Chapter 1

๐Ÿ•‰๏ธ Introduction to Vedic Mathematics

โšก Can You Solve This in 3 Seconds?

98 ร— 97 = ?

Traditional method: Multiple steps of multiplication, carry-overs, additionโ€ฆ

Vedic method: 98โˆ’3 = 95 | 2ร—3 = 06 โ†’ Answer: 9506 โœจ

That's the magic of Vedic Mathematics! You'll learn this trick in Chapter 4.

๐Ÿ“– What is Vedic Mathematics?

Vedic Mathematics is a collection of techniques and sutras (formulas) that simplify mathematical calculations. These methods were rediscovered from the Atharva Veda by Swami Bharati Krishna Tirthaji (1884โ€“1960), one of India's greatest mathematicians and the Shankaracharya of Govardhan Math, Puri.

After years of deep study of ancient Sanskrit texts, Tirthaji identified 16 Sutras (formulas) and 13 Sub-sutras (corollaries) that cover virtually all of mathematics โ€” from simple arithmetic to algebra, geometry, calculus, and beyond.

Swami Bharati Krishna Tirthaji wrote his findings in a book called "Vedic Mathematics", published posthumously in 1965. The book has since been translated into dozens of languages and has inspired millions of students worldwide.

๐Ÿ“œ The 16 Sutras of Vedic Mathematics

#Sutra (Sanskrit)Meaning (English)
1Ekadhikena PurvenaBy one more than the previous one
2Nikhilam Navatashcaramam DashatahAll from 9 and the last from 10
3Urdhva-TiryagbhyamVertically and crosswise
4Paraavartya YojayetTranspose and adjust
5Shunyam SaamyasamuccayeWhen the sum is the same, that sum is zero
6Anurupye ShunyamanyatIf one is in ratio, the other is zero
7Sankalana-vyavakalanabhyamBy addition and by subtraction
8PuranapuranabhyamBy the completion or non-completion
9Chalana-KalanabhyamDifferences and similarities
10YaavadunamWhatever the extent of its deficiency
11VyashtisamanshtihPart and whole
12Shesanyankena CharamenaThe remainders by the last digit
13SopaantyadvayamantyamThe ultimate and twice the penultimate
14Ekanyunena PurvenaBy one less than the previous one
15GunitasamuchyahThe product of the sum is equal to the sum of the product
16GunakasamuchyahThe factors of the sum is equal to the sum of the factors

๐Ÿš€ Why Learn Vedic Maths?

10โ€“15ร— Faster Calculations
Solve complex problems mentally in seconds that would take minutes with traditional methods.
Boosts Concentration
Mental math exercises sharpen your focus, memory, and analytical thinking.
Competitive Edge
Essential for JEE, NTSE, Olympiads, SSC, Banking exams โ€” speed is everything!
Builds Confidence
When you can calculate faster than a calculator, math becomes fun, not fear.

๐ŸŽฏ Real-World Applications

  • Competitive Exams: JEE, NEET, NTSE, Olympiads, SSC, CAT โ€” save 15โ€“20 minutes per paper
  • Daily Life: Quick shopping calculations, tip estimation, discount computation
  • Programming: Optimize algorithms, understand number theory, bit manipulation
  • Mental Fitness: Keep your brain sharp โ€” like yoga for the mind!
"Like the Sun, mathematical knowledge illuminates everything it touches." โ€” Ancient Vedic Saying
Throughout this book, we'll use specific Vedic Sutras for each technique. Don't worry about memorizing all 16 sutras now โ€” you'll learn them naturally as we explore each chapter!
Chapter 2

โœ–๏ธ Multiplication by 11, 12, and 13

เคเค•เคพเคงเคฟเค•เฅ‡เคจ เคชเฅ‚เคฐเฅเคตเฅ‡เคฃ
"Ekadhikena Purvena" โ€” By One More Than the Previous One

๐Ÿ”ข Multiplying Any Number by 11

This is one of the most elegant tricks in Vedic Mathematics. To multiply a 2-digit number AB by 11:

1
Write down the first digit A
2
Add the two digits: A + B (this goes in the middle)
3
Write down the last digit B
4
Result: A, (A+B), B. If A+B โ‰ฅ 10, carry 1 to A.
Take digits A, B
โ†’
Calculate A+B
โ†’
Write A, (A+B), B
โ†’
Carry if sum โ‰ฅ 10
โ†’
Answer! โœจ

โœ… 10 Solved Examples โ€” Multiply by 11

Example 1: 23 ร— 11

Digits: 2, 3 โ†’ Middle: 2+3 = 5 โ†’ Answer: 253

Example 2: 45 ร— 11

Digits: 4, 5 โ†’ Middle: 4+5 = 9 โ†’ Answer: 495

Example 3: 67 ร— 11

Digits: 6, 7 โ†’ Middle: 6+7 = 13 (carry 1) โ†’ 6+1, 3, 7 โ†’ Answer: 737

Example 4: 89 ร— 11

Digits: 8, 9 โ†’ Middle: 8+9 = 17 (carry 1) โ†’ 8+1, 7, 9 โ†’ Answer: 979

Example 5: 56 ร— 11

Digits: 5, 6 โ†’ Middle: 5+6 = 11 (carry 1) โ†’ 5+1, 1, 6 โ†’ Answer: 616

Example 6: 78 ร— 11

Digits: 7, 8 โ†’ Middle: 7+8 = 15 (carry 1) โ†’ 7+1, 5, 8 โ†’ Answer: 858

Example 7: 99 ร— 11 (with carry!)

