7 ka pahaada sabse zyada bachchon ko pareshaan karta hai! 😅 Aaj Trachtenberg ka × 7 niyam, jisme pahaada chahiye hi nahi. Achhi khabar: yeh Post 12.1 ke × 6 jaisa hi hai, bas ek shabd badalta hai: “digit khud” ki jagah “digit ka double”. Padosi ka aadha aur taaq pe 5 bilkul wahi.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle school wala tareeka (column method). 625 × 7, right se:
- Ikai: 7 × 5 = 35. Neeche 5 likho, 3 carry.
- Dahai: 7 × 2 = 14, carry 3 jodo: 14 + 3 = 17. Neeche 7 likho, 1 carry.
- Saikda: 7 × 6 = 42, carry 1 jodo: 42 + 1 = 43. Neeche 43 likho.
- Jawab: 4375. 7 ka pahaada (7 × 5, 7 × 2, 7 × 6) pakka hona chahiye.
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
625 × 7 = 4375
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: Post 12.1 ka × 6 niyam, Chapter 11 ka double, aur carry 2. Neeche ke boxes mein double, juft/taaq, padosi ka aadha aur × 5 dobara. Naye shabd:
📖 Shabd jo is post mein aayenge
- × 7 niyam: har digit ka double + padosi ka aadha (½ chhod kar) + 5 agar digit khud taaq.
- 7 = 2 + 5: 7 ko 2 aur 5 mein todte hain: × 2 (double) aur × 5 (× 10 ka aadha).
- Carry 2: jab jod 20 se 29 aaye: 23 → 3 likho, 2 carry. × 7 mein carry 2 tak aa sakta hai.
- Kadam ke chaar hisse: double + (taaq ho to 5) + padosi ka aadha + carry. Ek-ek karke jodo.
📏 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.
✌️ Double karna kya hai?
Double matlab number ko do baar lena, yaani number mein wahi number jodna. 7 ka double: 7 + 7 = 14. Yahi 2 × 7 bhi hai (GUNA box: 2 × 7 matlab 7 ko 2 baar jodo).
| Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Double | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |
(Table mein upar digit hai, neeche uska double. Jaise 6 ke neeche 12, kyunki 6 + 6 = 12.) Is chapter mein hum sirf ek digit (0 se 9) ka double karenge, to sabse bada double 18 hai.
⚖️ Juft aur taaq digit (even aur odd)
Chapter 5 mein dekha tha: jo number 2 barabar hisson mein bina kuch bache bant jaaye, woh juft (even) hai. Jo poora na bante, ek bach jaaye, woh taaq (odd) hai. Is chapter mein hum sirf ek digit (0 se 9) dekhenge:
| Juft digit (2 barabar hisse, kuch nahi bachta) | 0 | 2 | 4 | 6 | 8 |
|---|---|---|---|---|---|
| Taaq digit (ek bach jaata hai) | 1 | 3 | 5 | 7 | 9 |
Yaad karne ka tareeka: 0, 2, 4, 6, 8 juft (do-do karke ginti: 2, 4, 6, 8). Baaki 1, 3, 5, 7, 9 taaq. Jaise 6 laddoo, 2 bachche: 3-3, kuch nahi bacha → juft. 7 laddoo: 3-3, aur 1 bach gaya → taaq. Aur 0? 0 laddoo baantne pe dono ko 0, kuch nahi bacha, to 0 juft hai.
✂️ “Padosi ka aadha”: aadha karo, adhoora hissa chhod do
Aadha matlab 2 barabar hisse karke ek hissa (Chapter 5). Juft digit ka aadha seedha: 8 ka aadha 4 (4 + 4 = 8). Par taaq digit ka aadha poora nahi aata: 7 ka aadha “3 aur ek aadha” (3½, padho “saadhe teen”).
Is chapter ka niyam: taaq digit ka aadha karo to adhoora (½) hissa chhod do, sirf poora hissa lo. 7 ka aadha → 3½ → 3. Is ½ ko “chhodna” galti nahi hai: woh ½ kahin gaya nahi, woh “taaq pe 5” wale niyam mein wapas aata hai (neeche “Yeh Kaam Kyun Karta Hai” mein dekhenge).
| Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Aadha (½ chhod kar) | 0 | 0 | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 |
(Upar digit, neeche uska aadha. Jaise 9 ke neeche 4: 9 ka aadha 4½, ½ chhoda, to 4. Aur 1 ka aadha ½ hai, ½ chhoda to 0.) Pakka tareeka: taaq digit ho to pehle 1 kam karo (juft ban jaayega), phir aadha: 7 → 6 → 3. 9 → 8 → 4.
