🕉️ VEDIC MATHEMATICS — LEVEL 1: FOUNDATION

MODULE 6: Vedic Division — Part 1

Complete Study Material | Theory + Examples + Practice + Test Bank

"Division is not about 'how many times does it go into it?' but about pattern and remainder flow. Master division, and you master arithmetic." — Vedic Mathematics Teacher's Manual

📋 MODULE AT A GLANCE

🎯 LEARNING OUTCOMES

By the end of this module, the student will be able to:

1. State Sutra 4 (Paravartya Yojayet) and Sutra 12 (Shesanyankena Charamena) with their English meanings
2. Divide any number by 9 in under 5 seconds using the digit-sum method
3. Divide by 8 and 7 using the Vedic remainder flow method
4. Apply the flag method for simple two-digit divisors
5. Perform straight division (Dhvajanka method) for divisors up to 99
6. Use the Vedic remainder theorem to verify results
7. Divide numbers by divisors near a base (e.g., 98, 101)
8. Express answers as quotient and remainder correctly

PART 1: THEORY

1.1 — Introduction to Vedic Division

Why is Division Different?

Division is considered the most difficult of the four basic operations. Conventional division involves:

• Trial-and-error estimation of quotient digits
• Multiplication of quotient digit by divisor
• Subtraction and bringing down digits
• Multiple steps that are easy to get wrong

Vedic Mathematics provides three powerful approaches to division:

1.2 — Sutra 4: Paravartya Yojayet

What Does This Mean?

"Paravartya" means transpose (change sign, move to the other side). "Yojayet" means apply or use.

In division, this sutra tells us:

"Change the sign of the divisor's digits (except the first) and use them in a running total."

This is the foundation of:

• Division by numbers near a base
• The flag method (Dhvajanka)
• Solving equations (covered in Level 2)

1.3 — Sutra 12: Shesanyankena Charamena

What Does This Mean?

This sutra tells us that remainders follow a pattern that can be generated using the last digit of the divisor.

It is the basis for:

• Division by 9 (where remainders are just digit sums)
• Division by 19, 29, 39, etc. (using Ekadhikena Purvena)
• Recurring decimal patterns (1/19, 1/29, etc.)

In this module, we use it primarily for division by single-digit divisors near 10.

1.4 — Division by 9: The Easiest Vedic Division

The Pattern

Dividing by 9 has a magical property: Each remainder becomes the next digit's running total.

The Rule: For any number divided by 9:

• The first digit of the quotient = the first digit of the dividend
• Each subsequent quotient digit = previous quotient digit + next dividend digit
• The final remainder = last quotient digit + last digit of dividend

Example 1: 23 ÷ 9

But wait — remainder 5 is less than 9, so correct.

Example 2: 45 ÷ 9

Rule: When remainder ≥ 9, subtract 9 from remainder and add 1 to quotient.

Example 3: 23451 ÷ 9 (From your prompt)

Let me solve this step by step:

Correct Systematic Method for 23451 ÷ 9:

Result: Quotient = 2605, Remainder = 6

Check: 2605 × 9 = 23445, +6 = 23451 ✓

Example 4: 123456 ÷ 9

Let me solve quickly:

Quotient digits: 1,3,7,1,7 → 13717 | Remainder = 3

But let's verify the systematic way:

Better method (bar notation for carries):

123456 ÷ 9:

Quotient = 13706, Remainder = 2

Check: 13706×9=123354, +2=123356 (not matching — I made an error)

Let me do proper Vedic division by 9 from authentic source:

The Correct Algorithm for ÷9:

Write the number. Draw a vertical line after the first digit.

For 123456:

• Write as: 1 | 2 3 4 5 6
• Bring down 1 → Q=1
• 1+2=3 → Q=1,3
• 3+3=6 → Q=1,3,6
• 6+4=10 → write 0, carry 1 → Q=1,3,7,0
• 0+5=5 → Q=1,3,7,0,5
• 5+6=11 → R=11

Since R≥9, subtract 9: R=2, add 1 to Q: Q=1,3,7,0,6

Quotient = 13706, Remainder = 2

Check: 13706×9 = 123354, +2 = 123356 ✗ (not 123456)

So this is wrong. Let me use the authentic Vedic method:

The true Vedic method for ÷9:

The quotient digits are simply the running digit sums and the remainder is the final sum of all digits.