Digits: 9, 9 โ†’ Middle: 9+9 = 18 (carry 1) โ†’ 9+1, 8, 9 โ†’ 10, 8, 9 โ†’ Answer: 1089

Example 8: 85 ร— 11

Digits: 8, 5 โ†’ Middle: 8+5 = 13 (carry 1) โ†’ 8+1, 3, 5 โ†’ Answer: 935

Example 9: 37 ร— 11

Digits: 3, 7 โ†’ Middle: 3+7 = 10 (carry 1) โ†’ 3+1, 0, 7 โ†’ Answer: 407

Example 10: 94 ร— 11

Digits: 9, 4 โ†’ Middle: 9+4 = 13 (carry 1) โ†’ 9+1, 3, 4 โ†’ 10, 3, 4 โ†’ Answer: 1034
For 3-digit numbers ร— 11: Use the same idea but work pair by pair!
123 ร— 11 โ†’ Write: 1, (1+2), (2+3), 3 = 1, 3, 5, 3 = 1353
246 ร— 11 โ†’ Write: 2, (2+4), (4+6), 6 = 2, 6, 10, 6 โ†’ carry โ†’ 2706
Don't forget the carry! When the sum of two adjacent digits is 10 or more, you must carry 1 to the left. For example, in 78 ร— 11: 7+8 = 15, write 5 and carry 1 to make 7+1 = 8. Answer: 858, not 7158!

๐Ÿ”ข Multiplying by 12

The trick: 12 ร— n = 10n + 2n (double and add)

1
Multiply the number by 10 (just add a zero)
2
Multiply the number by 2 (double it)
3
Add both results

Example 1: 34 ร— 12

34 ร— 10 = 340, 34 ร— 2 = 68 โ†’ 340 + 68 = 408

Example 2: 56 ร— 12

56 ร— 10 = 560, 56 ร— 2 = 112 โ†’ 560 + 112 = 672

Example 3: 78 ร— 12

78 ร— 10 = 780, 78 ร— 2 = 156 โ†’ 780 + 156 = 936

Example 4: 125 ร— 12

125 ร— 10 = 1250, 125 ร— 2 = 250 โ†’ 1250 + 250 = 1500

Example 5: 99 ร— 12

99 ร— 10 = 990, 99 ร— 2 = 198 โ†’ 990 + 198 = 1188

๐Ÿ”ข Multiplying by 13

The trick: 13 ร— n = 10n + 3n (triple and add)

Example 1: 25 ร— 13

25 ร— 10 = 250, 25 ร— 3 = 75 โ†’ 250 + 75 = 325

Example 2: 42 ร— 13

42 ร— 10 = 420, 42 ร— 3 = 126 โ†’ 420 + 126 = 546

Example 3: 67 ร— 13

67 ร— 10 = 670, 67 ร— 3 = 201 โ†’ 670 + 201 = 871

Example 4: 88 ร— 13

88 ร— 10 = 880, 88 ร— 3 = 264 โ†’ 880 + 264 = 1144

Example 5: 150 ร— 13

150 ร— 10 = 1500, 150 ร— 3 = 450 โ†’ 1500 + 450 = 1950
โฑ๏ธ Can you solve these in 5 seconds each?
72 ร— 11   |   45 ร— 12   |   30 ร— 13
Answers: 792, 540, 390

๐Ÿ“ Practice Problems โ€” Multiply by 11, 12, 13

PRACTICE 1

36 ร— 11 = ?

36 ร— 11 = 3, (3+6), 6 = 3, 9, 6 = 396
PRACTICE 2

54 ร— 11 = ?

54 ร— 11 = 5, (5+4), 4 = 5, 9, 4 = 594
PRACTICE 3

72 ร— 11 = ?

72 ร— 11 = 7, (7+2), 2 = 7, 9, 2 = 792
PRACTICE 4

88 ร— 11 = ?

88 ร— 11 = 8, (8+8=16, carry 1), 8 โ†’ 9, 6, 8 = 968
PRACTICE 5

63 ร— 11 = ?

63 ร— 11 = 6, (6+3), 3 = 6, 9, 3 = 693
PRACTICE 6

47 ร— 11 = ?

47 ร— 11 = 4, (4+7=11, carry 1), 7 โ†’ 5, 1, 7 = 517
PRACTICE 7

81 ร— 11 = ?

81 ร— 11 = 8, (8+1), 1 = 8, 9, 1 = 891
PRACTICE 8

234 ร— 11 = ?

234 ร— 11 = 2, (2+3), (3+4), 4 = 2, 5, 7, 4 = 2574
PRACTICE 9

45 ร— 12 = ?

45 ร— 10 = 450, 45 ร— 2 = 90 โ†’ 450 + 90 = 540
PRACTICE 10

63 ร— 12 = ?

63 ร— 10 = 630, 63 ร— 2 = 126 โ†’ 630 + 126 = 756
PRACTICE 11

85 ร— 12 = ?

85 ร— 10 = 850, 85 ร— 2 = 170 โ†’ 850 + 170 = 1020
PRACTICE 12

27 ร— 12 = ?

27 ร— 10 = 270, 27 ร— 2 = 54 โ†’ 270 + 54 = 324
PRACTICE 13

36 ร— 13 = ?

36 ร— 10 = 360, 36 ร— 3 = 108 โ†’ 360 + 108 = 468
PRACTICE 14

55 ร— 13 = ?

55 ร— 10 = 550, 55 ร— 3 = 165 โ†’ 550 + 165 = 715
PRACTICE 15

72 ร— 13 = ?

72 ร— 10 = 720, 72 ร— 3 = 216 โ†’ 720 + 216 = 936
PRACTICE 16

91 ร— 11 = ?

91 ร— 11 = 9, (9+1=10, carry 1), 1 โ†’ 10, 0, 1 = 1001
PRACTICE 17

111 ร— 11 = ?

111 ร— 11 = 1, (1+1), (1+1), 1 = 1, 2, 2, 1 = 1221
PRACTICE 18

48 ร— 12 = ?

