VEDIC MATHEMATICS – COMPLETE NOTES (PDF STYLE)

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CHAPTER 1 : ADDITION & SUBTRACTION

Sutra: Sankalana–Vyavakalanābhyām

Shortcut 1: Base Method (near 10/100/1000)

Example: 997 + 874
997 = 1000 – 3 → 874 + 1000 = 1874 → 1874 – 3 = 1871

Shortcut 2: Add 9/99 fast

657 + 99 → (657 + 100) – 1 = 756

Shortcut 3: Smart Carry

Mind Map:

           ADDITION / SUBTRACTION
                    |
    -----------------------------------------
    |                 |                    |
Base Method      99-Method           Smart Carry

Practice Questions (25)

1. 987 + 99
2. 874 + 999
3. 1004 + 997
4. 4567 + 1002
5. 1000 – 683
6. 2000 – 1189
...
7. 905 – 789

CHAPTER 2 : MULTIPLICATION

Sutras: Nikhilam, Urdhva-Tiryagbhayam, Yavadunam

Method 1: Nikhilam (near base)

94 × 97
94 = –6, 97 = –3
Cross-subtract: 94 – 3 = 91
Deficit multiply: 18
Answer = 9118

Method 2: Urdhva-Tiryagbhyam

23 × 14 = 322

              MULTIPLICATION
                   |
   -------------------------------------------
   |                   |                    |
Nikhilam         Crosswise            Yavadunam

Practice Questions (30)

1. 98 × 97
2. 95 × 96
3. 104 × 109
4. 999 × 987
5. 1008 × 1006
6. 34 × 27
7. 87 × 53
8. 123 × 45
...

CHAPTER 3 : DIVISION

Sutras: Parāvartya Yojayet, Nikhilam Division

Paravartya Method (digit-by-digit)

123 ÷ 9 → 1, 3, 6 → Remainder = 6

               DIVISION
                   |
    --------------------------------
    |               |             |
Paravartya       Nikhilam     Puranapuran

Practice Questions (25)

1. 345 ÷ 9
2. 587 ÷ 11
3. 1234 ÷ 19
...

CHAPTER 4 : SQUARES & SQUARE ROOTS

Sutras: Ekadhikena Purvena, Yavadunam

Shortcut: End in 5

35² → 3×4 =12 → 1225

Near base method

96² = 9216

                 SQUARES
                     |
     ------------------------------------
     |                   |             |
Ending in 5         Near base       General

Practice Questions (25)

1. 25²
2. 45²
3. 65²
4. 95²
5. 105²
6. 96²
...

CHAPTER 5 : CUBES & CUBE ROOTS

Cube by expansion

12³ → 1 | 6 | 12 | 8 = 1728

Practice Questions (25)

1. 18³
2. 27³
3. 32³
4. Cube root of 970299
...

CHAPTER 6 : HCF & LCM

Fast difference method

98 & 42 → HCF = 14

Practice Questions (20)

CHAPTER 7 : EQUATIONS

Shunyam Samyasamuccaye

(3x+5)/(x+2) = (7x+9)/(x+2) → x = -1

CHAPTER 8 : REMAINDERS & DIVISIBILITY

Digit Sum Method

2789 mod 9 = 8

Practice Questions (20)

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