For 123456:

• Sum of digits = 1+2+3+4+5+6 = 21
• Remainder = 21 ÷ 9 → 21 = 2×9 + 3 → Remainder = 3
• Quotient = (Number - Remainder) ÷ 9 = (123456 - 3) ÷ 9 = 123453 ÷ 9 = 13717

Check: 13717×9 = 123453, +3=123456 ✓

So the correct quotient is 13717, remainder 3.

Moral: The running sum method works, but carries must propagate properly. For large numbers, use the digit sum method: remainder = sum of digits mod 9 (with 9 treated as 0), quotient = (number - remainder)/9.

Simplified Division by 9 Rule

But wait — that's just doing division normally. The Vedic speed comes from the running total method without multiplication.

Let me present the correct running total method:

Example: 23451 ÷ 9 (Correctly)

Write digits: 2 3 4 5 1

So Q digits: 2,6,0,5 = 2605, R=6 ✓

This matches your example.

So the rule is: Write each running total. When it reaches 9 or more, subtract 9 and carry 1 to the left.

1.5 — Division by 8 (The Vedic Way)

The Principle

Division by 8 is similar to division by 9, but instead of adding the current quotient digit to the next digit, we multiply by a factor or use a different rule.

Actually, the Vedic method for ÷8 uses the fact that 8 = 10 - 2. This relates to the Paravartya sutra.

Method for ÷8

For divisor = 8 = 10 - 2:

• Base = 10
• Complement = 2 (transposed, with sign changed: +2)

Procedure:

Write the dividend. For each digit except the last:

1. Bring down the first digit as the first quotient digit
2. Multiply it by the complement (2) and add to the next digit
3. Write the result as the next quotient digit (if < 8) else adjust
4. Continue to the end; the last result is the remainder

Example: 41 ÷ 8

Wait — 41÷8 = 5 remainder 1? 8×5=40, +1=41 ✓ Correct.

Example: 73 ÷ 8

So quotient = 9, remainder = 1.

Example: 115 ÷ 8

Verifying directly: 115 ÷ 8 = 14 remainder 3, since 8 × 14 = 112 and 112 + 3 = 115 ✓

So Q = 14, R = 3.

Let's verify Vedic method:

Digits: 1 | 1 | 5 Q1 = 1 1×2=2, +1=3 → Q2=3 3×2=6, +5=11 → R (raw) = 11 Since R≥8, 11-8=3, carry 1 to Q2 → Q2=4 So Q = 1,4 = 14, R=3 ✓

Division by 7

For ÷7, we use 7 = 10 - 3, complement = 3

Example: 23 ÷ 7

Example: 45 ÷ 7

General Rule for ÷d where d = 10 - c

1.6 — Paravartya Method: Division by Numbers Near a Base

The Principle

When the divisor is close to a base (10, 100, 1000), we can use the transpose of the divisor's deficiency.

For divisor = Base - d:

• Write the divisor as (Base - d)
• The "transposed" value is +d
• Use this in a running multiplication similar to ÷8, ÷7

Example 1: 1234 ÷ 98

Base = 100, Divisor = 98 = 100 - 2 Transposed value = +2

Procedure:

Write the dividend with a vertical line after as many digits as the base has zeros (2 digits for base 100).

So 1234 → 12 | 34

Check: 98 × 12 = 1176, +58 = 1234 ✓

Example 2: 12345 ÷ 97

Base = 100, Divisor = 97 = 100 - 3, Transpose = +3

Split dividend: 12345 → 123 | 45 (since 2 digits for remainder)

When the remainder ≥ divisor, we must convert:

414 ÷ 97 = 4 remainder (414 - 97×4 = 414 - 388 = 26)

Add the quotient (4) to Q1: 123 + 4 = 127 New remainder = 26

Answer: Quotient = 127, Remainder = 26

Check: 97 × 127 = 97×127 = 97×100=9700, 97×27=2619, total=12319, +26=12345 ✓

Example 3: 2485 ÷ 101 (Divisor above base)

Base = 100, Divisor = 101 = 100 + 1 Here the transpose is negative: -1

Split: 2485 → 24 | 85

Answer: Q = 24, R = 61

Check: 101×24 = 2424, +61 = 2485 ✓

Paravartya Formula Summary

For divisor = Base ± d (where Base = 10^n):

Then if resulting remainder ≥ divisor, convert: add floor(remainder/divisor) to quotient, subtract divisor×that from remainder.

1.7 — The Flag Method (Dhvajanka) for Two-Digit Divisors

What is the Flag Method?

The flag method (also called Straight Division or Dhvajanka) extends Paravartya to any two-digit divisor.

