Ab tak base 10 aur 100. Aaj base 1000: 997 × 996, 1004 × 1006, 1003 × 998. Niyam wahi, bas right hisse ko 3 khaane. Aur is post ka doosra, sabse zaroori hissa: base kaise chunein, aur kab yeh trick bilkul na lagaayein (jaise 56 × 43). Aakhir mein Speed Maths ki saari guna tricks ka ek naksha.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 997 × 996: 996 ko 1000 baar = 996000, usme se 996 ko 3 baar (2988) ghatao: 996000 − 2988 = 993012.
996 × 3 aur 6-digit ghatana: thoda bhaari. Trick mein: 997 − 4 aur 3 × 4.
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
997 × 996 = 993012
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: 1000 se doori (Post 3.2), 3 khaane wala niyam, bade numbers padhna (lakh!), aur minus kona + udhaar (8.1–8.2). Sab neeche ke boxes mein. Naye shabd:
📖 Shabd jo is post mein aayenge
- Base 1000: 1000 ke paas wale numbers (lagbhag 985 se 1015). 3 zero → right hissa 3 digit.
- Hazaar udhaar: base 1000 mein left hissa hazaar ginta hai; minus kona ke liye 1 hazaar (1000) udhaar lo.
- Lakh: 100 hazaar = 100000. 993012 = nau lakh teeraanve hazaar baarah.
- Base chunna: dono numbers jis round number ke sabse paas hon (aur ek hi ke paas hon), wahi base.
- Kab nahi: jab numbers kisi round number ke paas na hon (56 × 43), ya alag base ke paas hon (97 × 1003).
📏 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.
🎯 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 1000 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.
1000 se kitna kam? Post 3.2 wali trick: pehle do digit ko 9 se poora karo, aakhri ko 10 se. 1000 − 997: 9 − 9 = 0, 9 − 9 = 0, 10 − 7 = 3 → 003, yaani 3. 1000 − 988: 9 − 9 = 0, 9 − 8 = 1, 10 − 8 = 2 → 012, yaani 12.
| Number | Base 1000 se | Kaise nikala |
|---|---|---|
| 998 | 2 kam | 1000 − 998 = 2 |
| 996 | 4 kam | 0, 0, 10 − 6 = 4 → 004 |
| 989 | 11 kam | 0, 9 − 8 = 1, 10 − 9 = 1 → 011 |
| 1004 | 4 zyada | 1004 − 1000 = 4 |
| 1012 | 12 zyada | 1012 − 1000 = 12 |
Chhota raasta: 1000 se zyada wale (1001 se 1050 jaise) ka “kitna zyada” = uske aakhri teen digit: 1004 → 004 = 4.
🧱 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 1000 mein 3 zero hain. Isliye left hissa kitne hazaar ginta hai, aur right hisse ko jawab mein teen khaane milte hain. Niyam:
Right hisse mein digit = base ke zero (3)
- Right chhota pade (kam digit) → aage 0 bharo.
- Right bada pade (zyada digit) → sabse left wala extra hissa left hisse mein jodo (carry).
- 993 | 012: 12 ko teen digit mein likho: 012. 993 hazaar + 12 = 993000 + 12 = 993012.
- 995 | 006: 6 ko 006 likho. 995000 + 6 = 995006.
- Carry: maan lo kisi sawaal mein 979 | 1452 aaya: chaar digit, jagah teen. 1452 = 1 hazaar + 452 → 979 + 1 = 980 → 980452. Pakka: 979000 + 1452 = 980452 ✅.
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.