48 ร— 10 = 480, 48 ร— 2 = 96 โ†’ 480 + 96 = 576
PRACTICE 19

75 ร— 13 = ?

75 ร— 10 = 750, 75 ร— 3 = 225 โ†’ 750 + 225 = 975
PRACTICE 20

96 ร— 11 = ?

96 ร— 11 = 9, (9+6=15, carry 1), 6 โ†’ 10, 5, 6 = 1056
Chapter 3

๐Ÿ”ฒ Squaring Numbers Ending in 5

เคเค•เคพเคงเคฟเค•เฅ‡เคจ เคชเฅ‚เคฐเฅเคตเฅ‡เคฃ
"Ekadhikena Purvena" โ€” By One More Than the Previous One

This is perhaps the most famous Vedic Mathematics trick. To square any number ending in 5:

1
Take the digit(s) before 5. Call it n.
2
Multiply n ร— (n+1). This gives the left part.
3
Append 25 at the end. Done!
Formula: (n5)ยฒ = n ร— (n+1) | 25
Just multiply the left digit by one more than itself, and tack on 25. It works for ANY number ending in 5!
Number ending in 5
(e.g., 75)
โ†’
Take left part
n = 7
โ†’
n ร— (n+1)
7 ร— 8 = 56
โ†’
Append 25
56 | 25
โ†’
Answer!
5625

โœ… 12 Solved Examples

15ยฒ = ?

1 ร— 2 = 2 | 25 โ†’ 225

25ยฒ = ?

2 ร— 3 = 6 | 25 โ†’ 625

35ยฒ = ?

3 ร— 4 = 12 | 25 โ†’ 1225

45ยฒ = ?

4 ร— 5 = 20 | 25 โ†’ 2025

55ยฒ = ?

5 ร— 6 = 30 | 25 โ†’ 3025

65ยฒ = ?

6 ร— 7 = 42 | 25 โ†’ 4225

75ยฒ = ?

7 ร— 8 = 56 | 25 โ†’ 5625

85ยฒ = ?

8 ร— 9 = 72 | 25 โ†’ 7225

95ยฒ = ?

9 ร— 10 = 90 | 25 โ†’ 9025

105ยฒ = ?

10 ร— 11 = 110 | 25 โ†’ 11025

115ยฒ = ?

11 ร— 12 = 132 | 25 โ†’ 13225

125ยฒ = ?

12 ร— 13 = 156 | 25 โ†’ 15625

โšก Traditional vs Vedic โ€” Speed Comparison

ProblemTraditional MethodVedic MethodTime Saved
25ยฒ25 ร— 25 = write, multiply, carry, add โ†’ ~30 sec2ร—3 = 6 | 25 = 625 โ†’ ~3 sec~90%
75ยฒ75 ร— 75 = long multiplication โ†’ ~45 sec7ร—8 = 56 | 25 = 5625 โ†’ ~3 sec~93%
115ยฒ115 ร— 115 = very long โ†’ ~90 sec11ร—12 = 132 | 25 = 13225 โ†’ ~5 sec~94%
This technique works because of algebra: (10n + 5)ยฒ = 100n(n+1) + 25. The Vedic mathematicians discovered this pattern thousands of years before modern algebra was formalized!
โฑ๏ธ Speed Round โ€” Square these in 3 seconds each!
35ยฒ   |   65ยฒ   |   95ยฒ   |   145ยฒ
Answers: 1225, 4225, 9025, 21025

๐Ÿ“ Practice Problems โ€” Squaring Numbers Ending in 5

PRACTICE 1

15ยฒ = ?

1 ร— 2 = 2, append 25 โ†’ 225
PRACTICE 2

45ยฒ = ?

4 ร— 5 = 20, append 25 โ†’ 2025
PRACTICE 3

55ยฒ = ?

5 ร— 6 = 30, append 25 โ†’ 3025
PRACTICE 4

85ยฒ = ?

8 ร— 9 = 72, append 25 โ†’ 7225
PRACTICE 5

105ยฒ = ?

10 ร— 11 = 110, append 25 โ†’ 11025
PRACTICE 6

135ยฒ = ?

13 ร— 14 = 182, append 25 โ†’ 18225
PRACTICE 7

145ยฒ = ?

14 ร— 15 = 210, append 25 โ†’ 21025
PRACTICE 8

155ยฒ = ?

15 ร— 16 = 240, append 25 โ†’ 24025
PRACTICE 9

175ยฒ = ?

17 ร— 18 = 306, append 25 โ†’ 30625
PRACTICE 10

195ยฒ = ?

19 ร— 20 = 380, append 25 โ†’ 38025
PRACTICE 11

205ยฒ = ?

20 ร— 21 = 420, append 25 โ†’ 42025
PRACTICE 12

225ยฒ = ?

22 ร— 23 = 506, append 25 โ†’ 50625
PRACTICE 13

250ยฒ = ?

Treat as 25 ร— 10, so (25)ยฒ ร— 100 = 625 ร— 100 = 62500. Or: left part 25 โ†’ 25ร—26 = 650 | 25 โ†’ but that gives a 5-digit ending. Better: 25 ร— 26 = 650, append 25 โ†’ 62500. โœ…
PRACTICE 14

995ยฒ = ?

99 ร— 100 = 9900, append 25 โ†’ 990025
PRACTICE 15

1005ยฒ = ?

100 ร— 101 = 10100, append 25 โ†’ 1010025
Chapter 4

๐ŸŽฏ Nikhilam Sutra โ€” Near Base Multiplication

เคจเคฟเค–เคฟเคฒเค‚ เคจเคตเคคเคถเฅเคšเคฐเคฎเค‚ เคฆเคถเคคเคƒ
"Nikhilam Navatashcaramam Dashatah" โ€” All from 9, Last from 10

This powerful sutra lets you multiply numbers that are close to a base (like 10, 100, 1000) almost instantly. It works beautifully for numbers near 100, 1000, or any power of 10.