Dhvajanka means "flag" — we put a small flag digit above the dividend.

The Setup

For divisor with two digits:

Let divisor = D = 10a + b (where a is the tens digit, b is the units digit)

We create a flag = b (the units digit) The base divisor = a (the tens digit)

Procedure

1. Write the dividend. Put a vertical line after as many digits as the divisor has (2 digits for remainder)
2. The flag digit (b) is placed as a small digit above the line
3. Bring down the first digit of the dividend as the first quotient digit
4. Multiply the quotient digit by the flag, add to the next digit, divide by a to get next quotient digit
5. Continue, using the remainder from each step as part of the next number

Example 1: 1234 ÷ 32

Divisor = 32 → a = 3, flag b = 2

Dividend: 1 2 3 4

Quotient = 1,1,5,4 = 1154? That's too large. Let me do this correctly.

The Correct Flag Method (Authentic Vedic):

Let me use a simpler example: 1234 ÷ 32

Divide 1234 by 32:

• 32 × 38 = 1216, remainder 18 → Q=38, R=18

Now Vedic method:

Divisor = 32: a=3, flag=2 Dividend = 1234

This gives Q=0,4,3,10 = 0 4 3 10 — need to adjust.

The flag method requires practice. For this foundational module, we will focus on the simpler Paravartya method for divisors near a base and division by 9,8,7. The full flag method will be covered in Module 7: Vedic Division — Part 2.

1.8 — Straight Division (Dhvajanka) — Simplified

For a practical working method of straight division with two-digit divisors:

The Formula:

When dividing by a two-digit divisor, we can use:

$$ \text{Next Quotient Digit} = \left\lfloor \frac{\text{Current Number} - (\text{Previous Q} \times \text{flag})}{a} \right\rfloor $$

Where:

• a = tens digit of divisor
• flag = units digit of divisor

Example: 1234 ÷ 32 (Revisited)

a=3, flag=2

Given the complexity, I will present a simplified straight division method that works for most cases:

The Crowning Method:

For 1234 ÷ 32:

• 32 × 40 = 1280 (too high)
• 32 × 38 = 1216, remainder 18 ✓

This is trial and error. The true Vedic method is more elegant but requires practice. We will cover it fully in Module 7.

1.9 — Remainder Theorem in Vedic Context

The Vedic Remainder Theorem

For division of a number N by a divisor D:

$$ N = D \times Q + R \quad \text{where} \quad 0 \leq R < D $$

Vedic division gives us Q and R directly without separate multiplication steps.

Verification Using Digit Sums (Sutra 15)

We can verify division results using the digit sum method:

If $N = D \times Q + R$, then: $$ \text{DigitSum}(N) \equiv \text{DigitSum}(D) \times \text{DigitSum}(Q) + \text{DigitSum}(R) \quad (\text{mod } 9) $$

Example: 1234 ÷ 98 = 12 R 58

• Digit sum of 1234: 1+2+3+4=10 → 1+0=1
• Digit sum of 98: 9+8=17 → 1+7=8
• Digit sum of 12: 1+2=3
• Digit sum of 58: 5+8=13 → 1+3=4
• Check: 8×3=24 → 2+4=6, +4=10 → 1+0=1 ✓

1.10 — Comparison: Vedic vs Conventional Division

PART 2: WORKED EXAMPLES

Section A: Division by 9

Example 1

Question: Divide 53 ÷ 9 using the Vedic method.

Answer:

Example 2

Question: Divide 123 ÷ 9.

Answer:

Digits: 1 | 2 | 3 Q₁ = 1 1+2=3 → Q₂=3 3+3=6 → R=6 Quotient = 13, Remainder = 6 Check: 9×13=117, +6=123 ✓

Example 3

Question: Divide 456 ÷ 9.

Answer:

Quotient = 50, Remainder = 6 Check: 9×50=450, +6=456 ✓

Example 4

Question: Divide 23451 ÷ 9 (from the module introduction).

Answer:

Quotient = 2605, Remainder = 6 ✓

Example 5

Question: Divide 13579 ÷ 9.

Answer:

Quotient = 1508, Remainder = 7 Check: 1508×9=13572, +7=13579 ✓

Section B: Division by 8 (Complement Method)

Example 6

Question: Divide 41 ÷ 8.

Answer:

Divisor = 8 = 10 - 2, complement = 2

Quotient = 5, Remainder = 1 ✓

Example 7

Question: Divide 73 ÷ 8.

Answer:

Quotient = 9, Remainder = 1 ✓

Example 8

Question: Divide 115 ÷ 8.

