah hazaar chaar sau) |
Bade number padhna: 12400 mein right se paanchvi jagah Das hazaar (10000 wale) hai. 12400 = 1 das hazaar + 2 hazaar + 4 saikde, yaani 10000 + 2000 + 400.
🎯 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 100 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.
100 se kitna kam? Chapter 3 wali trick: Post 3.1 mein seekha tha ki 100 se ghatane ke liye dahai digit ko 9 se poora karo aur ikai digit ko 10 se poora karo. 100 − 97: dahai 9 → 9 − 9 = 0, ikai 7 → 10 − 7 = 3. Jawab 03, yaani 3. Ulti ginti se bhi: 97 se 98, 99, 100: teen kadam.
| Number | Base 100 se | Kaise nikala |
|---|---|---|
| 99 | 1 kam | 100 − 99 = 1 |
| 97 | 3 kam | 9 − 9 = 0, 10 − 7 = 3 → 03 |
| 96 | 4 kam | 100 − 96 = 4 |
| 92 | 8 kam | 100 − 92 = 8 |
| 88 | 12 kam | 9 − 8 = 1, 10 − 8 = 2 → 12 |
| 104 | 4 zyada | 104 − 100 = 4 |
| 112 | 12 zyada | 112 − 100 = 12 |
Chhota raasta: 100 se zyada wale (101 se 120 jaise) ka “kitna zyada” bas uske aakhri do digit hain: 107 → 07 = 7, 112 → 12. Kyunki 112 = 100 + 12.
🧱 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 100 mein 2 zero hain. Isliye left hissa kitne saikde ginta hai, aur right hisse ko jawab mein do khaane milte hain. Niyam:
Right hisse mein digit = base ke zero (2)
- Right chhota pade (kam digit) → aage 0 bharo.
- Right bada pade (zyada digit) → sabse left wala extra hissa left hisse mein jodo (carry).
- 93 | 12: 12 mein pehle se do digit hain. 93 saikde + 12 = 9300 + 12 = 9312.
- 95 | 6: 6 sirf ek digit hai. Use 06 likho: 0 dahai mein, 6 ikai mein. 95 saikde + 6 = 9500 + 6 = 9506. Agar 0 bhool gaye to “956” ban jaata, jo 9506 se bahut chhota hai (galat!). Yeh bilkul Post 6.3 wala 09 hai.
- Carry: 77 | 132: 132 mein teen digit, par jagah sirf do. 132 = 1 saikda + 32. Woh 1 saikda left ke saikdon mein jaata hai: 77 + 1 = 78 → 78 | 32 = 7832. Pakka: 7700 + 132 = 7832 ✅.
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.
➖ Minus wala right hissa aur udhaar (base 100)
Is chapter mein ek number base se upar hoga aur doosra neeche. Tab right hissa (kitna zyada × kitna kam) jodna nahi, ghatana hota hai. Ise hum − (minus) nishaan se dikhate hain. “−4” ko bolo “minus 4”, matlab “4 nikaalna hai”. Yeh koi naya number nahi, bas ek yaad-dilaane wala nishaan hai: “isko ghatana mat bhoolna!”
Udhaar ki yaad (Post 3.1): ghatane mein jab kisi jagah se kuch nikaalna ho aur wahan kam ho, to left wali jagah se 1 bundle udhaar lete hain. Jaise 1 dahai = 10 ikai, 1 saikda = 100.
Example: 100 | −09 (yeh 103 × 97 mein aayega). Pehle dhyaan: base 100 mein 2 zero, to right hissa do digit ka: 9 → 09. Matlab: 100 saikde mein se 9 nikaalo.
- Udhaar: 100 saikde mein se 1 saikda udhaar lo. Left mein 99 saikde bache.
- Woh 1 saikda = 100. Ab 100 − 09 nikaalo, Chapter 3 ki trick se: dahai 0 → 9 − 0 = 9, ikai 9 → 10 − 9 = 1. To 91.
- Jawab: 99 | 91 = 9991. Pakka: 9900 + 91 = 9991, aur 10000 − 9 = 9991 ✅.
Chhota yaad: minus wala right hissa ho to left mein se 1 ghatao, aur right ki jagah (100 − right) likho. Jaise 103 | −40 → 102 | 60 (yeh 108 × 95 mein aata hai).