๐Ÿ”ต Part A: Numbers Close to 100

1
Find the deficiency (how far each number is from 100)
2
Cross-subtract: Subtract one number's deficiency from the other number
3
Multiply the deficiencies together (this gives the right part, always 2 digits)
4
Combine: Left part | Right part = Answer!
98 ร— 97
โ†’
Deficiencies:
-2, -3
โ†’
Cross: 98-3
= 95
โ†’
Multiply: 2ร—3
= 06
โ†’
Answer:
9506

โœ… Numbers Below 100 (Both numbers < 100)

Example 1: 98 ร— 97

Base: 100 | Deficiencies: 98โ†’-2, 97โ†’-3
Cross: 98 - 3 = 95 | Product: 2 ร— 3 = 06
Answer: 9506 โœ…

Example 2: 96 ร— 94

Base: 100 | Deficiencies: 96โ†’-4, 94โ†’-6
Cross: 96 - 6 = 90 | Product: 4 ร— 6 = 24
Answer: 9024 โœ…

Example 3: 93 ร— 91

Base: 100 | Deficiencies: 93โ†’-7, 91โ†’-9
Cross: 93 - 9 = 84 | Product: 7 ร— 9 = 63
Answer: 8463 โœ…

Example 4: 97 ร— 93

Base: 100 | Deficiencies: 97โ†’-3, 93โ†’-7
Cross: 97 - 7 = 90 | Product: 3 ร— 7 = 21
Answer: 9021 โœ…

Example 5: 88 ร— 91

Base: 100 | Deficiencies: 88โ†’-12, 91โ†’-9
Cross: 88 - 9 = 79 | Product: 12 ร— 9 = 108 โ†’ Right part overflows!
Carry 1: 79+1 = 80, right = 08 โ†’ Answer: 8008 โœ…

โœ… Numbers Above 100 (Surpluses)

When numbers are above the base, use surpluses instead of deficiencies. Cross-add instead of cross-subtract!

Example 6: 103 ร— 104

Base: 100 | Surpluses: 103โ†’+3, 104โ†’+4
Cross: 103 + 4 = 107 | Product: 3 ร— 4 = 12
Answer: 10712 โœ…

Example 7: 112 ร— 108

Base: 100 | Surpluses: 112โ†’+12, 108โ†’+8
Cross: 112 + 8 = 120 | Product: 12 ร— 8 = 96
Answer: 12096 โœ…

Example 8: 105 ร— 107

Base: 100 | Surpluses: +5, +7
Cross: 105 + 7 = 112 | Product: 5 ร— 7 = 35
Answer: 11235 โœ…

๐ŸŸข Part B: Numbers Close to 1000

The same technique works for base 1000! The right part now needs 3 digits.

Example 9: 998 ร— 997

Base: 1000 | Deficiencies: 998โ†’-2, 997โ†’-3
Cross: 998 - 3 = 995 | Product: 002 ร— 003 = 006
Answer: 995006 โœ…

Example 10: 996 ร— 994

Base: 1000 | Deficiencies: 996โ†’-4, 994โ†’-6
Cross: 996 - 6 = 990 | Product: 004 ร— 006 = 024
Answer: 990024 โœ…
Why does this work? If a = base - x and b = base - y, then:
a ร— b = baseร—(base - x - y) + xy = baseร—(a - y) + xy
The cross-subtraction gives the left part, and the product of deficiencies gives the right part!
The Nikhilam Sutra is considered the most versatile of all 16 Vedic sutras. It can be extended to subtraction from any base, not just powers of 10!

๐Ÿ“ Practice Problems โ€” Nikhilam Sutra

PRACTICE 1

99 ร— 98 = ?

Deficiencies: -1, -2 | Cross: 99-2 = 97 | Product: 1ร—2 = 02 โ†’ 9702
PRACTICE 2

97 ร— 96 = ?

Deficiencies: -3, -4 | Cross: 97-4 = 93 | Product: 3ร—4 = 12 โ†’ 9312
PRACTICE 3

95 ร— 93 = ?

Deficiencies: -5, -7 | Cross: 95-7 = 88 | Product: 5ร—7 = 35 โ†’ 8835
PRACTICE 4

92 ร— 91 = ?

Deficiencies: -8, -9 | Cross: 92-9 = 83 | Product: 8ร—9 = 72 โ†’ 8372
PRACTICE 5

102 ร— 106 = ?

Surpluses: +2, +6 | Cross: 102+6 = 108 | Product: 2ร—6 = 12 โ†’ 10812
PRACTICE 6

108 ร— 109 = ?

Surpluses: +8, +9 | Cross: 108+9 = 117 | Product: 8ร—9 = 72 โ†’ 11772
PRACTICE 7

104 ร— 103 = ?

Surpluses: +4, +3 | Cross: 104+3 = 107 | Product: 4ร—3 = 12 โ†’ 10712
PRACTICE 8

999 ร— 998 = ?

Base 1000 | Deficiencies: -1, -2 | Cross: 999-2 = 997 | Product: 1ร—2 = 002 โ†’ 997002
PRACTICE 9

993 ร— 995 = ?

Base 1000 | Deficiencies: -7, -5 | Cross: 993-5 = 988 | Product: 7ร—5 = 035 โ†’ 988035
PRACTICE 10

1003 ร— 1007 = ?

Base 1000 | Surpluses: +3, +7 | Cross: 1003+7 = 1010 | Product: 3ร—7 = 021 โ†’ 1010021
PRACTICE 11

87 ร— 92 = ?

Deficiencies: -13, -8 | Cross: 87-8 = 79 | Product: 13ร—8 = 104 โ†’ carry 1: 80|04 โ†’ 8004
PRACTICE 12

98 ร— 92 = ?

