Post 7.1 mein base 10 ke paas wale numbers ka guna kiya. Ab wahi trick bade numbers pe: 97 × 96, 98 × 97, 88 × 89. Yeh sab 100 ke paas hain, to base hoga 100. Ek hi naya niyam seekhna hai: base 100 mein right hissa hamesha 2 digit ka hota hai (jitne base mein zero, utne digit). Phir 4-digit jawab do chhote kadmon mein!
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 97 × 96 ko aise socho: 97 ko 96 baar jodna hai. Itna lamba jod koi nahi karega! School wala tareeka (lamba guna): 97 × 6 = 582, phir 97 × 90 = 8730, phir 582 + 8730 = 9312. Teen bade kadam, carry ke saath.
Ek aur tareeka: 96 to 100 se 4 kam hai, to 97 ko 100 baar lo aur 4 baar ghatao: 9700 − 388 = 9312. Bhi theek, par 97 × 4 = 388 aur bada ghatana karna padta 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
97 × 96 = 9312
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
Is post mein chahiye: 100 se ghatana (Chapter 3), chhote numbers ka guna (3 × 4), aur 100 se guna (93 × 100 = 9300, peeche do zero). Naya: right hissa 2 digit ka, aur kam pade to aage 0 se bharna. Sab neeche ke boxes mein. Naye shabd:
📖 Shabd jo is post mein aayenge
- Base 100: 100 ke paas wale numbers (88 se 99 tak, aaj ke liye) ka base. 100 mein 2 zero, to right hissa 2 digit ka.
- Kitna kam (100 se): 100 − number. 97 → 3 kam, 88 → 12 kam. Chapter 3 ki trick: 9 se poora, aakhri 10 se.
- Left hissa (base 100 mein): yeh saikde (100 ke packet) ginta hai. 93 | 12 mein 93 saikde = 9300.
- 0 se bharna (padding): right hissa sirf 1 digit ka aaye (jaise 6), to aage 0 lagao: 06. Kyunki base 100 mein right ko 2 khaane milte hain.
- Carry (base 100 mein): right hissa 100 ya zyada (3 digit) ho jaaye to uska saikda left mein jaata hai. 77 | 132 → 78 | 32.
📏 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.
🔁 Chhota sa warm-up
- 100 − 96 = ?
- 93 × 100 = ?
- 9300 + 12 = ?
Answers dekho
- 4
- 9300
- 9312
Teeno aa gaye? Yahi milkar 97 × 96 = 9312 banta hai!
— 📌 charumam.com
🎬 Kahani: Do Baar Ka Kaam, Ek Baar Mein
Kabir ke papa ki dukaan pe 97 dabbe aaye, har dabbe mein 96 pencil. Papa ne kaha: “Kul kitni pencil? Calculator ki battery khatam hai.” Kabir ne copy nikaali aur lamba guna shuru kiya: 97 × 6, phir 97 × 90, phir jod…
Tabhi uski chhoti behen Meher boli: “Bhaiya, 97 to 100 se 3 kam hai, aur 96, 4 kam. 97 − 4 = 93, aur 3 × 4 = 12. Jawab 9312!”
Kabir ka lamba guna khatam hua: 9312. “Tujhe kaise aaya itni jaldi?” Meher hasi: “CharuMam ki class mein base 10 wala kiya tha. Bas 10 ki jagah 100 rakh diya!”
Aaj hum yahi karenge, aur ek chhota niyam bhi seekhenge jisse 98 × 97 jaise sawaal mein galti na ho. 💯
— 📌 charumam.com
🪄 Trick Step by Step: Base 100: Wahi Trick, Right Hissa 2 Digit Ka
💡 Is post ki ek badi baat: Dono numbers 100 se thode kam: left = ek number − doosre ka kitna kam, right = dono “kitna kam” ka guna, 2 digit mein (kam ho to aage 0). Jawab = left saikde + right. 97 × 96: 93 | 12 → 9312.
Step 1: Base chuno, zero gino
Sawaal: 97 × 96. Dono 100 ke paas. Base = 100. 100 mein 2 zero, to right hisse ko 2 khaane milenge.