🔁 Chhota sa warm-up
- 103 − 3 = ?
- 100 − 9 = ?
- 9900 + 91 = ?
Answers dekho
- 100
- 91
- 9991
Teeno aa gaye? Yahi milkar 103 × 97 = 9991!
— 📌 charumam.com
🎬 Kahani: Das Hazaar Se Sirf 9 Kam
Meena ke school ke 103 bachche picnic pe gaye, aur har ek ne 97 rupaye ka ticket liya. Teacher ne poochha: “Kul kitne rupaye jama hue?”
Arjun ne turant kaha: “Lagbhag 100 × 100 = 10000.” Teacher: “Lagbhag nahi, poora batao.”
Meena ne socha: 103 → 3 zyada, 97 → 3 kam. Ek upar ek neeche! Left: 103 − 3 = 100. Kona 3 × 3 = 9, nikaalna hai. 100 saikde = 10000, usme se 9: 9991!
Teacher: “Bilkul! 10000 se sirf 9 kam.” Aaj seekhenge yeh har baar kaise karna hai, chahe kona 09 ho ya 120. 🔀
— 📌 charumam.com
🪄 Trick Step by Step: Base 100, Alag Taraf: Left Tirchha, Kona Minus, Saikda Udhaar
💡 Is post ki ek badi baat: Ek number 100 se upar, ek neeche: left = upar wala − neeche wale ka kam; kona = doori × doori, 2 khaane mein, aur minus. Phir left − 1 | 100 − kona. 103 × 97: 100 | −09 → 99 | 91 = 9991.
Step 1: Base, taraf, khaane
Sawaal: 103 × 97. Base 100 (2 zero → 2 khaane). 103 upar, 97 neeche: alag taraf, kona minus hoga.
Step 2: Dooriyan
103 → 3 zyada. 97 → 3 kam.
Step 3: Left: tirchha
103 − 3 = 100 (3 hai 97 ka kam). Check: 97 + 3 = 100 ✅.
Step 4: Kona: guna, 2 khaane, minus
3 × 3 = 9 → 2 khaane: 09. Alag taraf, to −09. Ab: 100 | −09, matlab 100 saikde (10000) mein se 9 nikaalo.
Step 5: Udhaar
Left se 1 saikda udhaar: left 100 − 1 = 99. Woh 1 saikda = 100; usme se 09 nikaalo (Chapter 3: 9 − 0 = 9, 10 − 9 = 1): 91. Jawab 99 | 91 = 9991 ✅. (Seedha: 10000 − 9 = 9991, same.)
Aur jode (100 ke paas, alag taraf)
| Sawaal | Base se doori | Left (tirchha) | Kona (right) | Jawab |
|---|---|---|---|---|
| 102 × 98 | 2 zyada, 2 kam | 102 − 2 = 100 | 2 × 2 = 4, ghatao | 100 | −04 → 99 | 96 → 9996 |
| 105 × 95 | 5 zyada, 5 kam | 105 − 5 = 100 | 5 × 5 = 25, ghatao | 100 | −25 → 99 | 75 → 9975 |
| 104 × 97 | 4 zyada, 3 kam | 104 − 3 = 101 | 4 × 3 = 12, ghatao | 101 | −12 → 100 | 88 → 10088 |
| 108 × 95 | 8 zyada, 5 kam | 108 − 5 = 103 | 8 × 5 = 40, ghatao | 103 | −40 → 102 | 60 → 10260 |
| 106 × 99 | 6 zyada, 1 kam | 106 − 1 = 105 | 6 × 1 = 6, ghatao | 105 | −06 → 104 | 94 → 10494 |
| 101 × 98 | 1 zyada, 2 kam | 101 − 2 = 99 | 1 × 2 = 2, ghatao | 99 | −02 → 98 | 98 → 9898 |
| 112 × 96 | 12 zyada, 4 kam | 112 − 4 = 108 | 12 × 4 = 48, ghatao | 108 | −48 → 107 | 52 → 10752 |
| 103 × 91 | 3 zyada, 9 kam | 103 − 9 = 94 | 3 × 9 = 27, ghatao | 94 | −27 → 93 | 73 → 9373 |
Dhyaan do: 108 × 95 mein left 103 aaya aur kona 40: 103 | −40 → 102 | 60 → 10260. Left 100 se bada ho to jawab 5 digit ka, chhota ho to 4 digit ka.
