Post 7.2 mein 100 se thode kam wale numbers (97 × 96) kiye. Ab 100 se thode zyada: 104 × 107, 102 × 103, 112 × 115. Trick wahi, bas left mein ghatane ki jagah jodna (jaise 7.1 mein 12 × 13 kiya tha). Jawab 5 digit ka aayega, par mann mein ban jaayega!
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 104 × 107 ko todo: 104 ko 100 baar = 10400, aur 104 ko 7 baar = 728 (100 × 7 = 700, 4 × 7 = 28). Phir jodo: 10400 + 728 = 11128.
Theek hai, par 104 × 7 alag se karna aur phir 5-digit jod. Trick mein sirf 104 + 7 aur 4 × 7.
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
104 × 107 = 11128
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 zyada nikaalna (104 − 100 = 4, bas aakhri do digit dekho), chhota guna (4 × 7), aur 100 se guna (111 × 100 = 11100). Right hisse ke 2 khaane wala niyam (Post 7.2) yahan bhi. Neeche ke boxes dekho. Naye/purane shabd:
📖 Shabd jo is post mein aayenge
- Kitna zyada (100 se): number − 100. 104 → 4 zyada, 112 → 12 zyada. 100 aur 199 ke beech, bas aakhri do digit hi kitna zyada hain.
- Tirchha jodna: ek number mein doosre ka kitna zyada jodo. 104 × 107: 104 + 7 = 111 (ya 107 + 4 = 111).
- Left hissa: saikde ginta hai, aur ab 3 digit ka bhi ho sakta hai: 111 saikde = 11100.
- Right hissa (2 khaane): dono kitna zyada ka guna. 1 digit aaye to aage 0 (2 × 3 = 6 → 06), 3 digit aaye to saikda left mein.
- 5-digit number: 10000 ya zyada. 11128 = gyaarah hazaar ek sau atthaais.
📏 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
- 107 − 100 = ?
- 111 × 100 = ?
- 11100 + 28 = ?
Answers dekho
- 7
- 11100
- 11128
Teeno aa gaye? Yahi milkar 104 × 107 = 11128!
— 📌 charumam.com
🎬 Kahani: School Ke Naye Maidan Ka Hisaab
School ke naye khel ke maidan ki lambai 107 metre aur chaudai 104 metre hai. Principal Ma’am ne poochha: “Maidan ka area kitne square metre?” (Area = lambai × chaudai, yaani maidan mein 1 metre × 1 metre ke kitne chaukor dabbe samayenge. Square metre = aisa ek chaukor dabba.)
Rohan ne kaha: “Ma’am, 100 × 100 = 10000 se thoda zyada hoga.” “Kitna zyada?” Rohan atak gaya.
Zoya ne copy pe likha: 104 → 4 zyada, 107 → 7 zyada. 104 + 7 = 111, aur 4 × 7 = 28. “11128 square metre, Ma’am!”
Principal Ma’am ne calculator se check kiya aur muskurayin. Aaj hum Zoya wala tareeka seekhenge, aur chitra se dekhenge ki 111 aur 28 kahan se aate hain. 🚀
— 📌 charumam.com
🪄 Trick Step by Step: Base 100 Se Zyada: Tirchha Jodo, Kona Guna
💡 Is post ki ek badi baat: Dono numbers 100 se thode zyada: left = ek number + doosre ka kitna zyada, right = dono kitna zyada ka guna, 2 digit mein. 104 × 107: 111 | 28 → 11128.
Step 1: Base chuno
Sawaal: 104 × 107. Dono 100 ke paas, thode upar. Base = 100, 2 zero → right ko 2 khaane.
Step 2: Kitna zyada nikaalo
104 → 104 − 100 = 4 zyada. 107 → 7 zyada. (Aakhri do digit: 04 aur 07.)
Step 3: Left: tirchha jodo
104 + 7 = 111 (7 hai 107 ka kitna zyada). Doosri taraf: 107 + 4 = 111. Same ✅.
Step 4: Right: guna, 2 khaane
4 × 7 = 28. Do digit, theek.