🔢 Bahut bade numbers padhna: hazaar, lakh, das lakh
Place value ki jagahein right se aage badhti rehti hain, har agli jagah pichhli se 10 guna: Ikai (1), Dahai (10), Saikda (100), Hazaar (1000), Das hazaar (10000), Lakh (100000, yaani 100 hazaar), Das lakh (1000000).
| Number | Kaise padhein | Tukde |
|---|---|---|
| 993012 | nau lakh teeraanve hazaar baarah | 993 hazaar + 12 = 993000 + 12 |
| 995006 | nau lakh pachaanve hazaar chhe | 995000 + 6 |
| 1010024 | das lakh das hazaar chaubees | 1010 hazaar + 24 = 1010000 + 24 |
Teen-teen ka group: bade jawab ko right se teen-teen digit mein dekho: 993 | 012. Right ka group hazaar se chhota hissa hai (0 se 999), aur left ka group batata hai “kitne hazaar”. Base 1000 ki trick mein deewar bilkul yahin aati hai!
Hazaar se guna: 1000 = 10 × 10 × 10, isliye 1000 se guna = peeche teen 0: 993 × 1000 = 993000.
➖ Minus wala right hissa aur udhaar (base 1000)
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: 1001 | −006 (yeh 1003 × 998 mein aayega). Base 1000 mein 3 zero, to right teen digit ka: 6 → 006.
- Left mein se 1 hazaar udhaar: 1000 bache.
- Woh 1 hazaar = 1000. 1000 − 006, Post 3.2 ki trick: 9 − 0 = 9, 9 − 0 = 9, 10 − 6 = 4 → 994.
- Jawab: 1000 | 994 = 1000994.
🔁 Chhota sa warm-up
- 1000 − 996 = ?
- 993 × 1000 = ?
- 993000 + 12 = ?
Answers dekho
- 4
- 993000
- 993012
Teeno aa gaye? Yahi milkar 997 × 996 = 993012!
— 📌 charumam.com
🎬 Kahani: Motiyon Ke Dabbe
Ek mala banane wale kaarkhaane mein 997 dabbe aaye, har dabbe mein 996 moti. Maalik ne poochha: “Kul kitne moti?” Sab chup.
Unki beti Noor boli: “997 → 3 kam, 996 → 4 kam. 997 − 4 = 993, 3 × 4 = 12, teen khaane: 012. 993012, yaani nau lakh teeraanve hazaar baarah!”
Maalik: “Itni jaldi?” Noor: “CharuMam ki Speed Maths! Par ek baat: agar 56 × 43 poochhte to main yeh trick nahi lagaati.” “Kyun?” “Kyunki woh kisi base ke paas hi nahi!”
Aaj dono seekhenge: base 1000, aur kab rukna hai. 🧭
— 📌 charumam.com
🪄 Trick Step by Step: Base 1000: 3 Khaane, Aur Sahi Base Chunna
💡 Is post ki ek badi baat: Base 1000 ke paas: left = tirchha (kam → ghatao, zyada → jodo, alag taraf → upar wale mein se neeche ka kam), right = doori × doori, 3 khaane; alag taraf ho to minus aur 1 hazaar udhaar. Sabse pehle: dono ek hi base ke paas hain?
Step 1: Base chuno
997 aur 996 dono 1000 ke paas. Base 1000, 3 zero → 3 khaane.
Step 2: Dooriyan (Post 3.2 trick)
997 → 1000 − 997 = 3 kam. 996 → 4 kam.
Step 3: Left: tirchha
Dono kam → ghatao: 997 − 4 = 993 (ya 996 − 3).
Step 4: Right: 3 khaane
3 × 4 = 12 → 3 khaane: 012.
Step 5: Saath likho
993 | 012 = 993 hazaar + 12 = 993000 + 12 = 993012 ✅. Padho: nau lakh teeraanve hazaar baarah.