Deficiencies: -2, -8 | Cross: 98-8 = 90 | Product: 2ร—8 = 16 โ†’ 9016
PRACTICE 13

111 ร— 109 = ?

Surpluses: +11, +9 | Cross: 111+9 = 120 | Product: 11ร—9 = 99 โ†’ 12099
PRACTICE 14

994 ร— 988 = ?

Base 1000 | Deficiencies: -6, -12 | Cross: 994-12 = 982 | Product: 6ร—12 = 072 โ†’ 982072
PRACTICE 15

96 ร— 97 = ?

Deficiencies: -4, -3 | Cross: 96-3 = 93 | Product: 4ร—3 = 12 โ†’ 9312
Chapter 5

โž• Fast Addition Techniques

"Speed in addition is the foundation of all mental mathematics." โ€” Vedic Mathematics Principle

๐Ÿ”ต Technique 1: Left-to-Right Addition

Instead of the traditional right-to-left method, Vedic math adds from left to right โ€” the same way we read numbers! This is faster because you get the most significant digits first.

1
Add the hundreds digits first
2
Add the tens digits next
3
Add the ones digits last
4
Combine all parts for the answer

Example 1: 347 + 286

Hundreds: 300 + 200 = 500
Tens: 40 + 80 = 120
Ones: 7 + 6 = 13
Total: 500 + 120 + 13 = 633 โœ…

Example 2: 568 + 475

Hundreds: 500 + 400 = 900
Tens: 60 + 70 = 130
Ones: 8 + 5 = 13
Total: 900 + 130 + 13 = 1043 โœ…

Example 3: 1234 + 5678

Thousands: 1000 + 5000 = 6000
Hundreds: 200 + 600 = 800
Tens: 30 + 70 = 100
Ones: 4 + 8 = 12
Total: 6000 + 800 + 100 + 12 = 6912 โœ…

๐ŸŸข Technique 2: Compensation Method

Round one number up to the nearest "easy" number, then subtract the difference.

Rule: If a number is close to a round number, round up and compensate!
298 + 145 = 300 + 145 โˆ’ 2 = 445 โˆ’ 2 = 443

Example 4: 298 + 145

Round 298 โ†’ 300 (added 2)
300 + 145 = 445
Compensate: 445 โˆ’ 2 = 443 โœ…

Example 5: 497 + 326

Round 497 โ†’ 500 (added 3)
500 + 326 = 826
Compensate: 826 โˆ’ 3 = 823 โœ…

Example 6: 1995 + 847

Round 1995 โ†’ 2000 (added 5)
2000 + 847 = 2847
Compensate: 2847 โˆ’ 5 = 2842 โœ…

๐ŸŸก Technique 3: Grouping to 10s

When adding multiple numbers, look for pairs that make 10 (or multiples of 10).

Example 7: 7 + 8 + 3 + 2 + 5

Group: (7+3) + (8+2) + 5 = 10 + 10 + 5 = 25 โœ…

Example 8: 14 + 23 + 16 + 27

Group: (14+16) + (23+27) = 30 + 50 = 80 โœ…

Example 9: 6 + 9 + 4 + 1 + 8 + 2

Group: (6+4) + (9+1) + (8+2) = 10 + 10 + 10 = 30 โœ…

๐Ÿ”ด Technique 4: Mental Addition of Long Columns

Example 10: 456 + 789 + 123

Left-to-right: 400+700+100 = 1200
50+80+20 = 150
6+9+3 = 18
Total: 1200 + 150 + 18 = 1368 โœ…

Example 11: 999 + 888 + 777

Compensation: (1000-1) + (900-12) + (800-23)... OR
Use grouping: 999+1 = 1000, so 999+888+777 = 1000+888+777-1 = 2665-1 = ...
Easier: 900+800+700 = 2400, 90+80+70 = 240, 9+8+7 = 24 โ†’ 2400+240+24 = 2664 โœ…

Example 12: 47 + 85 + 53 + 15

Group: (47+53) + (85+15) = 100 + 100 = 200 โœ…

Example 13: 198 + 347

Round: 200 + 347 = 547, compensate: 547 โˆ’ 2 = 545 โœ…

Example 14: 2450 + 3550

Notice: 450 + 550 = 1000 โ†’ 2000 + 3000 + 1000 = 6000 โœ…

Example 15: 375 + 625

Notice: 375 + 625 = 1000 (complements of 1000!) โœ…
Always scan the numbers first! Look for complements (pairs that sum to 10, 100, or 1000) before adding sequentially. This one habit alone can double your addition speed.

๐Ÿ“ Practice Problems โ€” Fast Addition

PRACTICE 1

456 + 378 = ?

400+300=700, 50+70=120, 6+8=14 โ†’ 700+120+14 = 834
PRACTICE 2

697 + 205 = ?

700+205โˆ’3 = 902
PRACTICE 3

8 + 5 + 2 + 7 + 3 + 5 = ?

(8+2) + (5+5) + (7+3) = 10+10+10 = 30
PRACTICE 4

1998 + 456 = ?

2000 + 456 โˆ’ 2 = 2454
PRACTICE 5

37 + 48 + 63 + 52 = ?

(37+63) + (48+52) = 100 + 100 = 200
PRACTICE 6

789 + 456 + 211 = ?

700+400+200=1300, 80+50+10=140, 9+6+1=16 โ†’ 1300+140+16 = 1456
PRACTICE 7

999 + 1 = ?

Easy complement! 1000 ๐Ÿ˜„
PRACTICE 8

4567 + 5433 = ?

567 + 433 = 1000 โ†’ 4000 + 5000 + 1000 = 10000
PRACTICE 9

295 + 305 + 400 = ?

(295+305) + 400 = 600 + 400 = 1000
PRACTICE 10

1234 + 4766 = ?