Step 5: Saath likho
111 | 28: 111 saikde = 11100, plus 28 = 11128 ✅. Andaaza: 10000 se thoda zyada, bilkul theek.
Right 1 digit? Aage 0 (Post 7.2 jaisa)
102 × 103: 2 zyada, 3 zyada. Left: 102 + 3 = 105. Right: 2 × 3 = 6 → 2 khaane: 06. Jawab 105 | 06 = 10506. (0 bhoolte to 1056 aata, jo 100 × 100 = 10000 se bhi chhota hai. Galat!)
| Sawaal | Base se doori | Left (tirchha) | Kona (right) | Jawab |
|---|---|---|---|---|
| 101 × 101 | 1 zyada, 1 zyada | 101 + 1 = 102 | 1 × 1 = 1 | 102 | 01 → 10201 |
| 101 × 105 | 1 zyada, 5 zyada | 101 + 5 = 106 | 1 × 5 = 5 | 106 | 05 → 10605 |
| 102 × 103 | 2 zyada, 3 zyada | 102 + 3 = 105 | 2 × 3 = 6 | 105 | 06 → 10506 |
| 102 × 104 | 2 zyada, 4 zyada | 102 + 4 = 106 | 2 × 4 = 8 | 106 | 08 → 10608 |
| 103 × 103 | 3 zyada, 3 zyada | 103 + 3 = 106 | 3 × 3 = 9 | 106 | 09 → 10609 |
| 103 × 105 | 3 zyada, 5 zyada | 103 + 5 = 108 | 3 × 5 = 15 | 108 | 15 → 10815 |
| 104 × 106 | 4 zyada, 6 zyada | 104 + 6 = 110 | 4 × 6 = 24 | 110 | 24 → 11024 |
| 105 × 105 | 5 zyada, 5 zyada | 105 + 5 = 110 | 5 × 5 = 25 | 110 | 25 → 11025 |
| 106 × 107 | 6 zyada, 7 zyada | 106 + 7 = 113 | 6 × 7 = 42 | 113 | 42 → 11342 |
| 108 × 109 | 8 zyada, 9 zyada | 108 + 9 = 117 | 8 × 9 = 72 | 117 | 72 → 11772 |
Right 100 ya zyada? Carry
112 × 115: 12 zyada, 15 zyada. Left: 112 + 15 = 127. Right: 12 × 15 = 180 (12 × 15 = 12 × 10 + 12 × 5 = 120 + 60). 3 digit! 1 saikda left mein: 127 + 1 = 128, right 80. Jawab 128 | 80 = 12880.
110 × 110: 10 zyada, 10 zyada → 120 | 100 → right 100 = 1 saikda + 00 → 121 | 00 = 12100. Check: 110 ko 100 baar + 110 ko 10 baar = 11000 + 1100 = 12100 ✅.
113 × 117: 13 zyada, 17 zyada → 130 | 221 → 2 saikde left mein → 132 | 21 = 13221. (13 × 17 = 221 kaise? Post 6.3 ki bahan-trick: dahai same (1), ikai ka jod 3 + 7 = 10 → 1 × 2 = 2 | 3 × 7 = 21 → 221.)
Teeno type ek nazar mein
Dono kam (97 × 96): left mein ghatao. Dono zyada (104 × 107): left mein jodo. Right mein dono baar guna, aur khaane = base ke zero. Ek upar ek neeche (103 × 97): Chapter 8.
🆘 Atak gaye? Aise socho
- Kitna zyada? 100 se 199 tak: bas aakhri do digit. 108 → 08 → 8 zyada; 115 → 15 zyada.
- Jodun ya ghataun? Numbers base se zyada → jodo. Yaad: “zyada ho to aur zyada.”
- Right 1 digit? 0 lagao (06). 3 digit? Saikda left mein (127 | 180 → 128 | 80).
- Andaaza: 104 × 107 to 100 × 100 = 10000 se thoda zyada. Jawab 5 digit ka, 1 se shuru.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Maidan ka chitra. 104 × 107 ko ek aayat maano: chaudai 104 = 100 + 4, oonchai 107 = 100 + 7. Ise 4 tukdon mein baanto (Post 6.3 jaisa; chitra naap se nahi):
- Neela bada chaukor: 100 × 100 = 10000.