Base 1000 ke saare type
| Sawaal | Base se doori | Left (tirchha) | Kona (right) | Jawab |
|---|---|---|---|---|
| 998 × 997 | 2 kam, 3 kam | 998 − 3 = 995 | 2 × 3 = 6 | 995 | 006 → 995006 |
| 999 × 995 | 1 kam, 5 kam | 999 − 5 = 994 | 1 × 5 = 5 | 994 | 005 → 994005 |
| 991 × 989 | 9 kam, 11 kam | 991 − 11 = 980 | 9 × 11 = 99 | 980 | 099 → 980099 |
| 1004 × 1006 | 4 zyada, 6 zyada | 1004 + 6 = 1010 | 4 × 6 = 24 | 1010 | 024 → 1010024 |
| 1012 × 1005 | 12 zyada, 5 zyada | 1012 + 5 = 1017 | 12 × 5 = 60 | 1017 | 060 → 1017060 |
| 1003 × 998 | 3 zyada, 2 kam | 1003 − 2 = 1001 | 3 × 2 = 6, ghatao | 1001 | −006 → 1000 | 994 → 1000994 |
| 1005 × 996 | 5 zyada, 4 kam | 1005 − 4 = 1001 | 5 × 4 = 20, ghatao | 1001 | −020 → 1000 | 980 → 1000980 |
| 1010 × 990 | 10 zyada, 10 kam | 1010 − 10 = 1000 | 10 × 10 = 100, ghatao | 1000 | −100 → 999 | 900 → 999900 |
1003 × 998 (alag taraf) dhyaan se: 3 zyada, 2 kam. Left: 1003 − 2 = 1001. Kona: 3 × 2 = 6 → 3 khaane: −006. 1001 | −006 → 1 hazaar udhaar → 1000 | 994 = 1000994. (1000 − 006: Post 3.2: 9 − 0 = 9, 9 − 0 = 9, 10 − 6 = 4 → 994.) Padho: das lakh nau sau chauraanve.
Base kaise chunein?
| Sawaal | Dono kiske paas? | Base | Khaane |
|---|---|---|---|
| 8 × 7, 12 × 8 | 10 | 10 | 1 |
| 97 × 96, 103 × 97 | 100 | 100 | 2 |
| 997 × 996, 1003 × 998 | 1000 | 1000 | 3 |
| 97 × 1003 | alag (100 aur 1000) | ❌ koi ek nahi | seedha karo |
| 56 × 43 | kisi ke paas nahi | ❌ | seedha karo |
Kab NAHI: 56 × 43
56 aur 43, 10 se bahut door (46 aur 33 zyada), 100 se bhi door (44 aur 57 kam). Kona 44 × 57 khud ek bada guna ban jaata hai. Trick ka koi fayda nahi! Seedha todo: 56 ko 43 baar = 56 ko 40 baar + 56 ko 3 baar.
56 ko 3 baar: 56, 112, 168.
56 ko 4 baar: 56, 112, 168, 224.
40 baar = 4 baar ka 10 guna, aur 10 se guna = peeche ek 0 (Ch 5). To 56 ko 40 baar = 2240.
Ab jodo: 2240 + 168 = 2408.
Speed Maths ki guna tricks ka naksha
| Sawaal kaisa dikhe | Kaunsi trick | Kahan |
|---|---|---|
| Koi number × 11 | beech mein jod | Chapter 4 |
| × 5, × 25, × 50 | × 10 / × 100 phir aadha/chautha | Chapter 5 |
| 5 pe khatam ka square, ya dahai same + ikai jod 10 | dahai × agla, peeche ikai × ikai | Chapter 6 |
| Dono ek base (10, 100, 1000) ke paas, ek taraf | base method, kona jodo | Chapter 7 |
| Dono ek base ke paas, alag taraf | base method, kona ghatao, udhaar | Chapter 8 |
| Koi trick theek na baithe | seedha tod (place value) | Chapter 1–2 ki soch |
🆘 Atak gaye? Aise socho
- 3 khaane yaad? 1000 → 3 zero. 12 → 012, 6 → 006.
- Bada number padhna? Right se 3-3 ka group: 993 | 012 → 993 hazaar baarah. 10 lakh = 1000000.
- Base samajh nahi aaya? Dono numbers ko dekho: kis round number se dono ki doori chhoti (lagbhag 15 tak) hai?
- Koi base theek nahi baithta? Seedha todo: 56 ko 40 baar + 56 ko 3 baar = 2240 + 168.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Wahi chitra, bas bada. 997 × 996 ek aayat (naap se nahi): chaudai 997, oonchai 996.