🪙 × 5 = × 10 ka aadha (Chapter 5 yaad karo)
Chapter 5 mein seekha: kisi number × 5 = us number × 10, phir aadha, kyunki 5 = 10 ka aadha. Jaise 7 × 5: peeche 0 → 70, aadha → 35.
Noton se dekho: ₹70 matlab ₹10 ke 7 note. Inhe Aman aur Riya mein barabar baanto: dono ko 3-3 note (₹30), aur 1 note bach gaya. Use tod kar ₹5 Aman ko, ₹5 Riya ko. Har ek ko ₹30 + ₹5 = ₹35.
Dhyaan do: 7 ke aadhe se do cheezein mili: 3 note (dahai wala hissa, “7 ka aadha ½ chhod kar”) aur ek ₹5 (ikai mein), kyunki 7 taaq tha. Agar digit juft hota (jaise 6), to koi note nahi bachta: ₹60 ka aadha ₹30, ₹5 nahi. Yahi do baatein aaj ke niyam mein aayengi: “padosi ka aadha” aur “taaq pe 5”.
🔁 Chhota sa warm-up
- 6 ka double?
- 5 ka aadha, ½ chhod kar?
- 9 taaq hai?
Answers dekho
- 12 (6 + 6)
- 2 (5 ka aadha 2½)
- Haan (9 = 4 + 4 + 1)
Bas! × 7 ke auzaar taiyaar.
— 📌 charumam.com
🎬 Kahani: Hafte Ke Saat Din
Ek hafte mein 7 din. Riya ne socha: “Main 34 hafte se roz kahani padh rahi hoon. Kitne din ho gaye?”
Usne 034 likha: “Ikai 4: double 8, 4 juft, padosi nahi: 8. Dahai 3: double 6, 3 taaq to +5, padosi 4 ka aadha 2: 6 + 5 + 2 = 13 → 3 likho, 1 carry. Aage 0: padosi 3 ka aadha 1, carry 1: 2.”
“238 din!” Mummy ne calendar ginne ki koshish chhod di aur hans padi. 📅
Riya: “× 6 wala niyam, bas digit ka double!” Aaj yahi seekhenge. 7️⃣
— 📌 charumam.com
🪄 Trick Step by Step: Double + Padosi Ka Aadha, Taaq Ho To + 5
💡 Is post ki ek badi baat: × 7 ka niyam: aage 0 lagao. Right se left, har digit pe: digit ka double + padosi ka aadha (½ chhod kar). Agar digit khud taaq hai, to 5 aur. Carry (1 ya 2) agle kadam mein. Ikai ka padosi nahi.
Step 1: Aage 0
Sawaal: 34 × 7. Aage 0: 034.
Step 2: Ikai: double (+5 agar taaq)
Ikai 4: double 4 + 4 = 8. 4 juft → 5 nahi. Padosi nahi. Neeche 8.
Step 3: Dahai: double + 5? + aadha padosi
Dahai 3: double 3 + 3 = 6. 3 taaq → +5. Padosi 4 ka aadha 2. Jodo: 6 + 5 + 2 = 13 → 3 likho, 1 carry.
Step 4: Aage 0: aadha padosi + carry
0 ka double 0, 0 juft. Padosi 3 ka aadha 1 (½ chhoda). Carry 1. Jodo: 0 + 1 + 1 = 2.
Step 5: Jawab aur check
2 | 3 | 8 = 238. Check: 34 × 7 = 34 × 5 + 34 × 2 = 170 + 68 = 238 ✅ (34 × 5: 340 ka aadha 170.)