- Naarangi patti right mein: 4 chaudi, 100 oonchi → 400.
- Hari patti neeche: 100 chaudi, 7 oonchi → 700.
- Gulaabi kona: 4 × 7 = 28.
Neela + naarangi + hara = 10000 + 400 + 700 = 11100, yaani 111 saikde. Aur 111 = 104 + 7 (100 + 4 + 7)! Yahi left hissa. Gulaabi kona 28: right hissa. Kul 11100 + 28 = 11128.
Dhyaan do: 7.2 mein patti kaati thi (isliye ghatana), yahan pattiyan judi hui hain (isliye jodna). Dono mein kona = do dooriyon ka guna.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 103 × 108 = ?
3 zyada, 8 zyada. Left: 103 + 8 = 111. Right: 3 × 8 = 24. 111 | 24 → 11124.
✔️ Normal tareeke se check: 103 ko 100 baar + 103 ko 8 baar = 10300 + 824 = 11124 ✅
Example 2: 101 × 107 = ? (0 lagao)
1 zyada, 7 zyada. Left: 101 + 7 = 108. Right: 1 × 7 = 7 → 07. 108 | 07 → 10807.
✔️ Normal tareeke se check: 107 ko 100 baar + 107 = 10700 + 107 = 10807 ✅
Example 3: 109 × 109 = ?
9 zyada, 9 zyada. Left: 109 + 9 = 118. Right: 9 × 9 = 81. 118 | 81 → 11881.
✔️ Normal tareeke se check: 109 ko 100 baar + 109 ko 9 baar = 10900 + 981 = 11881 ✅
Example 4: 115 × 112 = ? (carry)
15 zyada, 12 zyada. Left: 115 + 12 = 127. Right: 15 × 12 = 180 → 1 saikda left mein → 128 | 80 → 12880.
✔️ Normal tareeke se check: 112 × 115 jaisa hi (order se farq nahi) ✅. 115 ko 100 baar + 115 ko 12 baar = 11500 + 1380 = 12880 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabein is “base se upar” wale tareeke ko bhi Nikhilam ka hi hissa maanti hain: wahi niyam, bas “kitna kam” ki jagah “kitna zyada”, aur left mein ghatane ki jagah jodna. Naam se zyada yaad rakho chitra: 4 tukde, teen milkar left, chautha kona right.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Dono 100 se 1–15 zyada (104 × 107) | ✅ Haan | Ek jod, ek chhota guna. |
| Right 1 digit (102 × 103) | ✅ Haan, 0 ke saath | 10506: 0 mat bhoolo. |
| Zyada thode bade (113 × 117) | ⚠️ Carry ke saath | Right 221 → 2 saikde left mein. |
| 100 se bahut upar (145 × 160) | ❌ Nahi | Right 45 × 60 = 2700 bada guna; seedha tareeka (tukdon mein guna) behtar. |
| 100 se kam (97 × 96) | ➡️ Post 7.2 | Left mein ghatao. |
| Ek upar ek neeche (104 × 97) | ➡️ Chapter 8 | Chapter 8 mein seekhenge. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Jodne ki jagah ghata diya
Sawaal: 104 × 107
❌ Galat: 104 − 7 = 97, right 28 → 9728.
✅ Sahi: zyada hain to jodo: 104 + 7 = 111 → 11128. Andaaza: 10000 se zyada hona chahiye, 9728 kam hai.
Galti 2: 0 bhool gaye
Sawaal: 102 × 103
❌ Galat: 105 aur 6 ko saath likh ke 1056.
✅ Sahi: 2 khaane: 06 → 10506.
Galti 3: Doosre ka nahi, poora number jod diya
Sawaal: 104 × 107
❌ Galat: 104 aur 107 dono jod ke left 211 le liya.
✅ Sahi: sirf doosre ka kitna zyada (7) jodo: 104 + 7 = 111.