Step 2: Kitna kam nikaalo
97 → 100 − 97 = 3 kam. 96 → 100 − 96 = 4 kam.
Step 3: Left: tirchha ghatao
97 − 4 = 93 (4 hai 96 ka kitna kam). Doosri taraf se check: 96 − 3 = 93. Same! ✅
Step 4: Right: guna, 2 digit mein
3 × 4 = 12. Do digit hain, 2 khaane bhar gaye. Bilkul theek.
Step 5: Jodo: left saikde + right
93 | 12. Left hissa 93 matlab 93 saikde: 93 × 100 = 9300. Phir right jodo: 9300 + 12 = 9312. Asal mein bas dono ko saath likh do: 93 aur 12 → 9312 ✅
Sabse zaroori niyam: right hissa 1 digit aaye to aage 0
98 × 97: 98 → 2 kam, 97 → 3 kam. Left: 98 − 3 = 95. Right: 2 × 3 = 6. Ab dhyaan! Base 100 mein right ko 2 khaane chahiye, aur 6 sirf ek digit hai. To aage 0 lagao: 06. Jawab 95 | 06 = 9506.
Agar 0 bhool gaye to “956” likh doge, jo galat hai: 98 × 97 to 90 × 90 = 8100 se bada hona chahiye, 956 bahut chhota hai. Place value se pakka: 95 saikde = 9500, plus 6 = 9506 ✅.
| Sawaal | Base se doori | Left (tirchha) | Kona (right) | Jawab |
|---|---|---|---|---|
| 99 × 98 | 1 kam, 2 kam | 99 − 2 = 97 | 1 × 2 = 2 | 97 | 02 → 9702 |
| 99 × 97 | 1 kam, 3 kam | 99 − 3 = 96 | 1 × 3 = 3 | 96 | 03 → 9603 |
| 98 × 97 | 2 kam, 3 kam | 98 − 3 = 95 | 2 × 3 = 6 | 95 | 06 → 9506 |
| 98 × 96 | 2 kam, 4 kam | 98 − 4 = 94 | 2 × 4 = 8 | 94 | 08 → 9408 |
| 97 × 97 | 3 kam, 3 kam | 97 − 3 = 94 | 3 × 3 = 9 | 94 | 09 → 9409 |
| 96 × 96 | 4 kam, 4 kam | 96 − 4 = 92 | 4 × 4 = 16 | 92 | 16 → 9216 |
| 95 × 97 | 5 kam, 3 kam | 95 − 3 = 92 | 5 × 3 = 15 | 92 | 15 → 9215 |
| 95 × 95 | 5 kam, 5 kam | 95 − 5 = 90 | 5 × 5 = 25 | 90 | 25 → 9025 |
| 94 × 96 | 6 kam, 4 kam | 94 − 4 = 90 | 6 × 4 = 24 | 90 | 24 → 9024 |
| 93 × 97 | 7 kam, 3 kam | 93 − 3 = 90 | 7 × 3 = 21 | 90 | 21 → 9021 |
Right hissa 100 ya zyada? Carry karo
88 × 89: 88 → 12 kam, 89 → 11 kam. Left: 88 − 11 = 77 (ya 89 − 12 = 77). Right: 12 × 11 = 132. Par right ko sirf 2 khaane, aur 132 mein 3 digit! 132 = 1 saikda + 32. Woh 1 saikda left mein jodo: 77 + 1 = 78. Right mein 32. Jawab 78 | 32 = 7832.
(12 × 11 kaise? Chapter 4 ki × 11 trick: 1, phir 1 + 2 = 3, phir 2 → 132.) Place value se: 77 saikde + 132 = 7700 + 132 = 7832 ✅.
Ek aur: 85 × 88: 15 kam, 12 kam. Left: 85 − 12 = 73. Right: 15 × 12 = 180 → 1 saikda left mein: 74 | 80 → 7480. Check: 85 = 100 se 15 kam, to 88 ko 100 baar − 88 ko 15 baar = 8800 − 1320 = 7480 ✅ (88 ko 15 baar = 88 ko 10 baar 880 + 88 ko 5 baar 440 = 1320).