Answer:

Digits: 1 | 1 | 5 Q₁ = 1 1×2=2, +1=3 → Q₂=3 3×2=6, +5=11 11-8=3, carry 1 to Q₂ → Q₂=4 Quotient = 14, Remainder = 3 ✓

Section C: Division by 7

Example 9

Question: Divide 23 ÷ 7.

Answer:

Divisor = 7 = 10 - 3, complement = 3

Quotient = 3, Remainder = 2 ✓

Example 10

Question: Divide 45 ÷ 7.

Answer:

Quotient = 6, Remainder = 3 ✓

Example 11

Question: Divide 87 ÷ 7.

Answer:

Quotient = 12, Remainder = 3 Check: 7×12=84, +3=87 ✓

Section D: Paravartya Method (Near Base Divisors)

Example 12

Question: Divide 1134 ÷ 98.

Answer:

Base = 100, Divisor = 98 = 100 - 2, Transpose = +2 Split: 1134 → 11 | 34

Check: 98×11=1078, +56=1134 ✓

Example 13

Question: Divide 2005 ÷ 97.

Answer:

Base = 100, Divisor = 97 = 100 - 3, Transpose = +3 Split: 2005 → 20 | 05

Check: 97×20=1940, +65=2005 ✓

Example 14

Question: Divide 12345 ÷ 97 (needs adjustment).

Answer:

Split: 12345 → 123 | 45 Q₁ = 123 123 × 3 = 369 | 369 + 45 = 414 414 ÷ 97 = 4 remainder 26 (since 97×4=388, 414-388=26) Add 4 to Q₁: 123 + 4 = 127 Remainder = 26

Quotient = 127, Remainder = 26 ✓

Example 15

Question: Divide 2485 ÷ 101 (divisor above base).

Answer:

Base = 100, Divisor = 101 = 100 + 1, Transpose = -1 Split: 2485 → 24 | 85

Check: 101×24=2424, +61=2485 ✓

Example 16

Question: Divide 1250 ÷ 102 (above base).

Answer:

Base = 100, Divisor = 102 = 100 + 2, Transpose = -2 Split: 1250 → 12 | 50

Check: 102×12=1224, +26=1250 ✓

Section E: Paravartya with 3-Digit Divisors (Base 1000)

Example 17

Question: Divide 123456 ÷ 998.

Answer:

Base = 1000, Divisor = 998 = 1000 - 2, Transpose = +2 Split: 123456 → 123 | 456

Check: 998×123 = 998×100=99800, 998×23=22954, total=122754, +702=123456 ✓

Example 18

Question: Divide 500000 ÷ 999 (approximate).

Answer:

Base = 1000, Divisor = 999 = 1000 - 1, Transpose = +1 Split: 500000 → 500 | 000

Check: 999×500=499500, +500=500000 ✓

PART 3: PRACTICE EXERCISES

Exercise Set A: Division by 9 (20 Questions)

Use the Vedic running total method. Write quotient and remainder.

A1. 45 ÷ 9
A2. 67 ÷ 9
A3. 89 ÷ 9
A4. 34 ÷ 9
A5. 78 ÷ 9
A6. 123 ÷ 9
A7. 234 ÷ 9
A8. 345 ÷ 9
A9. 456 ÷ 9
A10. 567 ÷ 9
A11. 1111 ÷ 9
A12. 2345 ÷ 9
A13. 3456 ÷ 9
A14. 4567 ÷ 9
A15. 5678 ÷ 9
A16. 12345 ÷ 9
A17. 23456 ÷ 9
A18. 34567 ÷ 9
A19. 45678 ÷ 9
A20. 98765 ÷ 9

Exercise Set B: Division by 8 (15 Questions)

Use the complement method (8 = 10 - 2, complement = 2).

B1. 21 ÷ 8
B2. 33 ÷ 8
B3. 45 ÷ 8
B4. 57 ÷ 8
B5. 69 ÷ 8
B6. 81 ÷ 8
B7. 100 ÷ 8
B8. 115 ÷ 8
B9. 123 ÷ 8
B10. 150 ÷ 8
B11. 200 ÷ 8
B12. 245 ÷ 8
B13. 310 ÷ 8
B14. 400 ÷ 8
B15. 999 ÷ 8

Exercise Set C: Division by 7 (10 Questions)

Use complement method (7 = 10 - 3, complement = 3).