Kona 100 se bada? 2 saikde udhaar
115 × 92: 15 zyada, 8 kam. Left: 115 − 8 = 107. Kona: 15 × 8 = 120, minus. Par 1 saikda (100) mein se 120 nahi nikal sakta! To 2 saikde (200) udhaar: left 107 − 2 = 105, right 200 − 120 = 80. Jawab 105 | 80 = 10580.
Seedha bhi: 107 saikde = 10700, 10700 − 120 = 10580 ✅.
Chhota niyam
Kona 100 se chhota ho to: left − 1 | 100 − kona. Bas! 106 × 99: 105 | −06 → 104 | 94 → 10494.
🆘 Atak gaye? Aise socho
- Kona ko 2 khaane? 9 → 09, phir minus: −09.
- 100 − kona? Chapter 3: dahai 9 se, ikai 10 se. 100 − 09 = 91, 100 − 28 = 72.
- Udhaar ke baad left? 1 kam: 100 → 99.
- Check: alag taraf ho to jawab “left saikde” se thoda kam. 103 × 97 → 10000 se thoda kam ✅.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Chitra (naap se nahi): 103 × 97 ek aayat: chaudai 103, oonchai 97. (Neeche chitra.)
- Oonchai 97 ko 100 banana hai, 3 aur chahiye. To right se 3 chaudi patti kaato. Neela hissa 103 − 3 = 100 chauda bacha.
- Patti (97 lambi) ko ghuma kar upar rakho. Neela hissa ab 100 ooncha: poora dabba 100 × 100 = 10000 hota…
- …par patti sirf 97 lambi hai aur neela 100 chauda! To upar right kone mein 3 × 3 = 9 ki jagah khaali (dotted).
- Asli area = 10000 − 9 = 9991.
Yahi 100 | −09 hai: poora dabba (100 saikde) minus khaali kona (9).
Ek aur: 108 × 95
5 chaudi patti kaato → neela 108 − 5 = 103 chauda. Upar rakho → 103 × 100 = 10300 ka dabba, par 8 × 5 = 40 khaali. 10300 − 40 = 10260.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 104 × 98 = ?
4 zyada, 2 kam. Left: 104 − 2 = 102. Kona: 4 × 2 = 8 → −08. 102 | −08 → 101 | 92 → 10192.
✔️ Normal tareeke se check: 104 ko 100 baar − 104 ko 2 baar = 10400 − 208 = 10192 ✅
Example 2: 107 × 96 = ?
7 zyada, 4 kam. Left: 107 − 4 = 103. Kona: 28 → −28. 103 | −28 → 102 | 72 → 10272.
✔️ Normal tareeke se check: 107 ko 100 baar − 107 ko 4 baar = 10700 − 428 = 10272 ✅
Example 3: 101 × 99 = ?
1 zyada, 1 kam. Left: 101 − 1 = 100. Kona: 1 → −01. 100 | −01 → 99 | 99 → 9999.
✔️ Normal tareeke se check: 101 ko 100 baar − 101 = 10100 − 101 = 9999 ✅
Example 4: 110 × 95 = ?
10 zyada, 5 kam. Left: 110 − 5 = 105. Kona: 50 → −50. 105 | −50 → 104 | 50 → 10450.
✔️ Normal tareeke se check: 110 ko 100 baar − 110 ko 5 baar = 11000 − 550 = 10450 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabein yahan bhi Nikhilam aur vinculum (digit ke upar ek chhoti line, jo batati hai ki yeh digit ghatana hai) ka use karti hain, aur phir use “theek” karti hain. Hamara udhaar wala tareeka wahi kaam karta hai, aur Chapter 3 ki “sab 9 se, aakhri 10 se” trick 100 − kona nikaalne mein seedhi kaam aati hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Ek 100 se thoda upar, ek neeche (103 × 97) | ✅ Haan | Left − 1 | 100 − kona. |
| Kona chhota (101 × 99, 104 × 98) | ✅ Bahut aasaan | Seconds mein. |
| Kona 100 se bada (115 × 92) | ⚠️ Chalega | 2 saikde udhaar, ya seedha ghatao. |
| Dono ek taraf (97 × 96) | ➡️ Chapter 7 | Kona jodo. |
| 100 se bahut door (130 × 70) | ❌ Nahi | Kona 30 × 30 khud ek bada guna hai, trick se aasaani nahi. Seedha todna behtar: 130 ko 70 baar = 100 ko 70 baar + 30 ko 70 baar. |
| Alag base (12 × 98) | ❌ Nahi | Seedha todo. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Kona jod diya
Sawaal: 103 × 97
❌ Galat: 100 | 09 → 10009.