Kab tak aasaan hai?
Jab tak “kitna kam” chhote hain (lagbhag 1 se 12), right ka guna mann mein ho jaata hai. 70 × 75 jaise numbers 100 se bahut door (30 kam, 25 kam); right 30 × 25 = 750 bada guna ban jaata hai. Wahan seedha tareeka (tukdon mein guna) behtar.
🆘 Atak gaye? Aise socho
- Kitna kam? Chapter 3: 100 − 96 → pehla digit 9 se poora (9 − 9 = 0), aakhri 10 se (10 − 6 = 4) → 04, yaani 4.
- Right 1 digit aaya? Aage 0 lagao: 6 → 06. Base 100 = 2 khaane.
- Right 3 digit aaya? Pehla digit (saikda) left mein jodo: 77 | 132 → 78 | 32.
- Check (andaaza): 97 × 96 to 100 × 100 = 10000 se thoda kam hona chahiye. 9312 bilkul theek lagta hai.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Ek aayat (rectangle) socho: chaudai 97, oonchai 96. Uska area (andar ke chhote 1 × 1 chaukor ki ginti) = 97 × 96. Post 7.1 mein 8 × 7 ke tiles ke saath jo kiya, wahi yahan karenge, bas chitra naap ke hisaab se nahi, samjhane ke liye hai (neeche chitra).
- Oonchai 96 ko 100 banana hai, to 4 aur chahiye (4 hai 96 ka kitna kam).
- Isliye aayat ke right se 4 chaudi patti kaato (naarangi). Neela hissa ab 97 − 4 = 93 chauda bacha: yahi tirchha ghatana!
- Patti ko ghuma kar neele hisse ke upar rakho. Neela hissa ab 96 + 4 = 100 ooncha. To 93 × 100 = 9300.
- Patti 96 lambi thi, neela 93 chauda. To patti ka 3 × 4 = 12 tukda baahar nikla (gulaabi). 3 hai 97 ka kitna kam, 4 hai 96 ka. Yahi right hissa!
Kul: 9300 + 12 = 9312. Area na bana, na mita, sirf jagah badli.
0 se bharna kyun? Left hissa 95 asal mein 9500 hai (95 × 100). Right 6 ko jodo: 9500 + 6 = 9506. Agar 6 ko dahai ki jagah likh do (956), to woh 9500 + 6 nahi raha. 06 likhne se 6 apni sahi jagah (ikai) pe rehta hai.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 98 × 96 = ?
2 kam, 4 kam. Left: 98 − 4 = 94 (ya 96 − 2 = 94). Right: 2 × 4 = 8 → 2 khaane: 08. 94 | 08 → 9408.
✔️ Normal tareeke se check: 98 ko 96 baar = 96 ko 100 baar − 96 ko 2 baar = 9600 − 192 = 9408 ✅
Example 2: 95 × 97 = ?
5 kam, 3 kam. Left: 95 − 3 = 92. Right: 5 × 3 = 15. 92 | 15 → 9215.
✔️ Normal tareeke se check: 97 ko 100 baar − 97 ko 5 baar = 9700 − 485 = 9215 ✅
Example 3: 99 × 99 = ?
1 kam, 1 kam. Left: 99 − 1 = 98. Right: 1 × 1 = 1 → 01. 98 | 01 → 9801.
✔️ Normal tareeke se check: 99 ko 100 baar − 99 = 9900 − 99 = 9801 ✅ (100 baar se ek baar kam, jaise Example 1–2)
Example 4: 88 × 89 = ? (carry wala)
12 kam, 11 kam. Left: 88 − 11 = 77. Right: 12 × 11 = 132 → 3 digit! 1 saikda left mein: 78 | 32 → 7832.