Galti 4: Carry nahi kiya
Sawaal: 112 × 115
❌ Galat: 127 | 180 ko seedha 127180 likh diya.
✅ Sahi: 180 ka 1 saikda left mein → 128 | 80 = 12880. Andaaza: 110 × 110 = 12100 ke paas.
🧠 Rule of thumb: Zyada hain to tirchha jodo; right mein guna; 2 khaane: kam pade to 0, zyada ho to saikda left mein.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, sab 100 se thode zyada. Target: 4 minute.
- 101 × 103 = ?
- 102 × 104 = ?
- 103 × 105 = ?
- 104 × 104 = ?
- 105 × 107 = ?
- 106 × 103 = ?
- 102 × 109 = ?
- 108 × 105 = ?
- 107 × 107 = ?
- 103 × 111 = ?
- 110 × 104 = ?
- 106 × 106 = ?
- 112 × 112 = ?
- 115 × 105 = ?
- 111 × 109 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 10403
- 10608
- 10815
- 10816
- 11235
- 10918
- 11118
- 11340
- 11449
- 11433
- 11440
- 11236
- 12544
- 12075
- 12099
Kaise kiya (kuch): 103 × 111: 103 + 11 = 114 | 3 × 11 = 33 → 11433. 112 × 112: 124 | 144 → 125 | 44 → 12544. 111 × 109: 120 | 99 → 12099.
— 📌 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 × 101 = ?
- 102 × 103 = ?
- 104 × 106 = ?
- 105 × 105 = ?
- 103 × 109 = ?
- 107 × 102 = ?
- 108 × 108 = ?
- 106 × 109 = ?
- 101 × 119 = ?
- 110 × 110 = ?
| 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
- 10201
- 10506
- 11024
- 11025
- 11227
- 10914
- 11664
- 11554
- 12019
- 12100
Dhyaan: 101 × 119: 1 zyada, 19 zyada → 120 | 19 → 12019. 108 × 108: 116 | 64 → 11664.
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. 104 × 107 mein left hissa?
Jawab aur kaaran dekho
Sahi jawab: (c) 111
- (a) galat ❌: 211: doosre ka kitna zyada nahi, poora number jod diya: 104 + 107 = 211.
- (b) galat ❌: 28: yeh to right hissa hai: 4 × 7 = 28.
- (c) sahi ✅: 104 + 7 = 111 (ya 107 + 4 = 111): doosre ka kitna zyada jodo.
- (d) galat ❌: 97: zyada wale mein ghata diya: 104 − 7 = 97. Dono 100 se zyada hain, to jodo.
Q2. 102 × 103 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 10506
- (a) galat ❌: 10505: right mein guna ki jagah jod: 2 + 3 = 5 → 105 | 05 → 10505.
- (b) sahi ✅: 2 zyada, 3 zyada: 102 + 3 = 105 | 2 × 3 = 6 → 2 khaane: 105 | 06 → 10506.
- (c) galat ❌: 1056: 6 ko 2 khaane nahi diye: 105 | 6 → 1056. Yeh 10000 se bhi chhota hai!
- (d) galat ❌: 10560: 6 ko dahai wale khaane mein likh diya: 105 | 60 → 10560.
Q3. 112 × 115 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 12880
- (a) sahi ✅: 12 zyada, 15 zyada: 112 + 15 = 127 | 12 × 15 = 180 → 1 saikda left mein: 127 + 1 = 128 | 80 → 12880.
- (b) galat ❌: 127180: carry nahi kiya: 127 | 180 → 127180.
- (c) galat ❌: 12780: 180 ka sirf 80 likha, 1 saikda left mein jodna bhool gaye: 127 | 80 → 12780.
- (d) galat ❌: 12980: left mein 2 saikde jod diye: 127 + 2 = 129 | 80 → 12980. 180 mein 1 hi saikda hai.
Q4. Dono numbers 100 se zyada hon to left mein kya karte hain?
Jawab aur kaaran dekho
Sahi jawab: (d) Doosre ka kitna zyada jodte hain
- (a) galat ❌: Ghatana tab, jab dono 100 se kam hon (97 − 4 = 93). Yahan ghatane se 104 − 7 = 97 aata, jo galat left hai.