34 × 7: number ke aage 0 lagao → 034. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 4 | 4 ka double: 4 + 4 = 8; 4 juft hai, to 5 nahi; padosi nahi (ikai ke right mein koi digit nahi). Kul: 8 | 8 | 0 |
| 2 | Dahai | 3 | 3 ka double: 3 + 3 = 6; 3 taaq hai, to 5 jodo; padosi 4 ka aadha 2. Jod: 6 + 5 + 2 = 13 | 3 | 1 |
| 3 | Saikda | 0 (aage wala) | aage wala 0: double 0 + 0 = 0; padosi 3 ka aadha 1 (aadha hissa chhod diya); haath ka carry 1. Jod: 0 + 1 + 1 = 2 | 2 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 2 | 3 | 8 → 238.
Carry 2 wala sawaal: 999 × 7
Sabse bade digit pe sabse bada jod: double 18 + 5 + aadha padosi 4 + carry 2 = 29. Isliye carry 2 tak aata hai.
999 × 7: number ke aage 0 lagao → 0999. Ab right se left (ikai se shuru) har digit pe niyam:
| Kadam | Jagah | Digit | Kaam | Likho | Carry aage |
|---|---|---|---|---|---|
| 1 | Ikai | 9 | 9 ka double: 9 + 9 = 18; 9 taaq hai, to 5 jodo; padosi nahi (ikai ke right mein koi digit nahi). Jod: 18 + 5 = 23 | 3 | 2 |
| 2 | Dahai | 9 | 9 ka double: 9 + 9 = 18; 9 taaq hai, to 5 jodo; padosi 9 ka aadha 4 (aadha hissa chhod diya); haath ka carry 2. Jod: 18 + 5 + 4 + 2 = 29 | 9 | 2 |
| 3 | Saikda | 9 | 9 ka double: 9 + 9 = 18; 9 taaq hai, to 5 jodo; padosi 9 ka aadha 4 (aadha hissa chhod diya); haath ka carry 2. Jod: 18 + 5 + 4 + 2 = 29 | 9 | 2 |
| 4 | Hazaar | 0 (aage wala) | aage wala 0: double 0 + 0 = 0; padosi 9 ka aadha 4 (aadha hissa chhod diya); haath ka carry 2. Jod: 0 + 4 + 2 = 6 | 6 | — |
Ab “Likho” wale digit neeche se upar, yaani left se right padho: 6 | 9 | 9 | 3 → 6993.
× 6 aur × 7 aamne-saamne
| Baat | × 6 | × 7 |
|---|---|---|
| Tod | 6 = 1 + 5 | 7 = 2 + 5 |
| Digit pe | digit khud | digit ka double |
| Padosi pe | aadha (½ chhod kar) | aadha (½ chhod kar) |
| Taaq digit pe | +5 | +5 |
| Sabse bada carry | 1 | 2 |
Ek-digit × 7 (7 ka pahaada bina ratte)
| Sawaal | Ikai (double) | Aage wala 0 | Jawab |
|---|---|---|---|
| 2 × 7 | 2 ka double: 2 + 2 = 4; 2 juft hai, to 5 nahi; padosi nahi (ikai ke right mein koi digit nahi). Kul: 4 → likho 4 | aage wala 0: double 0 + 0 = 0; padosi 2 ka aadha 1. Jod: 0 + 1 = 1 → likho 1 | 14 |
| 3 × 7 | 3 ka double: 3 + 3 = 6; 3 taaq hai, to 5 jodo; padosi nahi (ikai ke right mein koi digit nahi). Jod: 6 + 5 = 11 → likho 1, carry 1 | aage wala 0: double 0 + 0 = 0; padosi 3 ka aadha 1 (aadha hissa chhod diya); haath ka carry 1. Jod: 0 + 1 + 1 = 2 → likho 2 | 21 |
| 4 × 7 | 4 ka double: 4 + 4 = 8; 4 juft hai, to 5 nahi; padosi nahi (ikai ke right mein koi digit nahi). Kul: 8 → likho 8 | aage wala 0: double 0 + 0 = 0; padosi 4 ka aadha 2. Jod: 0 + 2 = 2 → likho 2 | 28 |