✔️ Normal tareeke se check: 88 = 100 se 12 kam, to 89 ko 100 baar − 89 ko 12 baar = 8900 − 1068 = 7832 ✅ (89 ko 12 baar = 89 ko 10 baar 890 + 89 ko 2 baar 178 = 1068)
— 📌 charumam.com
🕉️ Vedic Maths Connection
Yeh Post 7.1 wala hi Nikhilam tareeka hai, bas base 10 ki jagah 100. “Sab 9 se, aakhri 10 se” sutra ka kaam yahan seedha dikhta hai: 100 se kitna kam nikaalne ke liye Chapter 3 ki trick (88 → 9 − 8 = 1, 10 − 8 = 2 → 12 kam). Vedic Maths ki kitabein bhi base ke zero ginne ka niyam batati hain: jitne zero, utne digit right mein. Hamari wajah chitra mein hai: left hissa saikde hai, isliye right ko 2 khaane.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Dono 100 se 1–12 kam (97 × 96, 89 × 92) | ✅ Haan | Chhota guna, chhota ghatana: seconds mein. |
| Right 1 digit (98 × 97) | ✅ Haan, 0 ke saath | 06 likhna mat bhoolna. |
| Kitna kam thoda bade (85 × 88) | ⚠️ Ho jaayega | Right 15 × 12 = 180, carry karna padega. |
| 100 se bahut door (62 × 71) | ❌ Nahi | Right 38 × 29 bahut bada; seedha tareeka (tukdon mein guna) behtar. |
| 100 se zyada (104 × 107) | ➡️ Post 7.3 | Wahi trick, left mein jodna. |
| Ek 100 se kam, ek zyada (103 × 97) | ➡️ Chapter 8 | Right ghatana padta hai. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: 0 lagana bhool gaye
Sawaal: 98 × 97
❌ Galat: 95 aur 6 ko saath likh ke 956.
✅ Sahi: base 100 mein right ko 2 khaane: 06 → 9506. Andaaza: jawab 10000 ke paas hona chahiye.
Galti 2: Apna hi kitna kam ghata diya
Sawaal: 97 × 96
❌ Galat: 97 − 3 = 94, right 12 → 9412.
✅ Sahi: tirchha: 97 − 4 = 93 → 9312. Dono taraf se check: 96 − 3 bhi 93.
Galti 3: Carry ko right mein hi chhod diya
Sawaal: 88 × 89
❌ Galat: 77 | 132 ko seedha 77132 likh diya.
✅ Sahi: right ko 2 hi khaane: 132 ka 1 saikda left mein → 78 | 32 = 7832. Andaaza: 88 × 89 to 100 × 100 = 10000 se kam hona chahiye; 77132 bahut bada.
Galti 4: Kitna kam galat nikala
Sawaal: 93 × 97
❌ Galat: 93 ko 100 se 3 kam maan liya (asal mein 3 to 97 ka hai). Left: 93 − 3 = 90. Right: 3 × 3 = 9 → 09 → 9009 (galat).
✅ Sahi: 93 → 7 kam, 97 → 3 kam. Left: 93 − 3 = 90. Right: 7 × 3 = 21 → 9021.
🧠 Rule of thumb: Base 100 = 2 khaane right mein: 1 digit aaye to aage 0, 3 digit aaye to saikda left mein.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, sab 100 se thode kam. Pehle 0 wale (padding), aakhir mein carry wale. Target: 4 minute.
- 99 × 97 = ?
- 98 × 97 = ?
- 97 × 97 = ?
- 96 × 98 = ?
- 95 × 99 = ?
- 94 × 96 = ?
- 93 × 97 = ?
- 95 × 95 = ?
- 92 × 98 = ?
- 91 × 99 = ?
- 96 × 96 = ?
- 94 × 94 = ?
- 89 × 98 = ?
- 88 × 89 = ?
- 87 × 95 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 9603
- 9506
- 9409
- 9408
- 9405
- 9024
- 9021
- 9025
- 9016
- 9009
- 9216
- 8836
- 8722
- 7832
- 8265
Kaise kiya (kuch): 91 × 99: 9 kam, 1 kam → 91 − 1 = 90 | 09 → 9009. 89 × 98: 11 kam, 2 kam → 87 | 22 → 8722. 87 × 95: 13 kam, 5 kam → 82 | 65 → 8265.