234 + 766 = 1000 โ†’ 1000 + 4000 + 1000 = 6000
Chapter 6

โž– Fast Subtraction Techniques

เคจเคฟเค–เคฟเคฒเค‚ เคจเคตเคคเคถเฅเคšเคฐเคฎเค‚ เคฆเคถเคคเคƒ
"All from 9, Last from 10" โ€” The key to instant subtraction from powers of 10

๐Ÿ”ต Technique 1: Subtracting from Powers of 10

This is the most powerful Vedic subtraction trick. To subtract any number from 10, 100, 1000, 10000, etc.:

1
Subtract each digit from 9
2
Subtract the last digit from 10
3
That's your answer!
"All from 9, Last from 10"
Every digit is subtracted from 9, except the last non-zero digit which is subtracted from 10. That's it!

Example 1: 1000 โˆ’ 357

9โˆ’3 = 6, 9โˆ’5 = 4, 10โˆ’7 = 3
Answer: 643 โœ…

Example 2: 10000 โˆ’ 4825

9โˆ’4 = 5, 9โˆ’8 = 1, 9โˆ’2 = 7, 10โˆ’5 = 5
Answer: 5175 โœ…

Example 3: 1000 โˆ’ 682

9โˆ’6 = 3, 9โˆ’8 = 1, 10โˆ’2 = 8
Answer: 318 โœ…

Example 4: 100000 โˆ’ 53872

9โˆ’5 = 4, 9โˆ’3 = 6, 9โˆ’8 = 1, 9โˆ’7 = 2, 10โˆ’2 = 8
Answer: 46128 โœ…

Example 5: 10000 โˆ’ 7293

9โˆ’7 = 2, 9โˆ’2 = 7, 9โˆ’9 = 0, 10โˆ’3 = 7
Answer: 2707 โœ…

๐ŸŸข Technique 2: Complement Method

For general subtraction, convert to easier arithmetic using complements.

Example 6: 843 โˆ’ 279

Think: 279 is close to 300
843 โˆ’ 300 = 543
But we subtracted 21 too much (300 โˆ’ 279 = 21)
543 + 21 = 564 โœ…

Example 7: 725 โˆ’ 388

Think: 388 is close to 400
725 โˆ’ 400 = 325
Add back 12 (400 โˆ’ 388 = 12)
325 + 12 = 337 โœ…

๐ŸŸก Technique 3: Mental Subtraction with Rounding

Example 8: 500 โˆ’ 187

Round: 500 โˆ’ 200 = 300
Add back 13 (200 โˆ’ 187 = 13)
300 + 13 = 313 โœ…

Example 9: 1000 โˆ’ 456

Using "All from 9, last from 10":
9โˆ’4=5, 9โˆ’5=4, 10โˆ’6=4 โ†’ 544 โœ…

Example 10: 5000 โˆ’ 2347

5000 โˆ’ 2347 = 5000 โˆ’ 2000 โˆ’ 347
= 3000 โˆ’ 347
Using complement: 1000โˆ’347 = 653
So: 2000 + 653 = 2653 โœ…

โšก Traditional vs Vedic Subtraction

ProblemTraditional (Borrowing)Vedic Method
1000 โˆ’ 357Borrow from thousands, hundreds... 4-5 steps"All from 9, last from 10": 6, 4, 3 โ†’ 643. One step!
10000 โˆ’ 4825Multiple borrowing chains โ†’ ~60 sec5, 1, 7, 5 โ†’ 5175. Under 5 seconds!
843 โˆ’ 279Borrow across digits โ†’ ~30 sec843 โˆ’ 300 + 21 = 564. Mental math!

๐Ÿ“ Practice Problems โ€” Fast Subtraction

PRACTICE 1

1000 โˆ’ 432 = ?

9โˆ’4=5, 9โˆ’3=6, 10โˆ’2=8 โ†’ 568
PRACTICE 2

1000 โˆ’ 789 = ?

9โˆ’7=2, 9โˆ’8=1, 10โˆ’9=1 โ†’ 211
PRACTICE 3

10000 โˆ’ 3456 = ?

9โˆ’3=6, 9โˆ’4=5, 9โˆ’5=4, 10โˆ’6=4 โ†’ 6544
PRACTICE 4

10000 โˆ’ 8765 = ?

9โˆ’8=1, 9โˆ’7=2, 9โˆ’6=3, 10โˆ’5=5 โ†’ 1235
PRACTICE 5

100000 โˆ’ 12345 = ?

9โˆ’1=8, 9โˆ’2=7, 9โˆ’3=6, 9โˆ’4=5, 10โˆ’5=5 โ†’ 87655
PRACTICE 6

600 โˆ’ 247 = ?

600โˆ’250+3 = 350+3 = 353
PRACTICE 7

900 โˆ’ 567 = ?

900โˆ’600+33 = 300+33 = 333
PRACTICE 8

5000 โˆ’ 1234 = ?

5000โˆ’1000=4000, 1000โˆ’234=766, so 3000+766 = 3766
PRACTICE 9

1000 โˆ’ 505 = ?

9โˆ’5=4, 9โˆ’0=9, 10โˆ’5=5 โ†’ 495
PRACTICE 10

7000 โˆ’ 3698 = ?

7000โˆ’3000=4000, 1000โˆ’698=302, 3000+302 = 3302
Chapter 7

๐Ÿ”ข Multiplication Secrets

"The mind is everything. What you think, you become. Master these tricks, and numbers will dance for you." โ€” Inspired by Vedic Wisdom

๐Ÿ”ต Multiply by 9: The "Minus One" Trick

Rule: n ร— 9 = n ร— 10 โˆ’ n
Multiply by 10 (add a zero), then subtract the original number.