| 5 × 7 | 5 ka double: 5 + 5 = 10; 5 taaq hai, to 5 jodo; padosi nahi (ikai ke right mein koi digit nahi). Jod: 10 + 5 = 15 → likho 5, carry 1 | aage wala 0: double 0 + 0 = 0; padosi 5 ka aadha 2 (aadha hissa chhod diya); haath ka carry 1. Jod: 0 + 2 + 1 = 3 → likho 3 | 35 |
| 6 × 7 | 6 ka double: 6 + 6 = 12; 6 juft hai, to 5 nahi; padosi nahi (ikai ke right mein koi digit nahi). Kul: 12 → likho 2, carry 1 | aage wala 0: double 0 + 0 = 0; padosi 6 ka aadha 3; haath ka carry 1. Jod: 0 + 3 + 1 = 4 → likho 4 | 42 |
| 7 × 7 | 7 ka double: 7 + 7 = 14; 7 taaq hai, to 5 jodo; padosi nahi (ikai ke right mein koi digit nahi). Jod: 14 + 5 = 19 → likho 9, carry 1 | aage wala 0: double 0 + 0 = 0; padosi 7 ka aadha 3 (aadha hissa chhod diya); haath ka carry 1. Jod: 0 + 3 + 1 = 4 → likho 4 | 49 |
| 8 × 7 | 8 ka double: 8 + 8 = 16; 8 juft hai, to 5 nahi; padosi nahi (ikai ke right mein koi digit nahi). Kul: 16 → likho 6, carry 1 | aage wala 0: double 0 + 0 = 0; padosi 8 ka aadha 4; haath ka carry 1. Jod: 0 + 4 + 1 = 5 → likho 5 | 56 |
| 9 × 7 | 9 ka double: 9 + 9 = 18; 9 taaq hai, to 5 jodo; padosi nahi (ikai ke right mein koi digit nahi). Jod: 18 + 5 = 23 → likho 3, carry 2 | aage wala 0: double 0 + 0 = 0; padosi 9 ka aadha 4 (aadha hissa chhod diya); haath ka carry 2. Jod: 0 + 4 + 2 = 6 → likho 6 | 63 |
🆘 Atak gaye? Aise socho
- × 6 se farak? Sirf digit ka double. Baaki sab same.
- 5 kab? Jab digit khud taaq ho (1, 3, 5, 7, 9).
- Carry 2? Jod 20 ya zyada aaye to: 23 → 3 likho, 2 carry.
- Ek kadam mein 4 cheezein: double, 5 (agar taaq), padosi ka aadha, carry. Ungli pe gino.
- Check: number × 5 + number × 2 (170 + 68 = 238).
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Chaabi: 7 = 2 + 5. 34 × 7 = 34 × 2 + 34 × 5.
- × 2 wala hissa: har digit apne khaane mein double (Chapter 11 ka × 12 jaisa).
- × 5 wala hissa: Post 12.1 jaisa: × 10 se har khaane mein padosi aata hai, uska aadha (½ chhod kar). Aur taaq digit ke toote note ka 5 uske apne khaane mein.
- Teeno jodo: double + padosi ka aadha + (taaq pe 5). Bas!
Neeche chitra mein 34 × 7 ke khaane hain.
625 × 7 ke khaane
Yahan ikai 5 taaq hai (+5), par 2 aur 6 juft. Dekho kaise sirf ikai ke khaane mein 5 judta hai.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 7 × 7 = ?
Aage 0: 07. Ikai 7: double 7 + 7 = 14, 7 taaq → +5; 14 + 5 = 19 → 9 likho, carry 1. Aage wala 0: padosi 7 ka aadha 3, carry 1; 0 + 3 + 1 = 4 → 4 likho (aakhri kadam). Jawab: 4 | 9 → 49.
✔️ Normal tareeke se check: 7 ko 7 baar jodo: 7, 14, 21, 28, 35, 42, 49 ✅
Example 2: 89 × 7 = ?
Aage 0: 089. Ikai 9: double 9 + 9 = 18, 9 taaq → +5; 18 + 5 = 23 → 3 likho, carry 2. Dahai 8: double 8 + 8 = 16, 8 juft, padosi 9 ka aadha 4, carry 2; 16 + 4 + 2 = 22 → 2 likho, carry 2. Aage wala 0: padosi 8 ka aadha 4, carry 2; 0 + 4 + 2 = 6 → 6 likho (aakhri kadam). Jawab: 6 | 2 | 3 → 623.