✅ Sahi: alag taraf → minus: 9991. Andaaza: 103 × 97 mein left 100 saikde (10000) hai. Alag taraf mein chitra ka ek kona khaali rehta hai, isliye jawab left ke saikde (10000) se thoda kam hona chahiye. 10009 zyada hai, to galat.
Galti 2: Udhaar ke baad left wahi
Sawaal: 104 × 98
❌ Galat: 102 | 92 → 10292.
✅ Sahi: udhaar diya → left 1 kam: 101 | 92 → 10192.
Galti 3: Kona ko 1 khaana diya
Sawaal: 103 × 97
❌ Galat: kona 9 ko 10 mein se ghata ke right 1 likha → 99 | 1 → 991.
✅ Sahi: base 100 → 2 khaane: 100 − 09 = 91 → 9991.
Galti 4: 100 − kona galat
Sawaal: 107 × 96
❌ Galat: 100 mein se 28 ghatate waqt 82 likh diya (digits ulat gaye).
✅ Sahi: Chapter 3: 9 − 2 = 7, 10 − 8 = 2 → 72. Jawab 102 | 72 = 10272.
🧠 Rule of thumb: Alag taraf, base 100: left tirchha, kona 2 khaane mein minus, phir left − 1 | 100 − kona.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, sab ek 100 se upar ek neeche. Target: 5 minute.
- 101 × 99 = ?
- 102 × 98 = ?
- 103 × 98 = ?
- 104 × 99 = ?
- 105 × 97 = ?
- 102 × 96 = ?
- 106 × 98 = ?
- 107 × 97 = ?
- 103 × 94 = ?
- 108 × 96 = ?
- 105 × 95 = ?
- 109 × 98 = ?
- 104 × 93 = ?
- 112 × 97 = ?
- 115 × 92 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 9999
- 9996
- 10094
- 10296
- 10185
- 9792
- 10388
- 10379
- 9682
- 10368
- 9975
- 10682
- 9672
- 10864
- 10580
Kaise kiya (kuch): 104 × 93: 97 | −28 → 96 | 72 → 9672. 112 × 97: 109 | −36 → 108 | 64 → 10864. 109 × 98: 107 | −18 → 106 | 82 → 10682.
— 📌 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 × 98 = ?
- 102 × 99 = ?
- 103 × 97 = ?
- 104 × 96 = ?
- 106 × 94 = ?
- 105 × 98 = ?
- 107 × 99 = ?
- 110 × 98 = ?
- 103 × 95 = ?
- 108 × 99 = ?
| 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
- 9898
- 10098
- 9991
- 9984
- 9964
- 10290
- 10593
- 10780
- 9785
- 10692
Dhyaan: 110 × 98: 108 | −20 → 107 | 80 → 10780. 104 × 96: 100 | −16 → 99 | 84 → 9984.
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. 103 × 97 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 9991
- (a) galat ❌: 9909: udhaar ke baad right mein 100 − 09 ki jagah 09 hi likh diya: 99 | 09 → 9909.
- (b) sahi ✅: 3 zyada, 3 kam: 103 − 3 = 100 | −09 → 1 saikda udhaar: 99 | 91 → 9991.
- (c) galat ❌: 10009: kona ghatane ki jagah jod diya: 100 | 09 → 10009.
- (d) galat ❌: 991: kona ko 1 hi khaana diya: 10 − 9 = 1 → 99 | 1 → 991.
Q2. 104 × 98 mein left (udhaar se pehle)?
Jawab aur kaaran dekho
Sahi jawab: (a) 102
- (a) sahi ✅: 104 − 2 = 102 (2 hai 98 ka kam), ya 98 + 4 = 102.
- (b) galat ❌: 106: upar wale mein jod diya: 104 + 2 = 106.
- (c) galat ❌: 100: 104 mein se apna hi zyada ghata diya: 104 − 4 = 100.
- (d) galat ❌: 8: yeh to kona hai: 4 × 2 = 8.