- (b) galat ❌: Dono poore numbers jodne se 104 + 107 = 211 aata, jo left nahi.
- (c) galat ❌: 100 ghatane se sirf kitna zyada milta hai (104 − 100 = 4), left nahi.
- (d) sahi ✅: Jaise 104 × 107: 104 + 7 = 111.
Q5. 108 × 105 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 11340
- (a) galat ❌: 11640: 108 mein apna hi kitna zyada jod diya: 108 + 8 = 116 | 40 → 11640.
- (b) galat ❌: 11040: 105 mein apna hi kitna zyada jod diya: 105 + 5 = 110 | 40 → 11040.
- (c) sahi ✅: 8 zyada, 5 zyada: 108 + 5 = 113 | 8 × 5 = 40 → 11340.
- (d) galat ❌: 11313: right mein guna ki jagah jod: 8 + 5 = 13 → 113 | 13 → 11313.
Q6. Chitra mein left hissa (111 saikde) kin tukdon se bana?
Jawab aur kaaran dekho
Sahi jawab: (b) Neela + naarangi + hara
- (a) galat ❌: Naarangi + gulaabi = 400 + 28 = 428; yeh 111 saikde nahi.
- (b) sahi ✅: 10000 + 400 + 700 = 11100, yaani 111 saikde.
- (c) galat ❌: Neela akela 100 × 100 = 10000 hai, yaani sirf 100 saikde.
- (d) galat ❌: Gulaabi kona to right hissa hai: 4 × 7 = 28.
Q7. 110 × 110 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 12100
- (a) sahi ✅: 10 zyada, 10 zyada: 110 + 10 = 120 | 10 × 10 = 100 → 1 saikda left mein: 120 + 1 = 121 | 00 → 12100.
- (b) galat ❌: 120100: carry nahi kiya: 120 | 100 → 120100.
- (c) galat ❌: 1210: right ko 2 ki jagah 1 hi khaana diya: 121 | 0 → 1210.
- (d) galat ❌: 12000: 100 ko right mein 00 likha par uska 1 saikda left mein le jaana bhool gaye: 120 | 00 → 12000.
Q8. 109 × 109 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 11881
- (a) galat ❌: 11818: right mein guna ki jagah jod: 9 + 9 = 18 → 118 | 18 → 11818.
- (b) galat ❌: 10081: zyada wale mein ghata diya: 109 − 9 = 100 | 81 → 10081.
- (c) galat ❌: 21881: kitna zyada nahi, poora number jod diya: 109 + 109 = 218 | 81 → 21881.
- (d) sahi ✅: 9 zyada, 9 zyada: 109 + 9 = 118 | 9 × 9 = 81 → 11881.
Q9. Kis sawaal mein aaj wali (dono zyada) trick?
Jawab aur kaaran dekho
Sahi jawab: (c) 106 × 104
- (a) galat ❌: 106 upar, 94 neeche: ek upar ek neeche, yeh Chapter 8 ka type hai.
- (b) galat ❌: 16 × 14 base 10 ka hai (Post 7.1): 16 + 4 = 20 | 6 × 4 = 24 → carry: 22 | 4 → 224.
- (c) sahi ✅: Dono 100 se zyada: 106 + 4 = 110 | 6 × 4 = 24 → 11024.
- (d) galat ❌: 96 aur 94 dono 100 se kam: yeh Post 7.2 ka type hai.
Q10. 101 × 107 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 10807
- (a) galat ❌: 10707: left mein 107 hi utaar liya, 1 jodna bhool gaye: 107 | 07 → 10707.
- (b) sahi ✅: 1 zyada, 7 zyada: 101 + 7 = 108 | 1 × 7 = 7 → 2 khaane: 108 | 07 → 10807.
- (c) galat ❌: 1087: 7 ko 2 khaane nahi diye: 108 | 7 → 1087.
- (d) galat ❌: 10870: 7 ko dahai wale khaane mein likh diya: 108 | 70 → 10870.