✔️ Normal tareeke se check: 89 × 5 = 445 (890 ka aadha), 89 × 2 = 178, 445 + 178 = 623 ✅
Example 3: 305 × 7 = ? (beech mein 0)
Aage 0: 0305. Ikai 5: double 5 + 5 = 10, 5 taaq → +5; 10 + 5 = 15 → 5 likho, carry 1. Dahai 0: double 0 + 0 = 0, 0 juft, padosi 5 ka aadha 2, carry 1; 0 + 2 + 1 = 3 → 3 likho. Saikda 3: double 3 + 3 = 6, 3 taaq → +5, padosi 0 ka aadha 0; 6 + 5 + 0 = 11 → 1 likho, carry 1. Aage wala 0: padosi 3 ka aadha 1, carry 1; 0 + 1 + 1 = 2 → 2 likho (aakhri kadam). Jawab: 2 | 1 | 3 | 5 → 2135.
✔️ Normal tareeke se check: Column: 7 × 5 = 35 (5, carry 3); 7 × 0 = 0, 0 + 3 = 3; 7 × 3 = 21 → 2135 ✅
Example 4: 1357 × 7 = ?
Aage 0: 01357. Ikai 7: double 7 + 7 = 14, 7 taaq → +5; 14 + 5 = 19 → 9 likho, carry 1. Dahai 5: double 5 + 5 = 10, 5 taaq → +5, padosi 7 ka aadha 3, carry 1; 10 + 5 + 3 + 1 = 19 → 9 likho, carry 1. Saikda 3: double 3 + 3 = 6, 3 taaq → +5, padosi 5 ka aadha 2, carry 1; 6 + 5 + 2 + 1 = 14 → 4 likho, carry 1. Hazaar 1: double 1 + 1 = 2, 1 taaq → +5, padosi 3 ka aadha 1, carry 1; 2 + 5 + 1 + 1 = 9 → 9 likho. Aage wala 0: padosi 1 ka aadha 0; 0 + 0 = 0 → aage ka 0, nahi likhte. Jawab: 0 | 9 | 4 | 9 | 9 → 9499.
Dhyaan: aakhri kadam pe padosi 1 ka aadha 0 aur carry bhi 0, to aage kuch nahi likha.
✔️ Normal tareeke se check: 1357 × 5 = 6785 (13570 ka aadha), 1357 × 2 = 2714, 6785 + 2714 = 9499 ✅
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths mein 7 ke liye koi alag pahaada-trick nahi, par wahi soch milti hai: mushkil number ko aasaan tukdon mein todo. 7 = 2 + 5: double karna aasaan, aur × 5 = × 10 ka aadha (aasaan). Trachtenberg ne tukdon ko khaane-khaane jod kar ek line ka niyam bana diya.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Koi bhi number × 7 | ✅ Haan | Double + aadha padosi + taaq pe 5. |
| Ek-digit × 7 (8 × 7) | ✅ Haan | 16, phir 4 + 1 = 5 → 56. |
| Bahut saare 9 (999 × 7) | ✅ Dhyaan se | Carry 2 baar-baar. |
| × 70, × 700 | ✅ Haan | × 7, phir peeche 0 ya 00. |
| × 6 | ⬅️ Post 12.1 | Double nahi, digit khud. |
| × 8, × 9 | ➡️ Post 12.3 | Alag niyam: 10/9 se ghatao. × 8 aur × 9 ka tareeka agle post (12.3) mein. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: Double ki jagah digit (× 6 kar diya)
Sawaal: 34 × 7
❌ Galat: digit khud + aadha padosi + 5 → 204 (yeh 34 × 6 hai).
✅ Sahi: digit ka double: 238. Check: 204 + 34 = 238 (kyunki × 7 matlab × 6 aur ek baar number) ✅
Galti 2: Taaq pe 5 bhool gaye
Sawaal: 34 × 7
❌ Galat: 3 taaq par 5 nahi joda → 6 + 2 = 8 → 188.
✅ Sahi: 6 + 5 + 2 = 13 → 238.
Galti 3: Carry 2 ko 1 maan liya
Sawaal: 999 × 7
❌ Galat: ikai 23 pe 1 carry.
✅ Sahi: 23 = 2 dahai + 3, to 2 carry. Jawab 6993.
Galti 4: Poora padosi joda
Sawaal: 625 × 7
❌ Galat: padosi ka aadha nahi, poora → 7505.