Q3. 102 | −16 ko theek karo:
Jawab aur kaaran dekho
Sahi jawab: (d) 101 | 84 → 10184
- (a) galat ❌: Udhaar liya par left kam nahi kiya: 102 | 84 → 10284.
- (b) galat ❌: 16 ko 100 mein se ghatana bhool gaye: 101 | 16 → 10116.
- (c) galat ❌: Left 1 badha diya: 102 + 1 = 103 | 84 → 10384. Udhaar dene pe left ghatta hai.
- (d) sahi ✅: Left − 1: 102 − 1 = 101; right: 100 − 16 = 84 → 101 | 84 → 10184.
Q4. 107 × 96 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 10272
- (a) galat ❌: 10328: kona ghatane ki jagah jod diya: 103 | 28 → 10328.
- (b) galat ❌: 10372: right 100 − 28 = 72 kiya par left 1 kam nahi kiya: 103 | 72 → 10372.
- (c) sahi ✅: 7 zyada, 4 kam: 107 − 4 = 103 | −28 → udhaar: 102 | 72 → 10272.
- (d) galat ❌: 10282: 100 − 28 mein dono digit 10 se ghata diye: 10 − 2 = 8, 10 − 8 = 2 → 82 → 102 | 82 → 10282.
Q5. 115 × 92 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 10580
- (a) galat ❌: 10780: right 200 − 120 = 80 kiya par left se 2 ghatana bhool gaye: 107 | 80 → 10780.
- (b) sahi ✅: 15 zyada, 8 kam: 115 − 8 = 107 | −120 → 2 saikde udhaar: 107 − 2 = 105, 200 − 120 = 80 → 105 | 80 → 10580.
- (c) galat ❌: 10680: 2 saikde udhaar liye par left se sirf 1 ghataya: 107 − 1 = 106 | 80 → 10680.
- (d) galat ❌: 10820: kona jod diya: 107 | 120 → carry: 108 | 20 → 10820.
Q6. Chitra mein 103 × 97 ki khaali jagah kitni?
Jawab aur kaaran dekho
Sahi jawab: (a) 3 × 3 = 9
- (a) sahi ✅: Patti 97 lambi, dabba 100 chauda: 3 chaudi aur 3 oonchi jagah khaali.
- (b) galat ❌: 3 × 97 = 291 to kaati gayi naarangi patti ka area hai.
- (c) galat ❌: 100 × 100 = 10000 poora dabba hai (khaali jagah milakar).
- (d) galat ❌: 103 × 3 = 309 chitra mein kahin nahi; khaali jagah sirf 3 chaudi aur 3 oonchi hai.
Q7. 101 × 99 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 9999
- (a) galat ❌: 10001: kona jod diya: 100 | 01 → 10001.
- (b) galat ❌: 9901: udhaar ke baad right mein 100 − 01 ki jagah 01 hi likh diya: 99 | 01 → 9901.
- (c) galat ❌: 999: right ko 1 hi khaana diya: 10 − 1 = 9 → 99 | 9 → 999.
- (d) sahi ✅: 1 zyada, 1 kam: 101 − 1 = 100 | −01 → udhaar: 99 | 99 → 9999.
Q8. Kis sawaal mein aaj wali trick?
Jawab aur kaaran dekho
Sahi jawab: (c) 106 × 97
- (a) galat ❌: 106 aur 107 dono 100 se upar: yeh Post 7.3 ka type hai.
- (b) galat ❌: 16 × 7 base 10 ka hai (Post 8.1): 16 − 3 = 13 | −18 → 130 − 18 = 112.
- (c) sahi ✅: 106 upar, 97 neeche, dono 100 ke paas: 106 − 3 = 103 | −18 → 102 | 82 → 10282.
- (d) galat ❌: 96 aur 97 dono 100 se neeche: yeh Post 7.2 ka type hai.
Q9. 110 × 98 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 10780
- (a) galat ❌: 10880: right 100 − 20 = 80 kiya par left 1 kam nahi kiya: 108 | 80 → 10880.
- (b) sahi ✅: 10 zyada, 2 kam: 110 − 2 = 108 | −20 → udhaar: 107 | 80 → 10780.
- (c) galat ❌: 10820: kona jod diya: 108 | 20 → 10820.
- (d) galat ❌: 10800: kona bhool gaye: 108 | 00 → 10800.
