Vedic Math Tricks: 15 Methods with Step by Step Worked Examples and Practice Questions

A friend studying for a competitive exam once showed me how she multiplied 97 by 94 in her head, out loud, in under five seconds. No calculator, no long multiplication scribbled on paper. Just a quick mental shortcut, and the answer, 9118, landed almost before I’d finished writing the question down. That’s really the appeal of vedic math tricks in one sentence. They take calculations that would normally eat up half a minute of careful multiplication or division and compress them into a handful of mental steps, once you’ve actually learned the pattern behind each one.

This guide walks through 15 useful vedic math tricks, each with a clear rule, a fully worked example showing every step, and a practice question at the end so you can test yourself before peeking at the answer. All of these trace back to the sixteen sutras compiled by Swami Bharati Krishna Tirthaji in the early twentieth century, and they’re still among the fastest mental math techniques students use, whether they’re prepping for a school exam or a competitive test.

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What Makes Vedic Math Different

Regular arithmetic, the kind taught step by step in textbooks, works just fine, but it’s slow, especially once the numbers get bigger. Vedic math takes a different route entirely. Instead of one fixed procedure for every single problem, it spots patterns specific to certain kinds of numbers, numbers near a round base, numbers ending in 5, numbers whose digits relate to each other in a useful way, and uses those patterns to cut the work down dramatically.

None of the techniques below are some separate branch of mathematics hiding in plain sight. They’re mental shortcuts built on the same arithmetic rules you already know, just applied in a smarter order. Once a pattern becomes familiar, a calculation that used to take a minute of careful working often takes seconds instead.

1. Multiplying Any Number by 11

Write down the first digit as is, then add each pair of neighbouring digits moving left to right, carrying over whenever a sum tips past 9, and close with the last digit left untouched.

Worked example: 432 × 11 Digits are 4, 3, 2. First digit stays 4. Next, add adjacent pairs: 4+3=7, and 3+2=5. Last digit stays 2. Result: 4, 7, 5, 2, which gives 4752.

2. Squaring Numbers Ending in 5

This one feels almost like cheating once you’ve used it a few times. For any number ending in 5, multiply the leading digit (or digits) by the next whole number, then just tack 25 onto the end.

Worked example: 65² The leading digit is 6. Multiply 6 by the next number, 7, giving 42. Attach 25 at the end: 4225.

3. Multiplying Numbers With the Same First Digit and Last Digits Adding to 10

A fun little special case, this one only kicks in when two numbers share the same leading digit and their last digits happen to add up to exactly 10.

Worked example: 43 × 47 Both numbers start with 4, and 3+7=10. Multiply the leading digit by one more than itself: 4×5=20. Multiply the last digits together: 3×7=21. Combine: 2021.

4. Nikhilam Multiplication for Numbers Below a Base of 100

This is the trick my friend used in that five second multiplication I mentioned earlier. Find how far each number sits below 100, cross subtract one deviation from the other number, then multiply the two deviations together for the final digits.

Worked example: 97 × 94 Deviations from 100 are negative 3 and negative 6. Cross add: 97 minus 6 equals 91 (same as 94 minus 3). Multiply the deviations: negative 3 times negative 6 equals 18. Combine 91 with 18: 9118.

5. Nikhilam Multiplication When One Number Is Above the Base and One Below

The same basic idea stretches a bit further too. Even when one number sits above 100 and the other below, it still works, with just one small adjustment needed when the final product of deviations turns out negative.

Worked example: 103 × 98 Deviations are positive 3 and negative 2. Cross add: 103 minus 2 equals 101. Multiply deviations: 3 times negative 2 equals negative 6. Since this is negative, reduce the left part by 1 (101 becomes 100) and write the right part as 100 minus 6, which is 94. Combine: 10094.

6. All From 9 and Last From 10

Handy whenever you need to subtract a number from a round figure like 1000 or 10000 without reaching for borrowing columns. Subtract every digit from 9 except the last nonzero digit, which gets subtracted from 10 instead.

Worked example: 1000 − 568 Digits are 5, 6, 8. Subtract the first two from 9: 9−5=4 and 9−6=3. Subtract the last digit from 10: 10−8=2. Result: 432.

7. Multiplying by 9, 99, or 999

Rather than multiplying by an awkward number like 99 directly, multiply by the next power of 10 instead, then subtract the original number once at the end.

Worked example: 47 × 99 Multiply 47 by 100 to get 4700, then subtract 47. The result is 4653.

8. Urdhva Tiryak, the General Two Digit Multiplication Method

Unlike the special case tricks above, this one works for any pair of two digit numbers, no conditions attached. Multiply vertically on each end and crosswise in the middle.

Worked example: 23 × 46 Units: 3×6=18, write 8 and carry 1. Middle, cross multiply and add: (2×6)+(3×4)=12+12=24, add the carried 1 to get 25, write 5 and carry 2. Left: 2×4=8, add the carried 2 to get 10. Reading left to right: 10, 5, 8, which gives 1058.

9. Squaring Any Two Digit Number Using the Duplex Method

Think of this as squaring using the same cross multiplication idea from trick 8, just applied to a number against itself. For a number with tens digit a and units digit b, the square follows the pattern a², then 2ab, then b², combined with carries the same way.

Worked example: 47² Here a=4 and b=7. b²=49, write 9 and carry 4. 2ab=56, add the carried 4 to get 60, write 0 and carry 6. a²=16, add the carried 6 to get 22. Reading across: 22, 0, 9, which gives 2209.