✅ Sahi: aadha: 5 → 2, 2 → 1, 6 → 3. Jawab 4375.
🧠 Rule of thumb: × 7: double + padosi ka aadha (½ chhodo) + 5 agar digit khud taaq. Carry 2 tak.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, sab × 7. Target: 7 minute. Har digit ke neeche J/T likh lo.
- 3 × 7 = ?
- 6 × 7 = ?
- 8 × 7 = ?
- 12 × 7 = ?
- 17 × 7 = ?
- 25 × 7 = ?
- 36 × 7 = ?
- 43 × 7 = ?
- 58 × 7 = ?
- 64 × 7 = ?
- 78 × 7 = ?
- 95 × 7 = ?
- 142 × 7 = ?
- 306 × 7 = ?
- 777 × 7 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 21
- 42
- 56
- 84
- 119
- 175
- 252
- 301
- 406
- 448
- 546
- 665
- 994
- 2142
- 5439
Kaise kiya (kuch):
Aage 0: 078. Ikai 8: double 8 + 8 = 16, 8 juft → 6 likho, carry 1. Dahai 7: double 7 + 7 = 14, 7 taaq → +5, padosi 8 ka aadha 4, carry 1; 14 + 5 + 4 + 1 = 24 → 4 likho, carry 2. Aage wala 0: padosi 7 ka aadha 3, carry 2; 0 + 3 + 2 = 5 → 5 likho (aakhri kadam). Jawab: 5 | 4 | 6 → 546.
Aage 0: 0777. Ikai 7: double 7 + 7 = 14, 7 taaq → +5; 14 + 5 = 19 → 9 likho, carry 1. Dahai 7: double 7 + 7 = 14, 7 taaq → +5, padosi 7 ka aadha 3, carry 1; 14 + 5 + 3 + 1 = 23 → 3 likho, carry 2. Saikda 7: double 7 + 7 = 14, 7 taaq → +5, padosi 7 ka aadha 3, carry 2; 14 + 5 + 3 + 2 = 24 → 4 likho, carry 2. Aage wala 0: padosi 7 ka aadha 3, carry 2; 0 + 3 + 2 = 5 → 5 likho (aakhri kadam). Jawab: 5 | 4 | 3 | 9 → 5439.
— 📌 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.
- 2 × 7 = ?
- 4 × 7 = ?
- 5 × 7 = ?
- 9 × 7 = ?
- 10 × 7 = ?
- 11 × 7 = ?
- 14 × 7 = ?
- 20 × 7 = ?
- 22 × 7 = ?
- 50 × 7 = ?
| 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
- 14
- 28
- 35
- 63
- 70
- 77
- 98
- 140
- 154
- 350
Dhyaan:
Aage 0: 09. Ikai 9: double 9 + 9 = 18, 9 taaq → +5; 18 + 5 = 23 → 3 likho, carry 2. Aage wala 0: padosi 9 ka aadha 4, carry 2; 0 + 4 + 2 = 6 → 6 likho (aakhri kadam). Jawab: 6 | 3 → 63.
20 × 7: 2 × 7 = 14, peeche 0 → 140. 50 × 7: 5 × 7 = 35, peeche 0 → 350.
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. 💪
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📝 10 MCQs (Har Option Ka Kaaran)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 34 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 238
- (a) galat ❌: 458: padosi ka aadha nahi, poora joda.
- (b) sahi ✅: 034: 8; 6 + 5 + 2 = 13 (3, c1); 0 + 1 + 1 = 2 → 238.
- (c) galat ❌: 188: dahai 3 taaq par 5 bhool gaye.
- (d) galat ❌: 204: double nahi kiya (digit khud liya); yeh 34 × 6 hai.
Q2. × 7 aur × 6 ke niyam mein farak?
Jawab aur kaaran dekho
Sahi jawab: (a) × 7 mein digit ka double
- (a) sahi ✅: 7 = 2 + 5, 6 = 1 + 5: farak sirf digit ka double.
- (b) galat ❌: Padosi dono mein aadha hi, kyunki dono mein × 5 hai.
- (c) galat ❌: Taaq pe 5 dono mein judta hai.
- (d) galat ❌: Dono right se chalte hain.
