Vedic Maths Tricks

Quick Multiplication Tricks

Multiply any number by 11: Write the number, insert the digit sum between the digits. For 36 × 11: outer digits are 3 and 6, middle = 3+6=9 → answer: 396. If the sum exceeds 9, carry over: 89 × 11: 8+9=17, write 7 carry 1 → 9+1=9, so answer: 979.

Multiply numbers near 100 (Nikhilam method): Find the deviation from 100 for each number. For 97 × 94: deviations are -3 and -6. Left part: 97-6=91. Right part: (-3)×(-6)=18. Answer: 9118. For 98 × 103: deviations are -2 and +3. Left: 98+3=101. Right: (-2)×(3)=-06. Answer: 10094.

Multiply numbers near 10 (base method): For 9 × 8: deviations from 10 are -1 and -2. Left: 9-2=7. Right: (-1)×(-2)=2. Answer: 72. For 12 × 13: deviations +2 and +3. Left: 12+3=15. Right: 2×3=6. Answer: 156.

Vertical and crosswise (any 2-digit × 2-digit): For 23 × 47: Step 1 (units): 3×7=21, write 1 carry 2. Step 2 (crosswise): 2×7+3×4=14+12=26, plus carry 2=28, write 8 carry 2. Step 3 (hundreds): 2×4=8, plus carry 2=10. Answer: 1081.

Multiply by 9, 99, 999: Multiply by (10-1), (100-1), (1000-1). For 47×99: 47×100-47=4700-47=4653. For 236×9: 236×10-236=2360-236=2124.

Squaring Shortcuts

Square any number ending in 5 (Ekadhikena Purvena): Multiply the digits before 5 by one more than itself, then append 25. Examples: 25²: 2×3=6 → 625. 45²: 4×5=20 → 2025. 85²: 8×9=72 → 7225. 125²: 12×13=156 → 15625. 205²: 20×21=420 → 42025.

Square numbers near 50: Use (50+d)² = 2500 + 100d + d². For 53²: d=3, 2500+300+9=2809. For 48²: d=-2, 2500-200+4=2304. For 56²: d=6, 2500+600+36=3136.

Square numbers near 100: For n near 100, n² = (n-100)² + 200(n-100) + 10000 — simplified: left part = n+(n-100), right part = (n-100)². For 97²: n-100=-3. Left: 97-3=94. Right: 9. Answer: 9409. For 108²: n-100=8. Left: 108+8=116. Right: 64. Answer: 11664.

Square any 2-digit number (Duplex method): For 76²: think of it as (76). Duplex of single digit d = d². Duplex of two digits ab = 2ab. 76²: D(6)=36, write 6 carry 3. D(7,6)=2×42=84, +3=87, write 7 carry 8. D(7)=49, +8=57. Answer: 5776.

Fast Division Tricks

Divide by 9 (special case): Convert the number digit by digit. For 2314 ÷ 9: carry first digit (2). Add to next: 2+3=5. Add to next: 5+1=6. Sum of all digits is the remainder: 2+3+1+4=10, 10÷9=1 remainder 1. So 2314÷9=257 remainder 1.

Divisibility checks (instant): - Divisible by 2: last digit even - Divisible by 3: digit sum divisible by 3 (234: 2+3+4=9 ✓) - Divisible by 4: last two digits divisible by 4 - Divisible by 6: divisible by both 2 and 3 - Divisible by 9: digit sum divisible by 9 - Divisible by 11: alternating digit sum = 0 or multiple of 11 (253: 2-5+3=0 ✓)

Divide by 5: Multiply by 2, divide by 10. For 348÷5: 348×2=696, ÷10=69.6.

Divide by 25: Multiply by 4, divide by 100. For 648÷25: 648×4=2592, ÷100=25.92.

Addition and Subtraction Tricks

All from 9, last from 10 (complement subtraction): To subtract any number from a power of 10, subtract each digit from 9 (all from 9) and the last digit from 10. For 10000-3647: 9-3=6, 9-6=3, 9-4=5, 10-7=3. Answer: 6353. This is instant once memorised.

Left-to-right addition (faster than right-to-left for mental maths): For 456+378: add hundreds first: 400+300=700. Add tens: 50+70=120, total so far 820. Add units: 6+8=14, total 834. Left-to-right builds a running total that is easier to hold in memory.

Anchor subtraction: For 843-297: subtract 300 and add 3. 843-300=543, +3=546. Faster than column subtraction.

Doubling and halving for multiplication: 48×25 = 24×50 = 12×100 = 1200 (keep halving one and doubling the other until you reach a simple calculation).

Digit Sum Verification (Casting Out Nines)

This is one of the most practically useful Vedic Maths tools — it lets you instantly verify any multiplication or addition without re-doing the calculation.

How it works: The digit sum of a product equals the product of the digit sums. The digit sum of a sum equals the sum of the digit sums. If the check fails, there is an error.

Example — multiplication check: 234 × 567 = 132678. Digit sum of 234 = 2+3+4=9 → 9. Digit sum of 567 = 5+6+7=18 → 1+8=9. Product of digit sums = 9×9=81 → 8+1=9. Digit sum of 132678 = 1+3+2+6+7+8=27 → 2+7=9. Check passes ✓.

Example — detecting an error: If your answer had been 132688 instead, digit sum = 1+3+2+6+8+8=28 → 2+8=10 → 1+0=1. That does not equal 9, so there is an error. This takes 15 seconds and catches most arithmetic mistakes immediately.

Note: The digit sum check catches most errors but not all — for example, transposing two equal digits (swapping 234 to 243) keeps the digit sum the same. Use it as a quick sanity check, not a guarantee.

Applying Vedic Maths Tricks in Exams

JEE / NEET: Vedic multiplication and squaring tricks help most in Physics and Chemistry numericals where you multiply 2-digit and 3-digit numbers under time pressure. The digit sum check is useful when you are unsure whether you made an arithmetic slip.

Class 9–12 board exams: Squaring shortcuts help in Trigonometry (squaring sin/cos values), Coordinate Geometry (distance formula), and Algebra. The multiplication shortcuts reduce working time in Calculus problems.

Banking and SSC exams: Simplification, speed maths and approximation are explicitly tested. Vedic tricks for multiplication by 9/11/99, squaring, and dividing by 5/25 are directly applicable.

Mental maths competitions: Vedic Maths is the dominant technique in mental maths competitions. Full mastery of all 16 sutras is required for competition-level performance.

Practice method: Solve 20 problems daily using only Vedic methods, without reverting to column calculation. Time yourself. The speed gain compounds — after 4 weeks of daily 15-minute practice, most students reduce calculation time by 40–60%.