— 📌 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.
- 98 × 99 = ?
- 97 × 99 = ?
- 96 × 97 = ?
- 95 × 98 = ?
- 93 × 99 = ?
- 94 × 98 = ?
- 97 × 94 = ?
- 92 × 99 = ?
- 96 × 93 = ?
- 90 × 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
- 9702
- 9603
- 9312
- 9310
- 9207
- 9212
- 9118
- 9108
- 8928
- 8910
Dhyaan: 90 × 99: 10 kam, 1 kam → 90 − 1 = 89 | 10 → 8910. Right 10 do digit ka hai, 0 lagane ki zaroorat nahi.
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. 97 × 96 mein left hissa?
Jawab aur kaaran dekho
Sahi jawab: (b) 93
- (a) galat ❌: 12: yeh to right hissa hai: 3 × 4 = 12.
- (b) sahi ✅: 97 − 4 = 93 (ya 96 − 3 = 93): doosre ka kitna kam ghatao.
- (c) galat ❌: 94: 97 mein se apna hi kitna kam ghata diya: 97 − 3 = 94.
- (d) galat ❌: 92: 96 mein se apna hi kitna kam ghata diya: 96 − 4 = 92.
Q2. 98 × 97 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 9506
- (a) sahi ✅: 2 kam, 3 kam: 98 − 3 = 95 | 2 × 3 = 6 → 2 khaane: 95 | 06 → 9506.
- (b) galat ❌: 956: 6 ko 2 khaane nahi diye, seedha saath likh diya: 95 | 6 → 956. Jawab to 10000 ke paas hona chahiye.
- (c) galat ❌: 9560: 6 ko dahai wale khaane mein likh diya: 95 | 60 → 9560. 6 ikai mein jaata hai: 06.
- (d) galat ❌: 9606: 98 mein se apna hi kitna kam ghata diya: 98 − 2 = 96 | 06 → 9606.
Q3. Base 100 mein right hissa kitne digit ka hona chahiye?
Jawab aur kaaran dekho
Sahi jawab: (d) 2 (jitne 100 mein zero)
- (a) galat ❌: 1 khaana base 10 ke liye tha (8 × 7 → 5 | 6).
- (b) galat ❌: 3 khaane base 1000 ke liye hote hain (Post 7.4 mein dekhenge).
- (c) galat ❌: Niyam hai: zero jitne khaane. Kam ho to aage 0 (06), zyada ho to carry (77 | 132 → 78 | 32).
- (d) sahi ✅: 100 mein 2 zero, isliye right ko 2 khaane (jaise 06, 12).
Q4. 88 × 89 mein right hissa 132 aaya. Jawab?
Jawab aur kaaran dekho
Sahi jawab: (c) 7832
- (a) galat ❌: 7732: 132 ka sirf 32 likha, 1 saikda left mein jodna bhool gaye: 77 | 32 → 7732.
- (b) galat ❌: 7932: left mein 2 saikde jod diye: 77 + 2 = 79 | 32 → 7932. 132 mein 1 hi saikda hai.
- (c) sahi ✅: 12 kam, 11 kam: 88 − 11 = 77 | 132 → 132 ka 1 saikda left mein: 77 + 1 = 78 | 32 → 7832.
- (d) galat ❌: 77132: carry nahi kiya, seedha saath likh diya: 77 | 132 → 77132.
Q5. 100 − 88 = ? (88 ka kitna kam)
Jawab aur kaaran dekho
Sahi jawab: (b) 12
- (a) galat ❌: 88: sawaal ka number hi likh diya; 88 to number hai, uska kitna kam nahi.
- (b) sahi ✅: Chapter 3: dahai 9 se poora: 9 − 8 = 1, ikai 10 se poora: 10 − 8 = 2 → 12.
- (c) galat ❌: 22: dono digit 10 se poore kar diye: 10 − 8 = 2, 10 − 8 = 2 → 22. Dahai 9 se poori hoti hai.