Q3. 625 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 4375
- (a) galat ❌: 4370: ikai 5 taaq par 5 bhool gaye.
- (b) galat ❌: 7505: padosi poora joda, aadha nahi.
- (c) galat ❌: 375: aage wale 0 ka kadam bhool gaye.
- (d) sahi ✅: 0625: 10 + 5 = 15 (5, c1); 4 + 2 + 1 = 7; 12 + 1 = 13 (3, c1); 0 + 3 + 1 = 4 → 4375.
Q4. 999 × 7 mein ikai ka kadam?
Jawab aur kaaran dekho
Sahi jawab: (c) 18 + 5 = 23 → 3, carry 2
- (a) galat ❌: 14: double nahi kiya (yeh × 6 ka kadam hai).
- (b) galat ❌: 18: taaq pe 5 bhool gaye.
- (c) sahi ✅: Double 18, 9 taaq → +5, padosi nahi: 23. 3 likho, 2 carry.
- (d) galat ❌: 23 mein 2 dahai, to carry 2, 1 nahi.
Q5. 8 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 56
- (a) galat ❌: 16: sirf double kiya, aage wala kadam bhool gaye.
- (b) sahi ✅: 08: 16 (6, c1); 0 + 4 + 1 = 5 → 56.
- (c) galat ❌: 48: double nahi, digit khud; yeh 8 × 6 hai.
- (d) galat ❌: 96: padosi 8 ka aadha nahi, poora joda: 0 + 8 + 1 = 9.
Q6. 89 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 623
- (a) sahi ✅: 089: 18 + 5 = 23 (3, c2); 16 + 4 + 2 = 22 (2, c2); 0 + 4 + 2 = 6 → 623.
- (b) galat ❌: 618: ikai 9 taaq par 5 bhool gaye.
- (c) galat ❌: 1073: padosi poora joda.
- (d) galat ❌: 403: carry nahi jode.
Q7. × 7 mein sabse bada carry?
Jawab aur kaaran dekho
Sahi jawab: (d) 2
- (a) galat ❌: 1 sirf × 6 mein; × 7 mein 999 × 7 pe 23, 29 aate hain.
- (b) galat ❌: 3 ke liye jod 30 chahiye, par sabse bada 29.
- (c) galat ❌: 7 kabhi nahi; carry jod ka pehla digit hai.
- (d) sahi ✅: Sabse bada jod 18 + 5 + 4 + 2 = 29, to carry 2.
Q8. 64 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 448
- (a) galat ❌: 384: double nahi kiya; yeh 64 × 6 hai.
- (b) galat ❌: 768: padosi poora joda.
- (c) sahi ✅: 064: 8; 12 + 2 = 14 (4, c1); 0 + 3 + 1 = 4 → 448.
- (d) galat ❌: 348: carry nahi joda.
Q9. 305 × 7 mein dahai ke 0 ka kadam? (Ikai se carry 1 aaya)
Jawab aur kaaran dekho
Sahi jawab: (b) 0 + 2 + 1 = 3
- (a) galat ❌: 13: 0 ko 5 maan kar double 10 kar diya.
- (b) sahi ✅: 0 ka double 0, 0 juft, padosi 5 ka aadha 2, carry 1 → 3. Jawab 2135.
- (c) galat ❌: 6: padosi 5 poora joda.
- (d) galat ❌: 2: carry 1 bhool gaye.
Q10. 57 × 7 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 399
- (a) sahi ✅: 057: 14 + 5 = 19 (9, c1); 10 + 5 + 3 + 1 = 19 (9, c1); 0 + 2 + 1 = 3 → 399.
- (b) galat ❌: 344: taaq pe 5 bhool gaye (5 aur 7 dono taaq).
- (c) galat ❌: 289: carry nahi jode.
- (d) galat ❌: 739: padosi poora joda.
— 📌 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. 7 × 11 × 13 = 1001. To 1001 × 7 = ? Niyam se karo.
Solution dekho
(Pehle dekho: 7 × 11 = 77, aur 77 × 13 = 1001.)
01001 → ikai 1: double 2 + 5 = 7. Dahai 0: padosi 1 ka aadha 0 → 0. Saikda 0: padosi 0 → 0. Hazaar 1: double 2 + 5 = 7. Aage 0: padosi 1 ka aadha 0 → 0 (nahi likhte). Jawab 7007.