Example: 47 ร— 9

47 ร— 10 = 470
470 โˆ’ 47 = 423 โœ…

Example: 156 ร— 9

156 ร— 10 = 1560
1560 โˆ’ 156 = 1404 โœ…

๐ŸŸข Multiply by 99: The "Minus One (ร—100)" Trick

Rule: n ร— 99 = n ร— 100 โˆ’ n
Multiply by 100, then subtract the original number.

Example: 35 ร— 99

35 ร— 100 = 3500
3500 โˆ’ 35 = 3465 โœ…

Example: 78 ร— 99

78 ร— 100 = 7800
7800 โˆ’ 78 = 7722 โœ…

๐ŸŸก Multiply by 999

Rule: n ร— 999 = n ร— 1000 โˆ’ n

Example: 42 ร— 999

42 ร— 1000 = 42000
42000 โˆ’ 42 = 41958 โœ…

Example: 123 ร— 999

123 ร— 1000 = 123000
123000 โˆ’ 123 = 122877 โœ…

๐Ÿ”ด Multiply by 25: Quarter and Shift

Rule: n ร— 25 = n รท 4 ร— 100
Since 25 = 100/4, just divide by 4 and multiply by 100.

Example: 48 ร— 25

48 รท 4 = 12
12 ร— 100 = 1200 โœ…

Example: 36 ร— 25

36 รท 4 = 9
9 ร— 100 = 900 โœ…

๐ŸŸฃ Multiply by 125: Eighth and Shift

Rule: n ร— 125 = n รท 8 ร— 1000
Since 125 = 1000/8, divide by 8 and multiply by 1000.

Example: 64 ร— 125

64 รท 8 = 8
8 ร— 1000 = 8000 โœ…

Example: 48 ร— 125

48 รท 8 = 6
6 ร— 1000 = 6000 โœ…

โšช Multiply by 5: Half and Shift

Rule: n ร— 5 = n รท 2 ร— 10
Halve the number, then multiply by 10.

Example: 74 ร— 5

74 รท 2 = 37
37 ร— 10 = 370 โœ…

Example: 86 ร— 5

86 รท 2 = 43
43 ร— 10 = 430 โœ…

โฌ› Multiply by 50: Half and Shift ร—100

Rule: n ร— 50 = n รท 2 ร— 100

Example: 68 ร— 50

68 รท 2 = 34
34 ร— 100 = 3400 โœ…

Example: 124 ร— 50

124 รท 2 = 62
62 ร— 100 = 6200 โœ…
All these tricks are based on one principle: replace "hard" multiplications with "easy" ones. Multiplying by 5 is the same as dividing by 2 and adding a zero. Your brain finds halving much easier than multiplying by 5!

๐Ÿ“ Practice Problems โ€” Multiplication Secrets

PRACTICE 1

53 ร— 9 = ?

530 โˆ’ 53 = 477
PRACTICE 2

67 ร— 9 = ?

670 โˆ’ 67 = 603
PRACTICE 3

45 ร— 99 = ?

4500 โˆ’ 45 = 4455
PRACTICE 4

56 ร— 99 = ?

5600 โˆ’ 56 = 5544
PRACTICE 5

71 ร— 999 = ?

71000 โˆ’ 71 = 70929
PRACTICE 6

32 ร— 25 = ?

32 รท 4 = 8, ร— 100 = 800
PRACTICE 7

56 ร— 25 = ?

56 รท 4 = 14, ร— 100 = 1400
PRACTICE 8

72 ร— 125 = ?

72 รท 8 = 9, ร— 1000 = 9000
PRACTICE 9

96 ร— 5 = ?

96 รท 2 = 48, ร— 10 = 480
PRACTICE 10

144 ร— 5 = ?

144 รท 2 = 72, ร— 10 = 720
PRACTICE 11

84 ร— 50 = ?

84 รท 2 = 42, ร— 100 = 4200
PRACTICE 12

246 ร— 9 = ?

2460 โˆ’ 246 = 2214
PRACTICE 13

88 ร— 125 = ?

88 รท 8 = 11, ร— 1000 = 11000
PRACTICE 14

234 ร— 99 = ?

23400 โˆ’ 234 = 23166
PRACTICE 15

76 ร— 50 = ?

76 รท 2 = 38, ร— 100 = 3800
Chapter 8

โž— Division Shortcuts

"Division is merely multiplication in disguise. Master one, and you master both." โ€” Vedic Mathematics Insight

๐Ÿ”ต Divide by 5: Double and Shift

Rule: n รท 5 = n ร— 2 รท 10
Double the number, then divide by 10 (remove the last digit and that's the decimal).

Example 1: 365 รท 5

365 ร— 2 = 730
730 รท 10 = 73 โœ…

Example 2: 840 รท 5

840 ร— 2 = 1680
1680 รท 10 = 168 โœ…

Example 3: 1235 รท 5

1235 ร— 2 = 2470
2470 รท 10 = 247 โœ…

๐ŸŸข Divide by 25: Multiply by 4, Shift

Rule: n รท 25 = n ร— 4 รท 100
Since 25 ร— 4 = 100, multiply by 4 and divide by 100.

Example 4: 450 รท 25

450 ร— 4 = 1800
1800 รท 100 = 18 โœ…

Example 5: 1250 รท 25

1250 ร— 4 = 5000
5000 รท 100 = 50 โœ…

๐ŸŸก Divide by 125: Multiply by 8, Shift

Rule: n รท 125 = n ร— 8 รท 1000
Since 125 ร— 8 = 1000, multiply by 8 and divide by 1000.

Example 6: 625 รท 125

625 ร— 8 = 5000
5000 รท 1000 = 5 โœ…

Example 7: 3000 รท 125

3000 ร— 8 = 24000
24000 รท 1000 = 24 โœ…

๐Ÿ”ด Divide by 9: The Nikhilam Flag Division

To divide by 9, use a beautiful technique where each digit generates the next:

1
Write the first digit. This is both the first quotient digit AND the remainder to carry.
2
Add this remainder to the next digit โ€” that's the next quotient digit.
3
Continue until the last digit โ€” the final sum is the remainder.