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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. 113 × 117 do tareeke se karo.
Solution dekho
Base method: 13 zyada, 17 zyada → 130 | 221 → 2 saikde left mein → 132 | 21 → 13221.
Post 6.3 wali bahan-trick: 113 aur 117 mein aage ka hissa same hai (11), aur ikai ka jod 3 + 7 = 10. To aage: 11 × 12 = 132 (Post 6.2 ki table), peeche: 3 × 7 = 21. Jawab 132 | 21 → 13221.
Check: dono same ✅
Q2. 101 × 101 = 10201, 102 × 102 = 10404, 103 × 103 = 10609. Agla, 104 × 104?
Solution dekho
Pattern: left = 100 + 2 × kitna zyada (102, 104, 106 → 108), right = kitna zyada × khud (01, 04, 09 → 16). To 108 | 16 → 10816.
Check: 104 ko 100 baar + 104 ko 4 baar = 10400 + 416 = 10816 ✅
Q3. Ek khet 108 metre lamba, 105 metre chauda. Area?
Solution dekho
108 × 105 → 108 + 5 = 113 | 8 × 5 = 40 → 11340 square metre.
Check: 105 ko 100 baar + 105 ko 8 baar = 10500 + 840 = 11340 ✅
Q4. □ × 107 = 11342, aur □ 100 se zyada. □ = ?
Solution dekho
Right 42 bana 7 (107 ka kitna zyada) ko □ ke kitna zyada se guna karke. 7 ko kis se guna karein ki 42 aaye? 6 se (7 × 6 = 42). To □ ka kitna zyada 6, yaani □ = 100 + 6 = 106. Left check: 106 + 7 = 113 ✅ (113 | 42).
Check: 106 × 107 = 11342 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 7–8) | Area (khet, maidan), squares (104² = 104 × 104, 112²) aur daam (cost) ke sawaal. |
| Maths Olympiad | Pattern (101², 102², 103²) aur ulta sawaal. |
| NTSE / MAT | Mental calculation aur do tareekon se check. |
| SSC / Bank (aage) | 102 × 108 jaise guna simplification 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. Mental calculation = bina copy-pencil ke, mann mein hisaab karna.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “kam ho to ghatao, zyada ho to jodo, kona hamesha guna.” Roz 5 sawaal 101 se 112 tak ke. Agle post mein saare tricky sawaal ek saath: ulta sawaal, base 1000 aur dhokhe wale! 🚀
— 📌 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. 104 → 4 zyada, 107 → 7 zyada. Left: 104 + 7 = 111. Right: 4 × 7 = 28. Jawab 111 | 28 = 11128 ✅
| 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. Kya 125 × 125 pe chalegi?
Chalegi: 150 | 625 → 6 saikde left mein → 156 | 25 → 15625. Par 25 × 25 mann mein mushkil; Post 6.1 ki 5 wali trick (12 × 13 = 156, peeche 25) aasaan.
2. Left hissa 3 digit ka kyun?
Kyunki 100 se zyada numbers ka guna 10000 se bada hai, to saikde 100 se zyada (111 saikde).
3. 7.2 aur 7.3 mein farq?
Bas left: kam wale mein ghatana, zyada wale mein jodna. Right dono mein guna.
4. Agle post mein kya hai?
Post 7.4: Base Method ke tricky sawaal: ulta sawaal, 999 × 998, aur jahan trick dhokha de.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Kitna zyada = number − 100 (aakhri do digit).
- Left: tirchha jodo (104 + 7 = 111).
- Right: kitna zyada ka guna, 2 khaane (06).
- Right 3 digit → saikda left mein (112 × 115 = 12880).
- Chitra: neela + naarangi + hara = left, gulaabi kona = right.
- 104 × 107 = 11128; andaaza: 10000 se thoda zyada.
— charumam.com 🎯
👉 Aage Kya?
Chapter 7 ka aakhri post: Base Method Ke Tricky Sawaal: ulta sawaal (□ × 98 = 9506), 999 × 998 (base 1000 ki jhalak) aur dhokhe wale sawaal!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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