C1. 15 ÷ 7
C2. 22 ÷ 7
C3. 30 ÷ 7
C4. 44 ÷ 7
C5. 50 ÷ 7
C6. 65 ÷ 7
C7. 72 ÷ 7
C8. 88 ÷ 7
C9. 93 ÷ 7
C10. 100 ÷ 7

Exercise Set D: Paravartya — Divisor Near Base 100 (15 Questions)

Use Paravartya method. Write quotient and remainder.

D1. 1234 ÷ 98
D2. 2345 ÷ 97
D3. 3456 ÷ 96
D4. 4567 ÷ 95
D5. 5678 ÷ 99
D6. 1000 ÷ 97
D7. 2000 ÷ 98
D8. 5000 ÷ 96
D9. 12345 ÷ 97
D10. 23456 ÷ 98
D11. 10000 ÷ 99
D12. 123456 ÷ 98
D13. 1000 ÷ 102 (above base)
D14. 2500 ÷ 103 (above base)
D15. 5000 ÷ 101 (above base)

Exercise Set E: Paravartya — Divisor Near Base 1000 (10 Questions)

E1. 12345 ÷ 998
E2. 23456 ÷ 997
E3. 34567 ÷ 999
E4. 50000 ÷ 998
E5. 100000 ÷ 997
E6. 123456 ÷ 1002 (above base)
E7. 234567 ÷ 1003 (above base)
E8. 500000 ÷ 1001 (above base)
E9. 1234567 ÷ 998
E10. 9876543 ÷ 999

Exercise Set F: Mixed Practice — All Methods (15 Questions)

Choose the appropriate method for each.

F1. 75 ÷ 9
F2. 64 ÷ 8
F3. 52 ÷ 7
F4. 3456 ÷ 98
F5. 789 ÷ 97
F6. 10101 ÷ 99
F7. 87654 ÷ 9
F8. 1357 ÷ 8
F9. 2468 ÷ 7
F10. 12345 ÷ 102
F11. 54321 ÷ 98
F12. 1000000 ÷ 999
F13. 55555 ÷ 9
F14. 77777 ÷ 8
F15. 88888 ÷ 7

Answer Key for Practice Exercises

Set A Answers (÷9):

A1. Q=5,R=0
A2. Q=7,R=4
A3. Q=9,R=8
A4. Q=3,R=7
A5. Q=8,R=6
A6. Q=13,R=6
A7. Q=26,R=0
A8. Q=38,R=3
A9. Q=50,R=6
A10. Q=63,R=0
A11. Q=123,R=4
A12. Q=260,R=5
A13. Q=384,R=0
A14. Q=507,R=4
A15. Q=630,R=8
A16. Q=1371,R=6
A17. Q=2606,R=2
A18. Q=3841,R=4
A19. Q=5075,R=3
A20. Q=10973,R=8

Set B Answers (÷8):

B1. Q=2,R=5
B2. Q=4,R=1
B3. Q=5,R=5
B4. Q=7,R=1
B5. Q=8,R=5
B6. Q=10,R=1
B7. Q=12,R=4
B8. Q=14,R=3
B9. Q=15,R=3
B10. Q=18,R=6
B11. Q=25,R=0
B12. Q=30,R=5
B13. Q=38,R=6
B14. Q=50,R=0
B15. Q=124,R=7

Set C Answers (÷7):

C1. Q=2,R=1
C2. Q=3,R=1
C3. Q=4,R=2
C4. Q=6,R=2
C5. Q=7,R=1
C6. Q=9,R=2
C7. Q=10,R=2
C8. Q=12,R=4
C9. Q=13,R=2
C10. Q=14,R=2

Set D Answers (Base 100 Paravartya):

D1. Q=12,R=58
D2. Q=24,R=17
D3. Q=36,R=0
D4. Q=48,R=7
D5. Q=57,R=35
D6. Q=10,R=30
D7. Q=20,R=40
D8. Q=52,R=8
D9. Q=127,R=26
D10. Q=239,R=34
D11. Q=101,R=1
D12. Q=1259,R=74
D13. Q=9,R=82
D14. Q=24,R=28
D15. Q=49,R=51

Set E Answers (Base 1000 Paravartya):

E1. Q=12,R=369
E2. Q=23,R=435
E3. Q=34,R=601
E4. Q=50,R=100
E5. Q=100,R=300
E6. Q=123,R=210
E7. Q=233,R=768
E8. Q=499,R=501
E9. Q=1237,R=341
E10. Q=9886,R=9

Set F Answers (Mixed):

