16 Sutras of Vedic Maths 

🔢 Here are the 16 Sutras of Vedic Maths with Meaning and Examples:

1. Ekādhikena Pūrvena – By one more than the previous one

This is a favorite when it comes to squaring numbers ending in 5.
👉 Example: 25²
Take 2 (the digit before 5), multiply it with its next: 2×3 = 6
Now attach 25 → 625

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2. Nikhilam Navataścaramam Daśatah – All from 9 and the last from 10

This Sutra helps with subtraction and base multiplication.
👉 Example: 1000 – 879 =
Apply complements: 9–8 = 1, 9–7 = 2, 10–9 = 1 → 121

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3. Ūrdhva-Tiryagbhyām – Vertically and crosswise

A versatile technique for general multiplication.
👉 Example: 12 × 13
1×1 = 1
(1×3 + 2×1) = 5
2×3 = 6
So, the answer is 156

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4. Parāvartya Yojayet – Transpose and adjust

This is useful for division and recurring decimals.
👉 Example: 103 ÷ 9
We use the reciprocal method and adjust – result is 11 R4

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5. Shunyam Sāmyasamuccaye – When the sum is the same, it is zero

If two terms have the same value, their difference is zero.
👉 Example: In algebra, it simplifies complex expressions quickly.

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6. Ānurūpyena – Proportionately

Very helpful in multiplication near base values.
👉 Example: 98 × 97
Base = 100
98 → -2, 97 → -3
98 – 3 = 95, (-2×-3) = 06 → Answer = 9506

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7. Sūnyamanyat – If one is zero, the other is zero

This is a logical condition.
👉 Example: If x × y = 0, then either x = 0 or y = 0

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8. Sankalana-Vyavakalanābhyām – By addition and subtraction

👉 Example:
x + y = 10
x – y = 4
Add and divide:
→ x = 7, y = 3

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9. Pūranāpūranābhyām – By completion or non-completion

Complements help you subtract easily.
👉 Example: 1000 – 456
Apply complements: 543 + 1 = 544

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10. Chalana-Kalanābhyām – By differentiation

Used in algebraic simplifications and calculus-like thinking.

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11. Yāvadūnam – Whatever the deficiency

A brilliant shortcut for squaring numbers near a base.
👉 Example: 98²
Deficiency = 2
→ 98 – 2 = 96 | 2² = 04 → 9604

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12. Vyashti-Samashti – Part and whole

Useful for breaking complex problems into parts.

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13. Shesanyankena Charamena – The remainders by the last digit

Helpful in divisibility tests.
👉 Example: Used for checking divisibility by 7, 9, etc.

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14. Sopāntya-Dvayamantyam – Ultimate and twice the penultimate

A useful rule for digit-based divisibility.

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15. Ekanyūnena Pūrvena – By one less than the previous one

Perfect for multiplying numbers like 49 × 51.
👉 Example:
Use base 50:
49 = 50 – 1, 51 = 50 + 1
Answer = 50² – 1² = 2500 – 1 = 2499

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16. Gunitasamuccayah Samuccayagunitah – Product of the sum is equal to the sum of the product

👉 Example:
a×b + a×c = a×(b + c)

🎯 Where Do I Use These Sutras?

🧡 Final Thoughts

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