- Oonchai 996 ko 1000 banane ke liye 4 chahiye. Right se 4 chaudi patti kaato: neela 997 − 4 = 993 chauda.
- Patti ghuma kar upar: oonchai 1000. Neela + patti = 993 × 1000 = 993000.
- Patti 996 lambi, neela 993 chauda: 3 × 4 = 12 baahar nikla.
Kul 993000 + 12 = 993012. Left hissa ab hazaar ginta hai, isliye right ko 3 khaane (000 se 999).
Trick lagaun ya nahi? Kadmon ka naksha (flow chart)
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 998 × 997 = ?
2 kam, 3 kam. Left: 998 − 3 = 995. Right: 6 → 006. 995 | 006 → 995006.
✔️ Normal tareeke se check: 997 ko 1000 baar − 997 ko 2 baar = 997000 − 1994 = 995006 ✅
Example 2: 1005 × 1008 = ?
5 zyada, 8 zyada. Left: 1005 + 8 = 1013. Right: 40 → 040. 1013 | 040 → 1013040.
✔️ Normal tareeke se check: 1005 ko 1000 baar + 1005 ko 8 baar = 1005000 + 8040 = 1013040 ✅
Example 3: 1002 × 997 = ? (alag taraf)
2 zyada, 3 kam. Left: 1002 − 3 = 999. Kona: 6 → −006. 999 | −006 → 998 | 994 → 998994.
✔️ Normal tareeke se check: 1002 ko 1000 baar − 1002 ko 3 baar = 1002000 − 3006 = 998994 ✅
Example 4: 991 × 989 = ?
9 kam, 11 kam. Left: 991 − 11 = 980. Right: 9 × 11 = 99 → 099. 980 | 099 → 980099.
✔️ Normal tareeke se check: 991 ko 1000 baar − 991 ko 11 baar = 991000 − 10901 = 980099 ✅ (991 × 11 = 10901, Ch 4 trick)
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabein Nikhilam ko 10, 100, 1000, 10000 jaise bases pe dikhati hain. Is chapter mein hum 10, 100, 1000 pe hi ruke hain, kyunki wahan kitabon wala niyam (jitne zero, utne khaane) seedha chitra se samajh aata hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Dono 1000 ke paas (997 × 996) | ✅ Haan | 3 khaane. |
| Alag taraf (1003 × 998) | ✅ Haan | Hazaar udhaar. |
| Alag base (97 × 1003) | ❌ Nahi | Seedha: 97 × 1000 + 97 × 3. |
| Kisi base ke paas nahi (56 × 43) | ❌ Nahi | Seedha tod. |
| × 11 ya 5 pe khatam ka square | ➡️ Ch 4 / Ch 6 | Woh tricks zyada tez. |
| Doori 15 jitni (1015 × 985) | ⚠️ Soch ke | Kona 15 ko 15 baar = 15 ko 10 baar + 15 ko 5 baar = 150 + 75 = 225; chalega, par dhyaan se. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Base 1000 mein 2 khaane
Sawaal: 998 × 997
❌ Galat: 995 | 06 → 99506.
✅ Sahi: 3 khaane: 006 → 995006. Andaaza: jawab 1000 × 1000 (yaani 10 lakh) ke paas, 6 digit ka.
Galti 2: Alag base pe trick
Sawaal: 97 × 1003
❌ Galat: 97 − 3 jaisa kuch karke left 94 le liya.
✅ Sahi: alag base: seedha 97 × 1000 + 97 × 3 = 97000 + 291 = 97291.
Galti 3: Udhaar mein 1000 − kona galat
Sawaal: 1003 × 998
❌ Galat: 1000 | 004 likh diya (1000 − 006 galat nikala).
✅ Sahi: Post 3.2: 9, 9, 10 − 6 = 4 → 994 → 1000994.
Galti 4: Door numbers pe zabardasti trick
Sawaal: 56 × 43
❌ Galat: base 100 maan ke 44 × 57 ka guna shuru kiya, aur atak gaye.