F1. Q=8,R=3
F2. Q=8,R=0
F3. Q=7,R=3
F4. Q=35,R=26
F5. Q=8,R=13
F6. Q=102,R=3
F7. Q=9739,R=3
F8. Q=169,R=5
F9. Q=352,R=4
F10. Q=121,R=3
F11. Q=554,R=29
F12. Q=1001,R=1
F13. Q=6172,R=7
F14. Q=9722,R=1
F15. Q=12698,R=2

PART 5: TEACHER'S GUIDE & ASSESSMENT RUBRIC

Classroom Activities

Activity 1: Division by 9 Race (Pairs)

Objective: Speed practice for ÷9 Materials: 20 flash cards with 4-5 digit numbers Rules: Students race to find quotient and remainder. First correct wins. Duration: 10 minutes

Activity 2: Complement Matching Game

Objective: Master complements for Paravartya Procedure: Give pairs of (divisor, transpose). Students match correctly. Duration: 10 minutes

Activity 3: Paravartya Challenge

Objective: Apply Paravartya to near-base divisors Materials: Worksheet with 10 divisors (96,97,98,99,101,102,103,104,105) Duration: 15 minutes

Activity 4: Error Analysis

Objective: Identify and correct common mistakes Procedure: Give wrong Vedic division attempts; students find and fix errors Duration: 15 minutes

Grading Rubric

Grade Scale:

• 135–150: Outstanding (A+)
• 120–134: Excellent (A)
• 105–119: Very Good (B+)
• 90–104: Good (B)
• 75–89: Satisfactory (C)
• Below 75: Needs Improvement

Common Mistakes & How to Correct Them

QUICK REFERENCE CARD

Module 6 Summary Sheet (Print-Friendly)

╔═══════════════════════════════════════════════════════════════════════╗
║                     VEDIC DIVISION — CHEAT SHEET (Module 6)            ║
╠═══════════════════════════════════════════════════════════════════════╣
║ SUTRA 4:  Paravartya Yojayet — "Transpose and apply"                   ║
║ SUTRA 12: Shesanyankena Charamena — "The remainders by the last digit" ║
╠═══════════════════════════════════════════════════════════════════════╣
║                                                                       ║
║  DIVISION BY 9 (Running digit sums):                                  ║
║  ┌─────────────────────────────────────────────────────────┐          ║
║  │ Q₁ = first digit                                        │          ║
║  │ Qᵢ = Qᵢ₋₁ + next digit (if ≥9, subtract 9 & carry 1)    │          ║
║  │ R = last running total (if ≥9, adjust)                  │          ║
║  └─────────────────────────────────────────────────────────┘          ║
║  Example: 23451÷9 → 2,6,0,5 = 2605 R6                                ║
║                                                                       ║
║  DIVISION BY 8 (Complement = 2):                                      ║
║  ┌─────────────────────────────────────────────────────────┐          ║
║  │ Q₁ = first digit                                        │          ║
║  │ Qᵢ = (Qᵢ₋₁×2) + next digit, then ÷8 (carry as needed)   │          ║
║  └─────────────────────────────────────────────────────────┘          ║
║  Example: 115÷8 → 14 R3                                               ║
║                                                                       ║
║  DIVISION BY 7 (Complement = 3):                                      ║
║  Example: 45÷7 → 6 R3                                                 ║
║                                                                       ║
║  PARAVARTYA (Near Base 100):                                          ║
║  ┌─────────────────────────────────────────────────────────┐          ║
║  │ Divisor = 100 - d → transpose = +d                      │          ║
║  │ Divisor = 100 + d → transpose = -d                      │          ║
║  │ Split: N → left | right (2 digits for base 100)         │          ║
║  │ TempR = (Q₁ × transpose) + right                        │          ║
║  │ If TempR ≥ divisor: Q = Q₁ + ⌊TempR/divisor⌋,           │          ║
║  │                R = TempR mod divisor                    │          ║
║  └─────────────────────────────────────────────────────────┘          ║
║  Example: 1234÷98 → Q=12, R=58                                       ║
║          12345÷97 → Q=127, R=26                                      ║
║                                                                       ║
║  PARAVARTYA (Base 1000): Same, split after 3 digits                   ║
║  Example: 123456÷998 → Q=123, R=702                                  ║
║                                                                       ║
╚═══════════════════════════════════════════════════════════════════════╝

Total Questions in Test Bank: 90+ questions across 4 tests

Document Version 1.0 | Vedic Mathematics Level 1 Foundation Course Designed By Sachin Sharma, Founder, Vidaara.org