Fast Multiplication Ki Tricks | Class 8 Maths Book 1 Ch 6

📘 Class 8 · Ganita Prakash Book 1Ch 6 · We Distribute, Yet Things MultiplyPost 3 / 7⏱ 25–30 min

Fast Multiplication Ki Tricks ⚡

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

11 = 10 + ?
6253 × 10 = ?
99 = 100 − ?

Answers dekho

1
62530
1

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 1 — Distributive Property Kya Hai? aur Post 2 — Guna Mein Badlaav: Increments dekh lijiye.

— 📌 charumam.com

🎬 Kahani: Quiz Ka Fastest Finger

School quiz mein sawaal aaya: “6253 × 11?” Sab copy-pen nikaal rahe the. Tanvi ne 3 second mein bola: “68,783!” ⚡

Quiz master ne calculator dekha: sahi! Sab hairaan: “Tanvi, tune rata hua tha kya?”

Tanvi: “Nahi, maine sirf padosi digits jode.” Aaj yeh trick seekhenge, aur zyada zaroori, kyun chalti hai. 🏆

— 📌 charumam.com

📖 Concept: Mushkil Number = Aasaan Tukde (10 + 1, 100 − 1)

💡 Is post ki ek badi baat: 11 = 10 + 1, 101 = 100 + 1, 99 = 100 − 1. Distributive se: N × 11 = N × 10 + N. Number ko khiska ke khud mein jodo. Har trick bas yahi hai: mushkil guna ko aasaan tukdon (10, 100, 1000 se guna = zero lagana) mein todna.

Step 1: × 11: kyun padosi jodte?

6253 × 11 = 62530 + 6253:

	6	2	5	3	0
+		6	2	5	3
=	6	6+2	2+5	5+3	3

= 68783. WHY? Ek baar khiska hua number = har digit apne padosi ke neeche aa gaya. Isliye pehla digit, phir padosi ke jod, phir aakhri digit.

Step 2: × 11 with carry

4786 × 11: daayein se: 6 | 8 + 6 = 14 → 4, carry 1 | 7 + 8 + 1 = 16 → 6, carry 1 | 4 + 7 + 1 = 12 → 2, carry 1 | 4 + 1 = 5.

Jawab: 52646. Check: 47860 + 4786 = 52646 ✅

Niyam: hamesha daayein se chalo, taaki carry aage le ja sako.

Step 3: × 101 aur × 1001

× 101 = × 100 + × 1: number do jagah khiska ke jodo. Padosi nahi, “ek chhod ke padosi”.

5836 × 101 = 583600 + 5836 = 589436.

× 1001: 3-digit number ho to bas do baar likho! 457 × 1001 = 457457 (koi overlap nahi).

Step 4: × 99 aur × 999: ghataav

× 99 = × 100 − × 1: 487 × 99 = 48700 − 487 = 48213.

× 999 = × 1000 − × 1: 6215 × 999 = 6215000 − 6215 = 6208785.

WHY ghataav? 99 = 100 − 1, to a(b − c) = ab − ac.

Step 5: Aur tricks: × 5, × 25, aur base ke paas

× 5 = × 10 ÷ 2: 846 × 5 = 8460 ÷ 2 = 4230. × 25 = × 100 ÷ 4: 64 × 25 = 6400 ÷ 4 = 1600.

Base 100 ke paas: 98 × 97 = (100 − 2)(100 − 3) = 10000 − 300 − 200 + 6 = 9506 (Identity 1, Post 2 — Guna Mein Badlaav: Increments!).

Kab kaunsa? 11, 101 → khiska ke jodo. 99, 999 → khiska ke ghatao. 5, 25 → 10/100 se guna phir bhaag. Dono 100 ke paas → (100 − a)(100 − b).

🪜 Atak Gaye? Aise Socho

Guna karne wale ko 10, 100, 1000 ke paas dekho (11, 99, 101…).
Use “base ± chhota” likho.
Number ko base se guna (zero lagao), phir chhote hisse ko jodo/ghatao.
× 11 mein daayein se padosi jodo; carry aage.
Jawab ko anumaan (approx) se check: 6253 × 11 ≈ 6000 × 11 = 66000.

— 📌 charumam.com

🔐 Deep Concept: Ista-Gunana: Brahmagupta Ka “Pasand Ka Number” Tareeka

Brahmagupta (628 CE, Brāhmasphuṭasiddhānta 12.56) ne ista-guṇana bataaya: guna karne wale ko kisi pasand ke (aasaan) number se jod ya ghata ke likho. Sridharacharya (lagbhag 750 CE) aur Bhaskaracharya (Lilavati, 1150 CE) ne bhi aise tareeke likhe.