✅ Sahi: seedha tod: 56 ko 40 baar + 56 ko 3 baar = 2240 + 168 = 2408.
🧠 Rule of thumb: Pehle base chuno (ek hi, aur paas). Khaane = zero. Trick theek na baithe to seedha tod.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Mix drill: base 1000, aur kuch “kab nahi” wale. Target: 5 minute.
- 999 × 999 = ?
- 998 × 996 = ?
- 997 × 995 = ?
- 995 × 995 = ?
- 1001 × 1003 = ?
- 1004 × 1005 = ?
- 1006 × 1006 = ?
- 1010 × 1003 = ?
- 1002 × 998 = ?
- 1004 × 997 = ?
- 1001 × 999 = ?
- 1008 × 995 = ?
- 12 × 98 = ?
- 56 × 43 = ?
- 11 × 104 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 998001
- 994008
- 992015
- 990025
- 1004003
- 1009020
- 1012036
- 1013030
- 999996
- 1000988
- 999999
- 1002960
- 1176
- 2408
- 1144
Kaise kiya (kuch): 1008 × 995: 1003 | −040 → 1002 | 960 → 1002960. 12 × 98 alag base: 98 ko 10 baar (980) + 98 ko 2 baar (196) = 1176. 11 × 104: Ch 4 ki × 11 trick → 1144.
— 📌 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.
- 999 × 998 = ?
- 997 × 997 = ?
- 996 × 998 = ?
- 1002 × 1003 = ?
- 1005 × 1005 = ?
- 1003 × 1007 = ?
- 1001 × 998 = ?
- 1003 × 997 = ?
- 1005 × 995 = ?
- 994 × 999 = ?
| 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
- 997002
- 994009
- 994008
- 1005006
- 1010025
- 1010021
- 998998
- 999991
- 999975
- 993006
Dhyaan: 1005 × 995: 1000 | −025 → 999 | 975 → 999975. 994 × 999: 993 | 006 → 993006.
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. 997 × 996 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 993012
- (a) galat ❌: 993120: 12 ko galat khaanon mein likha: 993 | 120 → 993120.
- (b) galat ❌: 994012: 997 mein se apna hi kitna kam ghata diya: 997 − 3 = 994 | 012 → 994012.
- (c) sahi ✅: 3 kam, 4 kam: 997 − 4 = 993 | 3 × 4 = 12 → 3 khaane: 993 | 012 → 993012.
- (d) galat ❌: 99312: 12 ko 2 hi khaane diye: 993 | 12 → 99312.
Q2. Base 1000 mein right kitne digit ka?
Jawab aur kaaran dekho
Sahi jawab: (b) 3
- (a) galat ❌: 1 digit base 10 ke liye (10 mein 1 zero).
- (b) sahi ✅: 1000 mein 3 zero, to 3 digit (jaise 012).
- (c) galat ❌: 2 digit base 100 ke liye (100 mein 2 zero).
- (d) galat ❌: 4 digit base 10000 ke liye (10000 mein 4 zero).
Q3. 1003 × 998 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 1000994
- (a) sahi ✅: 3 zyada, 2 kam: 1003 − 2 = 1001 | −006 → 1 hazaar udhaar: 1000 | 994 → 1000994.
- (b) galat ❌: 1001006: kona ghatane ki jagah jod diya: 1001 | 006 → 1001006.
- (c) galat ❌: 1000006: udhaar se left 1000 kiya par right mein 1000 − 006 ki jagah 006 hi likh diya: 1000 | 006 → 1000006.
- (d) galat ❌: 1001994: right 1000 − 006 = 994 kiya par left 1 kam nahi kiya: 1001 | 994 → 1001994.
Q4. 56 × 43 pe base method kyun nahi?
Jawab aur kaaran dekho
Sahi jawab: (d) Dono kisi base ke paas nahi
- (a) galat ❌: Bada hona wajah nahi; 997 bhi bada hai aur trick chalti hai.