- (d) galat ❌: 2: sirf ikai ka 10 − 8 = 2 kiya; dahai ka 9 − 8 = 1 bhool gaye.
Q6. 95 × 97 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 9215
- (a) sahi ✅: 5 kam, 3 kam: 95 − 3 = 92 | 5 × 3 = 15 → 9215.
- (b) galat ❌: 9415: 97 mein se apna hi kitna kam ghata diya: 97 − 3 = 94 | 15 → 9415.
- (c) galat ❌: 9208: right mein guna ki jagah jod: 5 + 3 = 8 → 92 | 08 → 9208.
- (d) galat ❌: 9015: 95 mein se apna hi kitna kam ghata diya: 95 − 5 = 90 | 15 → 9015.
Q7. Chitra mein 97 × 96 ke liye 4 chaudi patti kyun kaati?
Jawab aur kaaran dekho
Sahi jawab: (d) Kyunki 96 ko 100 banne ke liye 4 chahiye
- (a) galat ❌: 97 − 93 = 4 sach hai, par 93 to kaatne ke baad bacha. Wajah: 96 ko 100 banne mein 4 chahiye.
- (b) galat ❌: Chhota hona wajah nahi; wajah hai 96 + 4 = 100.
- (c) galat ❌: 97 ko 100 banne ke liye 3 chahiye (97 + 3 = 100), 4 nahi. 4 to 96 ka kitna kam hai.
- (d) sahi ✅: Patti upar rakhne se oonchai 96 + 4 = 100 ho gayi.
Q8. 99 × 99 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 9801
- (a) galat ❌: 9802: right mein guna ki jagah jod: 1 + 1 = 2 → 98 | 02 → 9802.
- (b) galat ❌: 9810: 1 ko dahai wale khaane mein likh diya: 98 | 10 → 9810.
- (c) sahi ✅: 1 kam, 1 kam: 99 − 1 = 98 | 1 × 1 = 1 → 2 khaane: 98 | 01 → 9801.
- (d) galat ❌: 981: 1 ko 2 khaane nahi diye: 98 | 1 → 981.
Q9. Kis pe base 100 trick (aaj wali) sabse achhi?
Jawab aur kaaran dekho
Sahi jawab: (b) 96 × 98
- (a) galat ❌: 103 upar, 97 neeche: ek upar ek neeche, yeh Chapter 8 ka type hai.
- (b) sahi ✅: Dono 100 se thode kam (4 kam, 2 kam): 96 − 2 = 94 | 4 × 2 = 8 → 94 | 08 → 9408.
- (c) galat ❌: 62 aur 71, 100 se bahut door (38 kam, 29 kam); right 38 × 29 khud ek bada guna.
- (d) galat ❌: 104 aur 107 dono 100 se zyada: yeh Post 7.3 ka type hai.
Q10. 91 × 99 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 9009
- (a) sahi ✅: 9 kam, 1 kam: 91 − 1 = 90 | 9 × 1 = 9 → 2 khaane: 90 | 09 → 9009.
- (b) galat ❌: 909: 9 ko 2 khaane nahi diye: 90 | 9 → 909.
- (c) galat ❌: 9090: 9 ko dahai wale khaane mein likh diya: 90 | 90 → 9090.
- (d) galat ❌: 9109: left mein 91 hi utaar liya, 1 ghatana bhool gaye: 91 | 09 → 9109.
— 📌 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. □ × 98 = 9506, aur □ 100 se kam hai. □ = ?
Solution dekho
Ulta socho. Jawab 95 | 06: left 95, right 6. 98 → 2 kam. Right 6 kaise bana? 2 (98 ka kitna kam) ko □ ke kitna kam se guna karke. 2 ko kis se guna karein ki 6 aaye? 3 se (2 × 3 = 6). To □ ka kitna kam = 3. □ = 100 − 3 = 97. Left check: 98 − 3 = 95 ✅.