Kyun 10, 100, 1000 “pasand” ke? Kyunki hum base 10 mein likhte: 10 se guna = bas ek zero, digits khiske. Asli guna ka kaam khatam! Bacha sirf ek jod ya ghataav.

Sochne wali baat: 11 ka divisibility rule (Ch 5) aur 11 ka guna trick, dono 11 = 10 + 1 se nikle. Ek hi idea, do kaam. 🎯

Unifying idea: fast maths jaadu nahi; distributive property + base 10 ki aasaani.

sirf charumam.com readers ke liye 🔐

✏️ Solved Examples

Example 1 (Easy): 73 × 11 mann mein.

7 | 7 + 3 | 3 → 803.

Check: 730 + 73 = 803 ✅

📌 charumam.com

Example 2 (Medium): 8459 × 11 (carry ke saath).

Daayein se: 9 | 5 + 9 = 14 → 4 (c1) | 4 + 5 + 1 = 10 → 0 (c1) | 8 + 4 + 1 = 13 → 3 (c1) | 8 + 1 = 9 → 93049.

Check: 84590 + 8459 = 93049 ✅

📌 charumam.com

Example 3 (NCERT style): 346 × 999.

346000 − 346 = 345654.

Check: anumaan 346 × 1000 = 346000, thoda kam ✅; 345654 ÷ 999 = 346 ✅

📌 charumam.com

Tanvi ka raaz: 6253 × 11 = 62530 + 6253, aur jodne mein padosi digits hi milte. Agle round mein usne sabko trick sikha di: ab poori class “fastest finger”! ⚡

— 📌 charumam.com

🏠 Fast Multiplication Roz Ki Zindagi Mein

🛒 ₹99 wali cheezein: 7 × ₹99 = 700 − 7 = ₹693.
🏏 Cricket team: 11 khiladi × ₹2,350 kit = 23,500 + 2,350 = ₹25,850.
🎫 Ticket ₹25: 48 ticket = 4800 ÷ 4 = ₹1,200.
📦 Godown: 101 dabbe × 36 = 3636.
🧾 Bill check: calculator ke bina anumaan se galti pakadna.

Bazaar mein “₹999” wale daam isi liye: dimaag 999 ko 1000 se kam samajhta hai, par aap ab turant hisaab kar sakte! 😉

— 📌 charumam.com

🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
× 11	✅ Padosi jodo	Daayein se, carry
× 101	✅ Do jagah khiska ke jodo	“Ek chhod ke padosi”
× 99 / 999	✅ Base se guna − number	Ghataav
× 5 / 25	✅ × 10 ÷ 2 / × 100 ÷ 4	Bhaag aasaan
Dono 100 ke paas	✅ (100 − a)(100 − b)	Identity 1

— 📌 charumam.com

❌→✅ Worked Mistake

Sawaal: 58 × 11.

❌ Galat: 5 | 5 + 8 | 8 → “5138”. Jod 13 do digit ka hai, seedha likh diya!

✅ Sahi: 13 → 3 likho, 1 carry aage: 5 + 1 = 6 → 638. Check: 580 + 58 = 638 ✅

Doosri common galti: × 101 mein × 11 jaisa padosi jodna. 101 mein khiskaav do jagah ka hai.

🧠 Rule of thumb: Jod 9 se bada ho to ek digit likho, baaki carry aage: hamesha daayein se.

sirf charumam.com pe milenge!

📝 10 MCQs

Q1. 42 × 11 = ?

(a) 462

(b) 4062

(c) 442

(d) 420

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 4 | 4 + 2 | 2 = 462 ✅
(b) galat: Jod 6 ek digit hai, beech mein 0 nahi.
(c) galat: Beech mein 4 + 2 = 6 aana tha.
(d) galat: Yeh sirf 42 × 10 hai, isliye yeh galat.

Q2. 67 × 11 = ?

(a) 737

(b) 6137

(c) 677

(d) 7137

Solution dekho

Sahi jawab: (a)

(a) sahi: 6 + 7 = 13 → 3, carry → 737 ✅
(b) galat: 13 ko seedha nahi likhte, carry.
(c) galat: Beech mein 13 aana tha, 7 nahi.
(d) galat: Carry ek baar hi jodo.

