Vedic Mathematics is a system of mathematics that was rediscovered from ancient Indian texts by Bharati Krishna Tirthaji in the early 20th century. It comprises 16 sutras (word formulas) and 13 sub-sutras that provide shortcut methods for a wide range of calculations. These are not tricks — they are mathematically rigorous methods that simply find smarter paths to the same answer.
Why Vedic Maths Matters for Indian Students Today
In competitive examinations like JEE, NEET, and CAT, time is the primary constraint. A student who can multiply 97 × 98 in 3 seconds instead of 30 seconds has a significant advantage. Vedic maths shortcuts are particularly useful in:
- Quantitative aptitude sections of competitive exams
- Board exam calculations where a calculator is not allowed
- Mental arithmetic for checking your work quickly
- Impressing your maths teacher (genuinely — these methods are beautiful)
Sutra 1: Nikhilam Navatashcharamam Dashatah (For Multiplication Near 10s)
"All from 9 and the last from 10"
This sutra works when both numbers are near a power of 10 (10, 100, 1000).
Example: 97 × 98
Base = 100. Complements: 97→3, 98→2. Left part: 97−2 = 95 (or 98−3 = 95). Right part: 3×2 = 06. Answer: 9506.
Example: 8 × 7
Base = 10. Complements: 8→2, 7→3. Left: 8−3=5. Right: 2×3=6. Answer: 56.
Sutra 2: Ekadhikena Purvena (For Squaring Numbers Ending in 5)
"By one more than the previous"
Example: 75² = ?
Step 1: Right part is always 25. Step 2: Left part = 7 × (7+1) = 7 × 8 = 56. Answer: 5625.
Example: 125² = ?
Right part = 625 (for 3-digit ending in 5: right part = 025+600 — use standard: 125²=15625). Left part = 12×13 = 156. Answer: 15625.
Sutra 3: Anurupyena (Proportionality)
"Proportionality" — used for division by near-10 numbers and fraction simplification.
Example: 1/19 = ?
Using Ekadhikena: 1 divided by 19. Previous digit 1+1=2. Write: 1, then multiply each digit by 2 to get the next digit (mod 10, carry the rest). This gives the repeating decimal 0.052631578947368421... in a systematic way.
Sutra 4: Urdhva-Tiryagbhyam (Vertical and Crosswise Multiplication)
"Vertically and Crosswise" — a general multiplication method that works for any size numbers.
Example: 23 × 14
Step 1 (rightmost): 3×4 = 12. Write 2, carry 1. Step 2 (cross): 2×4 + 3×1 + carry 1 = 8+3+1 = 12. Write 2, carry 1. Step 3 (leftmost): 2×1 + carry 1 = 3. Answer: 322.
Sutra 5: Shunyam Saamyasamuccaye (If the Samuccaya is Zero, the Samuccaya is Zero)
Applied to solving certain types of equations quickly. If the sum of the numerators equals the sum of the denominators on both sides, the answer is 0.
Example: 1/(x−3) + 1/(x−4) = 1/(x−5) + 1/(x−2)
Sum of LHS denominators: (x−3)+(x−4) = 2x−7. Sum of RHS denominators: (x−5)+(x−2) = 2x−7. Equal! Therefore x = (7/2) i.e. x = 3.5. One-second solution.
Sutra 6: Yavadunam (For Squaring Numbers Near Multiples of 10)
Example: 98² = ?
Deviation from 100 = −2. Square: 98²: left part = 98−2 = 96. Right part = (−2)² = 04. Answer: 9604.
Sutra 7: Paravartya Yojayet (Division by Non-Base Numbers)
"Transpose and Apply" — for dividing by numbers like 11, 12, 9, 8 without long division.
Example: 1234 ÷ 11
Write dividend: 1, 2, 3, 4. Divisor is 11; flag digit = 1. Working: 1 | 1+2=3 | 3+3=6 | 6+4=10 → quotient 112 remainder 2. So 1234 ÷ 11 = 112 R2. Verification: 112×11+2 = 1232+2 = 1234 ✓.
How to Learn Vedic Maths Effectively
Do not try to learn all sutras at once. Start with Nikhilam (multiplying near 100 — huge exam impact) and Ekadhikena (squaring numbers ending in 5 — instant 2-second calculation). Practise each sutra with at least 20 examples before moving to the next. Once learned, these methods become automatic.
Every formula in MathVis includes a Vedic maths method in the "Tricks and Alternative Methods" section where applicable, alongside mental maths and exam shortcuts. Use it as your Vedic maths reference guide.