Vedic Maths Multiplication Tricks — Step-by-Step with Examples
Four Vedic Maths methods that cover multiplication for any pair of numbers — from quick shortcuts for specific cases to the general technique for any digits.
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Method 1 — Nikhilam (Base Method) for Numbers Near 100
The Nikhilam Sutra ('All from 9, last from 10') provides the fastest multiplication method when both numbers are near 100. Step 1: Find each number's complement from 100. Step 2: Cross-subtract to get the left part of the answer. Step 3: Multiply the complements for the right part (use 2 digits, pad with zero if needed).
Example 1: 96 × 97. Complements: 4 and 3. Right: 4×3=12. Left: 96−3=93 (or 97−4=93). Answer: 9312. Example 2: 98 × 94. Complements: 2 and 6. Right: 2×6=12. Left: 98−6=92. Answer: 9212. Example 3: 99 × 91. Complements: 1 and 9. Right: 1×9=09. Left: 99−9=90. Answer: 9009. Example 4: 93 × 88. Complements: 7 and 12. Right: 7×12=84. Left: 93−12=81. Answer: 8184. For numbers above 100 (e.g., 103×107): surpluses are 3 and 7. Right: 21. Left: 103+7=110. Answer: 11021.
Method 2 — Nikhilam with Base 10 (for Numbers Near 10)
The same logic applies for numbers near 10. Use base 10. Step 1: Find complements from 10. Step 2: Cross-subtract for left part. Step 3: Multiply complements for right part (1 digit).
Example 1: 7 × 8. Complements: 3 and 2. Right: 3×2=6. Left: 7−2=5. Answer: 56. Example 2: 6 × 9. Complements: 4 and 1. Right: 4×1=4. Left: 6−1=5. Answer: 54. Example 3: 12 × 13. Surpluses: 2 and 3. Right: 2×3=6. Left: 12+3=15. Answer: 156. Example 4: 14 × 12. Surpluses: 4 and 2. Right: 4×2=8. Left: 14+2=16. Answer: 168. This technique also works with base 50, 1000, and other convenient bases by scaling appropriately.
Method 3 — Urdhva-Tiryagbhyam (General Method for Any 2-Digit × 2-Digit)
Urdhva-Tiryagbhyam (Vertically and Crosswise) is the universal Vedic multiplication method. For any AB × CD: Right column (ones): B×D. Middle column (tens): A×D + B×C. Left column (hundreds): A×C. Carry forward when any column result ≥ 10.
Example 1: 23 × 41. Ones: 3×1=3. Tens: 2×1+3×4=2+12=14 (write 4, carry 1). Hundreds: 2×4=8+1=9. Answer: 943. Example 2: 56 × 78. Ones: 6×8=48 (write 8, carry 4). Tens: 5×8+6×7=40+42=82+4=86 (write 6, carry 8). Hundreds: 5×7=35+8=43. Answer: 4368. Check: 56×78=4368. ✓ Example 3: 67 × 89. Ones: 7×9=63 (write 3, carry 6). Tens: 6×9+7×8=54+56=110+6=116 (write 6, carry 11). Hundreds: 6×8=48+11=59. Answer: 5963.
Method 4 — Special Multipliers: 11, 12, 99, 101, 25
Multiply by 11: for 2-digit AB×11, sum digits and place between. AB×11 = A, (A+B), B with carry if A+B≥10. Example: 73×11 — 7, 7+3=10, 3 → carry makes 8, 0, 3 → 803. Multiply by 12: n×12 = n×10 + n×2. Example: 47×12 = 470+94 = 564. Multiply by 99: n×99 = n×100 − n. Example: 63×99 = 6300−63 = 6237. Multiply by 101: n×101 = n×100 + n. Example: 45×101 = 4500+45 = 4545. For 3-digit: 423×101 = 42300+423 = 42723. Multiply by 25: n×25 = n×100÷4. Example: 68×25 = 6800÷4 = 1700. Multiply by 125: n×125 = n×1000÷8. Example: 72×125 = 72000÷8 = 9000.
Practice Problems with Solutions
Apply the best method for each. (1) 96 × 93 = ? [Nikhilam: complements 4,7. Right: 28. Left: 96−7=89. Answer: 8928] (2) 34 × 56 = ? [Urdhva: Ones: 4×6=24 (write 4, carry 2). Tens: 3×6+4×5=18+20=38+2=40 (write 0, carry 4). Hundreds: 3×5=15+4=19. Answer: 1904] (3) 85 × 85 = ? [Squaring ending in 5: 8×9=72, append 25 → 7225] (4) 97 × 103 = ? [Base 100: 97 is −3, 103 is +3. Right: (−3)×3=−09, left: 97+3=100. For cross products: 100×100−9=10000−9=9991. Or: (100−3)(100+3)=100²−9=9991] (5) 47 × 99 = ? [n×99: 47×100−47=4700−47=4653] (6) 63 × 11 = ? [Trick: 6, 6+3=9, 3 → 693] (7) 112 × 108 = ? [Base 100, surpluses 12 and 8. Right: 12×8=96. Left: 112+8=120. Answer: 12096]
Frequently Asked Questions
Which Vedic multiplication method is best to learn first?
Start with the Nikhilam base method (numbers near 100) — it gives the most dramatic speed-up for the least effort, and the 'aha' moment of calculating 97×98 mentally in 3 seconds is motivating. After that, learn the special multipliers (×11, ×99, ×25) which cover a large fraction of exam questions. Urdhva-Tiryagbhyam (general method) should be learned third as it requires more practice to become automatic.
Does Urdhva-Tiryagbhyam work for 3-digit numbers?
Yes — Urdhva-Tiryagbhyam extends to 3-digit × 3-digit multiplication with 5 steps (ones, tens, hundreds, thousands, ten-thousands positions). The calculation gets longer but follows the same vertically-and-crosswise pattern. Most competitive exam questions involve 2-digit multiplication, so mastering the 2-digit method first is the priority.
How is Vedic multiplication different from the standard algorithm?
The standard long multiplication algorithm works from right to left, writing partial products for each digit of the multiplier and then summing. Vedic methods work in a single pass and exploit properties of the numbers (proximity to base, digit patterns) to skip steps. Vedic methods are faster when you recognise the right technique for the type of numbers involved — standard multiplication is more uniform but slower.
Can I use Vedic multiplication in Class 10 and 12 board exams?
Yes — you can use any method mentally and write the final numerical result. Board exams do not prescribe a specific multiplication algorithm; you are free to use whichever method gives you the correct answer fastest. The working shown in your answer sheet only needs to demonstrate conceptual steps (e.g., algebraic expansion) — the arithmetic within those steps can use any method you choose.
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