Q3. 11 = ?

(a) 10 + 1

(b) 12 − 2

(c) 5 + 6

(d) 100 − 89

Solution dekho

Sahi jawab: (a)

(a) sahi: 10 se guna aasaan, isliye 10 + 1 ✅
(b) galat: Sahi barabari, par aasaan nahi.
(c) galat: 5, 6 se guna aasaan nahi.
(d) galat: Bekaar ka lamba tareeka.

Q4. 234 × 101 = ?

(a) 23634

(b) 2574

(c) 23434

(d) 2340

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 23400 + 234 = 23634 ✅
(b) galat: Yeh 234 × 11 hai, 101 nahi.
(c) galat: Jod galat kiya gaya hai.
(d) galat: Yeh sirf 234 × 10 hai.

Q5. 512 × 1001 = ?

(a) 512512

(b) 51712

(c) 5632

(d) 512000

Solution dekho

Sahi jawab: (a)

(a) sahi: 3-digit ko do baar likho ✅
(b) galat: Yeh 512 × 101 jaisa galat.
(c) galat: Yeh 512 × 11 hai, isliye yeh galat.
(d) galat: 512 × 1000 hi hai, +512 bhool gaye.

Q6. 63 × 99 = ?

(a) 6237

(b) 6300

(c) 6363

(d) 6177

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 6300 − 63 = 6237 ✅
(b) galat: 63 ghataana bhool gaye.
(c) galat: Ghataana tha, jodna nahi.
(d) galat: Ghataav galat kiya, isliye yeh galat.

Q7. 86 × 5 = ?

(a) 430

(b) 4300

(c) 86

(d) 415

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi jawab: 860 ÷ 2 = 430 ✅
(b) galat: ÷ 2 bhool gaye, isliye yeh galat.
(c) galat: 5 se guna to karna tha.
(d) galat: Bhaag galat kiya gaya.

Q8. 96 × 97 = ? (base 100)

(a) 9312

(b) 9300

(c) 9412

(d) 9212

Solution dekho

Sahi jawab: (a)

(a) sahi: 10000 − 400 − 300 + 12 = 9312 ✅
(b) galat: 4 × 3 = 12 jodna bhool gaye.
(c) galat: Ghataav 700 ka tha, 600 nahi.
(d) galat: Jod-ghataav mein galti.

Q9. Ista-gunana kisne bataaya?

(a) Brahmagupta

(b) Pythagoras

(c) Euclid

(d) Fibonacci

Solution dekho

Sahi jawab: (a)

(a) sahi: Brāhmasphuṭasiddhānta 12.56 ✅
(b) galat: Unka yeh tareeka nahi tha.
(c) galat: Euclid ka kaam geometry tha.
(d) galat: Fibonacci baad mein aaye.

Q10. × 11 trick kis taraf se?

(a) Daayein se

(b) Baayein se

(c) Beech se

(d) Kahin se bhi

Solution dekho

Sahi jawab: (a)

(a) sahi: Carry aage le jaane ke liye ✅
(b) galat: Baayein se carry ulta padta.
(c) galat: Beech se shuru ka koi fayda nahi.
(d) galat: Carry ki wajah se disha zaroori.

— 📌 charumam.com

❓ FAQs (Bachchon Ke Asli Sawaal)

1. × 11 trick kyun?

N × 11 = N × 10 + N. Khiska hua number jodne pe har digit padosi se milta.

2. Bade numbers pe bhi?

Haan, kitne bhi digit: pehla, padosi ke jod, aakhri. Carry dhyaan se.

3. × 111?

111 = 100 + 10 + 1: teen padosi (ek, do, teen digits) jodo.

4. × 9?

× 10 − × 1: 47 × 9 = 470 − 47 = 423.

5. Kya yeh Vedic maths hai?

Kuch tareeke milte-julte hain. Par yahan hum “kyun” distributive se samajh rahe, sirf trick nahi.

6. Aage kya?

Ek number ka khud se guna, (a + b)²: Post 4 — (a + b)² Ka Formula.

— 📌 charumam.com

🏋️ Practice Zone (12 Sawaal)

Q1. Easy 35 × 11?

Solution dekho

385. Check: 350 + 35 ✅

Q2. Easy 78 × 11?

Solution dekho

7 + 8 = 15 → 858. Check: 780 + 78 ✅

Q3. Easy 56 × 101?