- (b) galat ❌: Aakhri digit se farq nahi padta; 1003 × 998 mein bhi 3 hai aur trick chalti hai.
- (c) galat ❌: Base 10 se hota hai (8 × 7), bas yeh numbers 10 ke paas nahi.
- (d) sahi ✅: 10 se 46 aur 33 door, 100 se 44 aur 57 door. Seedha tod: 56 ko 40 baar + 56 ko 3 baar = 2240 + 168 = 2408.
Q5. 97 × 1003 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 97291
- (a) galat ❌: 97003: 97 × 3 ki jagah sirf 3 joda: 97000 + 3 = 97003.
- (b) galat ❌: 97300: 97 × 3 ki jagah 300 joda (3 ke peeche do 0): 97000 + 300 = 97300.
- (c) sahi ✅: Alag base, seedha: 97 × 1000 + 97 × 3 = 97000 + 291 = 97291.
- (d) galat ❌: 97091: 97 × 3 = 291 ki jagah sirf 91 joda: 97000 + 91 = 97091.
Q6. 993012 ko kaise padhein?
Jawab aur kaaran dekho
Sahi jawab: (b) Nau lakh teeraanve hazaar baarah
- (a) galat ❌: Nau hazaar teen sau baarah = 9312, sirf 4 digit ka; 993012 bahut bada hai.
- (b) sahi ✅: 993 hazaar = 9 lakh 93 hazaar, aur 012 = baarah.
- (c) galat ❌: 993 hazaar to sahi padha, par baarah (12) bhool gaye; yeh 993000 hai.
- (d) galat ❌: Ninyaanve lakh = 9900000, 7 digit ka; 993012 to 6 digit ka hai.
Q7. 1005 × 1008 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 1013040
- (a) sahi ✅: 5 zyada, 8 zyada: 1005 + 8 = 1013 | 5 × 8 = 40 → 3 khaane: 1013 | 040 → 1013040.
- (b) galat ❌: 101340: 40 ko 2 hi khaane diye: 1013 | 40 → 101340.
- (c) galat ❌: 1013400: 40 ko galat khaanon mein likha: 1013 | 400 → 1013400.
- (d) galat ❌: 1013013: right mein guna ki jagah jod: 5 + 8 = 13 → 1013 | 013 → 1013013.
Q8. Kis sawaal pe base 1000 trick?
Jawab aur kaaran dekho
Sahi jawab: (d) 1004 × 996
- (a) galat ❌: 97 × 96 base 100 ka hai (Post 7.2).
- (b) galat ❌: 56 × 43 kisi base ke paas nahi; seedha tod.
- (c) galat ❌: 12 × 8 base 10 ka hai (Post 8.1).
- (d) sahi ✅: Dono 1000 ke paas: 1004 − 4 = 1000 | −016 → 999 | 984 → 999984.
Q9. 991 × 989 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 980099
- (a) galat ❌: 980990: 99 ko galat khaanon mein likha: 980 | 990 → 980990.
- (b) galat ❌: 982099: 991 mein se apna hi kitna kam ghata diya: 991 − 9 = 982 | 099 → 982099.
- (c) sahi ✅: 9 kam, 11 kam: 991 − 11 = 980 | 9 × 11 = 99 → 3 khaane: 980 | 099 → 980099.
- (d) galat ❌: 98099: 99 ko 2 hi khaane diye: 980 | 99 → 98099.
Q10. 1000 − 006 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 994
- (a) galat ❌: 993: teeno digit 9 se poore kar diye: 9 − 0 = 9, 9 − 0 = 9, 9 − 6 = 3 → 993. Aakhri digit 10 se poora hota hai.
- (b) sahi ✅: Post 3.2: pehle do digit 9 se: 9 − 0 = 9, 9 − 0 = 9; aakhri 10 se: 10 − 6 = 4 → 994.
- (c) galat ❌: 4: sirf aakhri digit ka 10 − 6 = 4 kiya; pehle do digit ke 9 bhool gaye.