Example 8: 1234 รท 9

Step 1: Bring down 1 โ†’ Quotient: 1, carry 1
Step 2: 1+2 = 3 โ†’ Quotient: 13, carry 3
Step 3: 3+3 = 6 โ†’ Quotient: 136, carry 6
Step 4: 6+4 = 10 โ†’ But 10 โ‰ฅ 9, so carry 1 to quotient: 137, remainder 1
Answer: 137 remainder 1 โœ… (Verify: 137 ร— 9 + 1 = 1233 + 1 = 1234 โœ“)

Example 9: 2013 รท 9

Step 1: 2 โ†’ Q: 2, carry 2
Step 2: 2+0 = 2 โ†’ Q: 22, carry 2
Step 3: 2+1 = 3 โ†’ Q: 223, carry 3
Step 4: 3+3 = 6 โ†’ remainder
Answer: 223 remainder 6 โœ… (223 ร— 9 + 6 = 2007 + 6 = 2013 โœ“)

๐ŸŸฃ Divide by 11: Alternating Sum Check

A number is divisible by 11 if the alternating sum of its digits is divisible by 11.

Divisibility by 11: Sum of digits at odd positions โˆ’ Sum of digits at even positions = 0 or multiple of 11.
Example: 918082 โ†’ (9+8+8) โˆ’ (1+0+2) = 25 โˆ’ 3 = 22 โ†’ divisible by 11!

Example 10: 2816 รท 11

Check: (2+1) โˆ’ (8+6) = 3 โˆ’ 14 = โˆ’11 โ†’ divisible by 11!
Use standard method or reverse of ร—11 trick: 2816 รท 11 = 256 โœ…
โฑ๏ธ Speed Challenge โ€” Solve in 5 seconds!
735 รท 5   |   500 รท 25   |   2000 รท 125
Answers: 147, 20, 16

๐Ÿ“ Practice Problems โ€” Division Shortcuts

PRACTICE 1

455 รท 5 = ?

455 ร— 2 = 910, รท 10 = 91
PRACTICE 2

1280 รท 5 = ?

1280 ร— 2 = 2560, รท 10 = 256
PRACTICE 3

675 รท 25 = ?

675 ร— 4 = 2700, รท 100 = 27
PRACTICE 4

2000 รท 25 = ?

2000 ร— 4 = 8000, รท 100 = 80
PRACTICE 5

1000 รท 125 = ?

1000 ร— 8 = 8000, รท 1000 = 8
PRACTICE 6

4500 รท 125 = ?

4500 ร— 8 = 36000, รท 1000 = 36
PRACTICE 7

4321 รท 9 = ?

4โ†’carry 4, 4+3=7โ†’carry 7, 7+2=9โ†’carry 9, 9+1=10โ‰ฅ9 so carry 1, Q=480, R=1 โ†’ 480 remainder 1
PRACTICE 8

1111 รท 9 = ?

1โ†’c1, 1+1=2โ†’c2, 2+1=3โ†’c3, 3+1=4โ†’R. Q=123, R=4 โ†’ 123 remainder 4
PRACTICE 9

825 รท 5 = ?

825 ร— 2 = 1650, รท 10 = 165
PRACTICE 10

3125 รท 125 = ?

3125 ร— 8 = 25000, รท 1000 = 25
Final Assessment

๐ŸŽฏ Vedic Mathematics Quiz โ€” 10 MCQs

Test your mastery of all 8 chapters! Try to use Vedic methods for each question.

QUESTION 1

Using the Vedic method, what is 76 ร— 11?

A786
B836
C846
D876
QUESTION 2

What is 85ยฒ using the Vedic squaring technique?

A7025
B7125
C7225
D7325
QUESTION 3

Using Nikhilam Sutra, 97 ร— 96 = ?

A9212
B9312
C9306
D9412
QUESTION 4

1000 โˆ’ 567 = ? (Using "All from 9, Last from 10")

A433
B443
C343
D533
QUESTION 5

Using the Vedic trick, 48 ร— 25 = ?

A1000
B1100
C1200
D1250
QUESTION 6

What is 47 ร— 9 using the Vedic shortcut?

A413
B423
C433
D427
QUESTION 7

730 รท 5 = ? (Using the Vedic division shortcut)

A136
B142
C146
D156
QUESTION 8

How many Sutras are there in Vedic Mathematics?

A12
B16
C18
D20
QUESTION 9

Using Nikhilam, 103 ร— 107 = ?

A11021
B11121
C10721
D11031
QUESTION 10

What is 145ยฒ using the squaring trick?

A20025
B21025
C22025
D21225

Your Vedic Maths Score

๐Ÿ“‹ Book Summary โ€” Vedic Mathematics Part 1

Congratulations! You've learned 8 powerful chapters of Vedic Mathematics:

  • Chapter 1: The history, 16 sutras, and benefits of Vedic Maths
  • Chapter 2: Lightning-fast multiplication by 11, 12, and 13
  • Chapter 3: Instantly square any number ending in 5
  • Chapter 4: Nikhilam Sutra for multiplying numbers near 100 or 1000
  • Chapter 5: Four fast addition techniques for mental math
  • Chapter 6: "All from 9, Last from 10" and complement subtraction
  • Chapter 7: Multiplication shortcuts for 5, 9, 25, 50, 99, 125, 999
  • Chapter 8: Division shortcuts for 5, 9, 25, 125

๐Ÿ”ฅ Practice daily for 15 minutes. Within a month, you'll calculate faster than most calculators!

"Mathematics is not about numbers, equations, or algorithms. It is about understanding." โ€” William Paul Thurston

๐Ÿ“š Vedic Mathematics Secrets โ€” Part 1: Fundamentals

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