Solution dekho

5656. Check: 5600 + 56 ✅

Q4. Easy 24 × 99?

Solution dekho

2400 − 24 = 2376. Check ✅

Q5. Medium 3517 × 11?

Solution dekho

3 | 8 | 6 | 8 | 7 → 38687. Check: 35170 + 3517 ✅

Q6. Medium 6948 × 11?

Solution dekho

76428. Check: 69480 + 6948 ✅

Q7. Medium 4723 × 101?

Solution dekho

472300 + 4723 = 477023. Check ✅

Q8. Medium 738 × 1001?

Solution dekho

738738. Check ✅

Q9. NCERT style 5281 × 999?

Solution dekho

5281000 − 5281 = 5275719. Check ✅

Q10. NCERT style 93 × 94 (base 100)?

Solution dekho

10000 − 700 − 600 + 42 = 8742. Check: 93 × 94 = 8742 ✅

Q11. NCERT style 104 × 107 (base 100)?

Solution dekho

10000 + 700 + 400 + 28 = 11128. Check ✅

Q12. NCERT style 2468 × 25?

Solution dekho

246800 ÷ 4 = 61700. Check ✅

Answer Key — charumam.com exclusive

🧠 HOTS (Sochne Wale Sawaal)

Q1. abc (3-digit) × 1001 hamesha 7, 11, 13 se bata. Kyun?

Solution dekho

1001 = 7 × 11 × 13. Check: 457457 ÷ 13 = 35189 ✅

Q2. × 111 ka trick banao: 42 × 111?

Solution dekho

4 | 4 + 2 | 4 + 2 | 2 → 4662. Check: 4200 + 420 + 42 ✅

Q3. 9999 × 9999?

Solution dekho

(10000 − 1)² = 100000000 − 20000 + 1 = 99980001. Check ✅

Q4. 2-digit ab × 11 kab 4-digit?

Solution dekho

ab × 11 ≥ 1000 → ab ≥ 1000 ÷ 11 ≈ 90.9 → ab = 91 se 99 (yaani a = 9 aur a + b se carry). Check: 90 × 11 = 990 (3-digit), 91 × 11 = 1001 ✅

sirf charumam.com pe milenge!

🏆 Olympiad Corner

Q1. 123456 × 11?

Solution dekho

1358016.

Q2. 999 × 999?

Solution dekho

998001.

Q3. 12 × 101 × 1001?

Solution dekho

1213212.

Q4. 37 × 3 × 1001?

Solution dekho

111 × 1001 = 111111.

sirf charumam.com readers ke liye 🔐

💗 CharuMam Motivation

Tanvi ka “jaadu” ek line ka saboot hai: 11 = 10 + 1. Har trick ke peeche ka kyun samjho, phir aap khud nayi tricks bana sakoge! 🚀

— 📌 charumam.com

🟢 Master Recap

💡 Chaabi: 11 = 10 + 1, 101 = 100 + 1, 99 = 100 − 1. Distributive se: N × 11 = N × 10 + N. Number ko khiska ke khud mein jodo. Har trick bas yahi hai: mushkil guna ko aasaan tukdon (10, 100, 1000 se guna = zero lagana) mein todna.
× 11: padosi jodo (daayein se, carry).
× 101: do jagah khiska ke jodo.
× 1001: 3-digit ko do baar likho.
× 99, 999: base se guna − number.
× 5, 25: × 10 ÷ 2, × 100 ÷ 4.
Brahmagupta: ista-guṇana.

— charumam.com 🎯

👉 Aage Kya?

Ab number ka khud se guna, (a + b)², chitra ke saath: Post 4 — (a + b)² Ka Formula.

← Pichla: Post 2 — Guna Mein Badlaav: Increments 📚 Chapter 6 ke saare posts Agla: Post 4 — (a + b)² Ka Formula →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Quiz Ka Fastest Finger

📖 Concept: Mushkil Number = Aasaan Tukde (10 + 1, 100 − 1)

Step 1: × 11: kyun padosi jodte?

Step 2: × 11 with carry

Step 3: × 101 aur × 1001

Step 4: × 99 aur × 999: ghataav

Step 5: Aur tricks: × 5, × 25, aur base ke paas

🪜 Atak Gaye? Aise Socho

🔐 Deep Concept: Ista-Gunana: Brahmagupta Ka “Pasand Ka Number” Tareeka

✏️ Solved Examples

🏠 Fast Multiplication Roz Ki Zindagi Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

You may also like