Q10. 100 − 28 = ? (Chapter 3 trick)
Jawab aur kaaran dekho
Sahi jawab: (a) 72
- (a) sahi ✅: Dahai 9 se poora: 9 − 2 = 7, ikai 10 se poora: 10 − 8 = 2 → 72.
- (b) galat ❌: 82: dono digit 10 se poore kar diye: 10 − 2 = 8, 10 − 8 = 2 → 82.
- (c) galat ❌: 71: dono digit 9 se poore kar diye: 9 − 2 = 7, 9 − 8 = 1 → 71. Aakhri (ikai) 10 se poora hota hai.
- (d) galat ❌: 28: sawaal ka number hi likh diya; 28 to ghatana hai.
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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. 101 × 99, 102 × 98, 103 × 97, 104 × 96, 105 × 95: pattern?
Solution dekho
Sab mein left 100. Kona 1, 4, 9, 16, 25. Jawab: 9999, 9996, 9991, 9984, 9975. Har ek 10000 se 1 × 1, 2 × 2, 3 × 3, 4 × 4, 5 × 5 kam!
Check: 104 × 96: 100 | −16 → 99 | 84 → 9984 ✅
Q2. Do numbers 100 se barabar door hain (ek upar, ek neeche). Guna 9964. Numbers?
Solution dekho
Barabar door hain, to left 100 hi aayega (jaise 106 − 6 = 100). 10000 se kitna kam? Farq 36 hai. 36 = 6 × 6, to doori 6. Numbers 106 aur 94.
Check: 106 × 94: 100 | −36 → 99 | 64 → 9964 ✅
Q3. 104 bachche, har ek ₹97. Kul?
Solution dekho
104 × 97: 4 zyada, 3 kam. Left: 101. Kona: 12 → −12. 101 | −12 → 100 | 88 → ₹10088.
Check: 104 ko 100 baar − 104 ko 3 baar = 10400 − 312 = 10088 ✅
Q4. 103 × 97 aur 100 × 100: kaun bada, kitna?
Solution dekho
103 × 97 = 9991, 100 × 100 = 10000. 100 × 100 bada, 9 se. Jod same (200), par jo barabar hon unka guna bada (Post 7.2 ki HOTS jaisa).
Check: 10000 − 9991 = 9 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 7–8) | Kul daam (cost) wale sawaal (104 bachche × ₹97), area aur guna check. |
| Maths Olympiad | Pattern (10000 − 1, 4, 9, 16) aur ulta sawaal (guna 9964). |
| NTSE / MAT | Tulna (kaun bada) aur mental maths. |
| SSC / Bank (aage) | Simplification mein 103 × 97 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.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “alag taraf, left se ek udhaar, sau mein se kona.” Agle post mein base 1000 aur sabse zaroori sawaal: trick kab lagaayein, kab nahi! 🔀
— 📌 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 100. 103 → 3 zyada, 97 → 3 kam. Left: 103 − 3 = 100. Kona: 3 × 3 = 9 → 2 khaane: 09, minus. 100 | −09 → 1 saikda udhaar → 99 | 91 = 9991 ✅
| 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. Kona minus kyun?
Chitra mein patti upar rakhne pe ek kona khaali rehta hai; poore dabbe mein se woh ghatana padta hai.
2. Udhaar ki jagah seedha ghata sakte hain?
Haan: 100 | −09 = 10000 − 9 = 9991. Udhaar bas jaldi likhne ka tareeka.
3. Left 100 se kam aaye to?
Jaise 104 × 93: 97 | −28 → 96 | 72 = 9672. Jawab 4 digit ka.
4. Agle post mein kya hai?
Post 8.3: base 1000 (997 × 996, 1003 × 998) aur kab yeh trick lagaayein, kab nahi.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Alag taraf → kona minus.
- Base 100 → kona 2 khaane (09).
- Left − 1 | 100 − kona (99 | 91).
- Kona 100 se bada → 2 saikde udhaar (115 × 92 = 10580).
- Chitra: poora dabba − khaali kona.
- Andaaza: jawab “left saikde” se thoda kam.
— charumam.com 🎯
👉 Aage Kya?
Ab base 1000 aur poore chapter ka nakshaa: Post 8.3 mein 997 × 996, 1003 × 998, aur sabse zaroori: base method kab lagaayein, kab nahi!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
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