Check: 1001 × 7 = 7000 + 7 = 7007 ✅
Q2. Ek hafte mein 7 din. 52 hafte mein kitne din? Saal ke 365 din se kitna kam?
Solution dekho
52 × 7: 052 → ikai 2: double 4. Dahai 5: double 10 + 5 (taaq) + padosi 2 ka aadha 1 = 16 → 6, carry 1. Aage 0: padosi 5 ka aadha 2 + carry 1 = 3. Jawab 364. 365 − 364 = 1 din kam.
Check: 52 × 7 = 52 × 5 + 52 × 2 = 260 + 104 = 364 ✅ (52 × 5 = 260, 52 × 2 = 104)
Q3. × 7 = × 6 + number. 46 × 6 = 276. To 46 × 7 = ? Niyam se bhi karke milaao.
Solution dekho
276 + 46 = 322. Niyam se: 046 → 12 (2, c1); 8 + 3 + 1 = 12 (2, c1); 0 + 2 + 1 = 3 → 322 ✅
Q4. Kaunse ek-digit number × 7 karne pe jawab ki ikai 1 aati hai?
Solution dekho
Ikai pe: double + (taaq ho to 5). Double hamesha juft hota hai, to ikai 1 (taaq) ke liye 5 judna chahiye: digit taaq. Taaq digit: 1 → 2 + 5 = 7; 3 → 6 + 5 = 11 ✅; 5 → 15; 7 → 19; 9 → 23. Sirf 3. Check: 3 × 7 = 21 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Hafte/din ke sawaal, guna, pahaada check. |
| Maths Olympiad | 1001 = 7 × 11 × 13 jaise pattern, ikai wale sawaal. |
| NTSE / MAT | Mental maths aur number series. |
| SSC / Bank (aage) | Simplification mein × 7. |
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. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “double, aadha padosi, taaq pe paanch.” × 6 aur × 7 ko saath practice karo: pehle × 6, phir usme number jodo, aur niyam se milaao. Agle post mein × 8 aur × 9: “10 se ghatao, 9 se ghatao”! 7️⃣
— 📌 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)
Aage 0: 0625. Ikai 5 (taaq): double 10, plus 5: 10 + 5 = 15 → 5, carry 1. Dahai 2 (juft): double 4, padosi 5 ka aadha 2, carry 1: 4 + 2 + 1 = 7. Saikda 6 (juft): double 12, padosi 2 ka aadha 1: 12 + 1 = 13 → 3, carry 1. Aage 0: padosi 6 ka aadha 3, carry 1: 0 + 3 + 1 = 4. Jawab 4375 ✅
| 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. 7 ka pahaada phir bhi seekhna chahiye?
Seekh lo to achha, par yeh niyam bina pahaade ke bhi sahi jawab deta hai, aur pahaada check karne mein bhi kaam aata hai.
2. Double aur 5 dono kab?
Jab digit taaq ho: double bhi, 5 bhi. Juft ho to sirf double.
3. Check ka sabse aasaan tareeka?
× 7 = × 6 + number, ya × 5 + × 2.
4. Agle post mein kya hai?
Post 12.3: × 9 (10 se, 9 se baaki + padosi, aakhir mein 1 kam) aur × 8 (baaki ka double, aakhir mein 2 kam). Yaani × 8 aur × 9 ka tareeka agle post (12.3) mein aayega.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- 7 = 2 + 5.
- × 7: double + padosi ka aadha (½ chhodo) + 5 agar digit khud taaq.
- × 6 se farak: digit ki jagah double.
- Carry 2 tak (sabse bada jod 29).
- Ikai ka padosi nahi; aakhri kadam 0 aaye to nahi likhte.
- Check: × 6 + number, ya × 5 + × 2.
— charumam.com 🎯
👉 Aage Kya?
Ab × 8 aur × 9: Post 12.3 mein ek naya andaaz: “10 se ghatao, 9 se ghatao”, aur aakhir mein 1 ya 2 kam. Chapter 3 aur Chapter 10 ki yaad aayegi!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
💛 Post Achha Laga? Like, Share, Subscribe, Follow!
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- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
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