Check: 97 × 98 = 9506 ✅ (upar table mein bhi hai)
Q2. 99 × 99 = 9801, 98 × 98 = 9604, 97 × 97 = 9409. Agla, 96 × 96?
Solution dekho
Pattern: kitna kam 1, 2, 3, 4. Right = kitna kam × kitna kam: 1, 4, 9, 16. Left = 100 − 2 × kitna kam: 98, 96, 94, 92. To 96 × 96 → 92 | 16 → 9216.
Check: 96 ko 100 baar − 96 ko 4 baar = 9600 − 384 = 9216 ✅
Q3. 96 dabbe, har dabbe mein 94 pencil. Kul?
Solution dekho
96 × 94: 4 kam, 6 kam. Left: 96 − 6 = 90. Right: 4 × 6 = 24. 90 | 24 → 9024 pencil.
Check: 94 ko 100 baar − 94 ko 4 baar = 9400 − 376 = 9024 ✅
Q4. Kaun bada: 98 × 92 ya 95 × 95?
Solution dekho
98 × 92: 2 kam, 8 kam → 90 | 16 → 9016. 95 × 95: 5 kam, 5 kam → 90 | 25 → 9025. Dono ka left 90 hi hai (kyunki 2 + 8 = 5 + 5 = 10 kam)! Right mein 16 aur 25 ki tulna: 25 bada, to 95 × 95 bada, 9 se.
Check: 9025 − 9016 = 9 ✅. Seekh: jab do numbers ka jod same ho (98 + 92 = 190 aur 95 + 95 = 190), to jo numbers aapas mein barabar (ya paas-paas) hon, unka guna bada.
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 7–8) | Area, daam (cost: dabbe × ek dabbe ka daam) aur squares (96² = 96 × 96, 99²) mein jaldi jawab ya check. |
| Maths Olympiad | Pattern (99², 98², 97²) aur ulta sawaal (□ × 98 = 9506). |
| NTSE / MAT | Mental maths aur tulna (kaun bada: 98 × 92 ya 95 × 95). |
| SSC / Bank (aage) | Simplification mein 97 × 96 jaise guna 5 second 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
Har din 5 jode lo jo 100 se 1–9 kam hon, aur bolo: “teen kam, chaar kam, tiraanve, baarah.” Galti se bachne ka mantra: “do zero, do khaane.” Agle post mein 100 se zyada wale: 104 × 107! 💯
— 📌 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. 97 → 3 kam, 96 → 4 kam. Left: 97 − 4 = 93. Right: 3 × 4 = 12 (2 digit, theek). Jawab 93 | 12 = 9312 ✅
| 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. Base 100 mein right 2 digit ka hi kyun?
Kyunki left hissa saikde ginta hai (93 → 9300). Jo bacha (right), woh 100 se chhota hona chahiye, yaani 2 digit (00 se 99).
2. Kya 50 × 50 pe chalega?
Chalega: 50 kam, 50 kam → 50 − 50 = 0 | 2500 → 25 saikde left mein → 25 | 00 → 2500. Sahi, par itna lamba carry; seedha 5 × 5 = 25, peeche do zero aasaan.
3. Doosri taraf se ghatana kyun same aata hai?
97 − 4 aur 96 − 3 dono “100 − 3 − 4 = 93” hi hain.
4. Agle post mein kya hai?
Post 7.3: base 100 se zyada: 104 × 107 = 11128, left mein jodna.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Base 100: 2 zero → right hissa 2 digit.
- Kitna kam = 100 − number (Chapter 3 trick).
- Left: tirchha ghatao (97 − 4 = 93).
- Right: kitna kam ka guna; 1 digit → aage 0 (06).
- Right 3 digit → saikda left mein (77 | 132 → 7832).
- 97 × 96 = 9312, 98 × 97 = 9506; andaaza: 10000 se thoda kam.
— charumam.com 🎯
👉 Aage Kya?
Ab 100 se zyada wale: Post 7.3 mein 104 × 107 jaise guna, jahan left mein jodna hai aur 5-digit jawab aata hai!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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- 🌐 Website: charumam.com
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