- (d) galat ❌: 1006: ghatane ki jagah jod diya: 1000 + 6 = 1006.
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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. 999 × 999 = 998001. 99 × 99 = 9801, 9 × 9 = 81. Pattern se 9999 × 9999?
Solution dekho
9 × 9 → 8 | 1, 99 × 99 → 98 | 01, 999 × 999 → 998 | 001. Base 10000: 1 kam, 1 kam → 9998 | 0001 → 99980001.
Check: 9999 ko 10000 baar − 9999 = 99990000 − 9999 = 99980001 ✅
Q2. Do numbers 1000 se barabar door (ek upar, ek neeche). Guna 999964. Numbers?
Solution dekho
Left 1000, to 1000000 − 999964 = 36 kam. 36 = 6 × 6 → doori 6. Numbers 1006 aur 994.
Check: 1006 × 994: 1000 | −036 → 999 | 964 → 999964 ✅
Q3. Ek bahut bada khet 1004 metre lamba, 1007 metre chauda hai. Area (kitne square metre)?
Solution dekho
4 zyada, 7 zyada. Left: 1011. Right: 28 → 028. 1011 | 028 → 1011028 square metre (das lakh gyaarah hazaar atthaais).
Check: 1004 ko 1000 baar + 1004 ko 7 baar = 1004000 + 7028 = 1011028 ✅
Q4. 97 × 1003 pe base method kyun nahi, aur jawab?
Solution dekho
97 base 100 ke paas, 1003 base 1000 ke paas: alag base. Seedha: 97 × 1000 + 97 × 3 = 97000 + 291 = 97291.
Check: 1003 ko 97 baar = 1003 ko 100 baar − 1003 ko 3 baar = 100300 − 3009 = 97291 ✅
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🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 7–8) | Bade area aur daam (cost) ke sawaal, aur bade numbers padhna (lakh). |
| Maths Olympiad | Pattern (9 × 9, 99 × 99, 999 × 999) aur ulta sawaal. |
| NTSE / MAT | Sahi tareeka chunna: kab trick, kab seedha. |
| SSC / Bank (aage) | 998 × 997 jaise guna aur simplification. |
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.
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👩🏫 CharuMam Ka Tip
Sabse badi seekh: trick ek auzaar hai, zaroorat nahi. Pehle sawaal ko dekho, phir auzaar chuno. Agle post mein Chapter 8 ke saare tricky sawaal! 🧭
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⏱ 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 1000 (3 khaane). 997 → 3 kam, 996 → 4 kam. Left: 997 − 4 = 993. Right: 3 × 4 = 12 → 012. Jawab 993 | 012 = 993012 ✅
| 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. Base 10000 bhi hota hai?
Haan: 9997 × 9996 → 9993 | 0012 → 99930012 (4 khaane). Niyam same.
2. Kya koi bhi round number base ban sakta hai?
Is chapter ka niyam sirf 10, 100, 1000 jaise bases ke liye hai (jinme peeche sirf 0 hon aur shuru mein 1). Inhi pe “jitne zero, utne khaane” seedha chalta hai.
3. Sabse zaroori kya hai?
Trick lagane se pehle check: ek hi base, aur paas. Warna seedha tod.
4. Agle post mein kya hai?
Post 8.4: Above and Below Base ke tricky sawaal: ulte sawaal, pattern aur dhokhe.
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🟢 Recap: Aaj Kya Seekha
- Base 1000 → 3 khaane (993 | 012).
- Alag taraf → minus kona, 1 hazaar udhaar (1003 × 998 = 1000994).
- Base = dono jis round number ke paas.
- Alag base ya door numbers → seedha tod.
- Bade jawab: 3-3 ka group, lakh mein padho.
- Naksha: × 11 (Ch 4), × 5 (Ch 5), squares (Ch 6), base method (Ch 7–8).
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👉 Aage Kya?
Chapter 8 ka aakhri post: Above And Below Base Ke Tricky Sawaal: ulte sawaal (□ × 97 = 10088), pattern, aur dhokhe!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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