🧮 VEDIC MATHS SUTRAS & SUB-SUTRAS

The Secret Language of Fast Calculations ✨

🌿 What are Sutras in Vedic Maths?

📜 Sutra means a short formula or rule
Think of Sutras as mental tools that tell your brain:

💡 “Don’t calculate the long way — think smart.”

✔ There are 16 Main Sutras
✔ Supported by 13 Sub-Sutras
✔ They apply to addition, subtraction, multiplication, division, algebra & more

🎨 How to Understand Sutras (Very Important!)

❌ Sutras are NOT to be memorized blindly
✅ They are thinking patterns

👉 One Sutra can solve hundreds of problems

🟣 THE 16 MAIN SUTRAS (With Meaning & Use)

🟢 1. Ekadhikena Purvena

Meaning: By one more than the previous one

🧠 Used for:

• Division by 9, 11

• Squaring numbers ending in 5

✨ Example use:

• 25², 35²

• 154 ÷ 11

🟡 2. Nikhilam Navataścaramam Daśataḥ

Meaning: All from 9 and the last from 10

🧠 Used for:

• Fast subtraction

• Multiplication near 10, 100, 1000

✨ Example use:

• 100 − 47

• 98 × 97

🔵 3. Urdhva–Tiryagbhyām

Meaning: Vertically and crosswise

🧠 Used for:

• General multiplication

• Any size numbers

✨ Example use:

• 23 × 14

• Algebraic multiplication

🟣 4. Parāvartya Yojayet

Meaning: Transpose and apply

🧠 Used for:

• Division

• Solving equations

✨ Example use:

• 143 ÷ 11

• Linear equations

🟢 5. Śūnyam Sāmyasamuccaye

Meaning: When the sum is zero

🧠 Used for:

• Solving equations quickly

✨ Example:

• If both sides equal → result is zero

🟡 6. (Ānurūpye) Śūnyamanyat

Meaning: If one is zero, the other is zero

🧠 Used for:

• Algebraic simplifications

🔵 7. Saṅkalana–Vyavakalanābhyām

Meaning: By addition and subtraction

🧠 Used for:

• Simultaneous equations

🟣 8. Pūraṇāpūraṇābhyām

Meaning: By completion or non-completion

🧠 Used for:

• Fractions

• Algebra

🟢 9. Calana–Kalanābhyām

Meaning: Differences and similarities

🧠 Used for:

• Calculus-like logic

• Pattern recognition

🟡 10. Yāvadūnam

Meaning: Whatever the deficiency

🧠 Used for:

• Squaring numbers near base

✨ Example:

• 98²

• 102²

🔵 11. Vyāṣṭi–Samaṣṭiḥ

Meaning: Part and whole

🧠 Used for:

• Algebra

• Factoring

🟣 12. Śeṣānyankena Caramena

Meaning: Remainders by the last digit

🧠 Used for:

• Checking answers

• Remainders

🟢 13. Sopāntyadvayamantyam

Meaning: Ultimate and twice the penultimate

🧠 Used for:

• Special algebraic identities

🟡 14. Ekānyūnena Pūrvena

Meaning: One less than the previous

🧠 Used for:

• Multiplication by numbers like 99, 999

🔵 15. Guṇitasamuccayaḥ

Meaning: Product of sums

🧠 Used for:

• Factorization

• Verification

🟣 16. Guṇakasamuccayaḥ

Meaning: Factors of the sum

🧠 Used for:

• Algebraic validation

🌈 THE 13 SUB-SUTRAS (Supporting Powers)

Think of Sub-Sutras as helpers 🧩

✨ Key Sub-Sutras Explained Simply:

1️⃣ Ādyamādyena – First by first
2️⃣ Antyamantyena – Last by last
3️⃣ Kevalaih Saptakam Guṇyat – Multiply by 7
4️⃣ Vestanam – Oscillation (zig-zag thinking)
5️⃣ Yāvadūnam Tāvadūnikṛtya – Deficiency logic
6️⃣ Antyayoreva – Only the last digits
7️⃣ Samuccaya-Guṇitaḥ – Product of totals
8️⃣ Lopaṇasthāpanābhyām – Elimination & retention
9️⃣ Vilokanam – Observation
🔟 Gunitasamucchayah – Checking answers
1️⃣1️⃣ Samuccaya – Collective sum
1️⃣2️⃣ Gunaka – Factor method
1️⃣3️⃣ Vyastisamasti – Part-whole relation

🧠 These are mostly used in advanced algebra & verification

🎯 How Sutras & Sub-Sutras Work Together

🟣 Sutra → Main rule
🟢 Sub-Sutra → How to apply or verify

👉 Together they create:
✨ Speed
✨ Accuracy
✨ Confidence

🌟 Final Understanding (Very Important)

💡 Vedic Maths is not about shortcuts
💡 It is about structured intelligent thinking

Once you understand Sutras:

• Calculator fear disappears

• Maths becomes playful

• Brain becomes sharper