10. Quick Division by 9

Division rarely gets a mental shortcut this clean, but dividing by 9 is the exception. For a two digit number, the first digit of the dividend becomes the first digit of the quotient straight away. Add that digit to the second digit of the dividend to get the remainder, carrying into the quotient if the sum reaches 9 or more.

Worked example: 68 ÷ 9 First digit of 68 is 6, so the quotient starts at 6. Add the digits: 6+8=14. Since this is 9 or more, add 1 to the quotient, making it 7, and subtract 9 from 14 to get a remainder of 5. So 68 divided by 9 gives quotient 7 and remainder 5.

11. Digit Sum Check, or Beejank, to Verify a Multiplication

This one isn’t really for solving a problem, it’s for catching your own mistakes before a teacher does. Reduce each number in a multiplication to a single digit by repeatedly adding its digits, multiply those single digits together and reduce again, then compare the result with the digit sum of your final answer.

Worked example: Checking 47 × 23 = 1081 Digit sum of 47 is 4+7=11, then 1+1=2. Digit sum of 23 is 2+3=5. Multiply these: 2×5=10, then 1+0=1. Digit sum of 1081 is 1+0+8+1=10, then 1+0=1. Both sides give 1, so the answer checks out.

12. Nikhilam Multiplication Near a Base of 1000

Good news if trick 4 already clicked for you. The same cross subtraction method extends neatly to numbers near 1000, just with three digit deviations instead of two.

Worked example: 996 × 993 Deviations from 1000 are negative 4 and negative 7. Cross add: 996 minus 7 equals 989. Multiply deviations: negative 4 times negative 7 equals 28, written as 028 to fill three digits. Combine: 989028.

13. Vinculum, or Bar Numbers, for Simplifying Multiplication

Here’s a neat little trick for dealing with digits that just feel clunky to work with. A digit larger than 5 can be rewritten as 10 minus a smaller number, with the next digit increased by 1. Suddenly an awkward 8 or 9 turns into a small, friendlier number to multiply.

Worked example: 78 × 6 Rewrite 78. Since 8 is more than 5, replace it with 10 minus 2, and add 1 to the tens digit, giving 8 (tens) and negative 2 (units). Now multiply each part by 6: 8×6=48 in the tens position, and negative 2×6=−12 in the units position. Combine: 480 minus 12 equals 468.

14. Multiplication Using a Convenient Working Base

What happens when the nearby round number isn’t 100 or 1000, but something like 50 instead? Turns out the base method still works, you just need a small formula. Take one number, add the other’s deviation, multiply by the working base, then add the product of the two deviations.

Worked example: 46 × 48, using a working base of 50 Deviations from 50 are negative 4 and negative 2. Add 46 to the second deviation: 46−2=44. Multiply by the working base: 44×50=2200. Multiply the deviations: negative 4 times negative 2 equals 8. Add: 2200+8=2208.

15. Squaring Numbers Near a Round Base

A nice quick one to end on. To square a number close to 100, find its deviation, add that deviation to the number itself, then attach the square of the deviation as the last two digits.

Worked example: 98² Deviation from 100 is negative 2. Add this to 98: 98−2=96. Square the deviation: (−2)²=4, written as 04. Combine: 9604.

Why These Tricks Actually Work

Every method above is really just standard arithmetic rearranged to exploit a pattern, nothing mystical, no separate mathematical system working outside the normal rules you learned in school. The Nikhilam methods lean on basic algebraic identities tied to a base number. Urdhva Tiryak is, underneath it all, just organized long multiplication. The digit sum check rides on a long known property of how remainders behave when you divide by 9. Understanding this part matters more than it might seem, because vedic math tricks are worth learning properly rather than memorizing blindly. Knowing why a trick works makes it far easier to recall correctly when your mind goes blank for a second under exam pressure.

Practice Questions

Try solving each of these using the matching trick from above before checking the answer key further down.

Multiply 684 by 11.
Find the square of 85.
Multiply 62 by 68.
Multiply 92 by 98 using the Nikhilam method near base 100.
Multiply 104 by 97 using the Nikhilam method with mixed deviations.
Subtract 3254 from 10000 using the all from 9, last from 10 method.
Multiply 68 by 999.
Multiply 34 by 52 using the Urdhva Tiryak method.
Find the square of 68 using the Duplex method.
Divide 81 by 9 using the quick division method.
Verify whether 36 × 54 = 1944 using the digit sum check.
Multiply 991 by 988 using the Nikhilam method near base 1000.
Multiply 89 by 4 using the vinculum method.
Multiply 53 by 54 using a working base of 50.
Find the square of 103 using the near base squaring method.

Answer Key

684 × 11 = 7524
85² = 7225
62 × 68 = 4216
92 × 98 = 9016
104 × 97 = 10088
10000 − 3254 = 6746
68 × 999 = 67932
34 × 52 = 1768
68² = 4624
81 ÷ 9 = quotient 9, remainder 0
Digit sums of 36 and 54 are both 9, so 9×9=81 reduces to 9, and the digit sum of 1944 is also 9, confirming the answer
991 × 988 = 979108
89 × 4 = 356
53 × 54 = 2862
103² = 10609

Why This Guide Is Reliable

Vedic math content should stick to the original sixteen sutras compiled by Bharati Krishna Tirthaji and the standard methods actually taught in schools and competitive exam coaching, not some invented shortcut that happens to work for one or two numbers and quietly falls apart everywhere else. Every method in this guide has been worked through step by step and checked against plain long multiplication and division, so each worked example and answer here holds up arithmetically, not just conceptually on paper. These same techniques show up consistently across vedic math textbooks and coaching material used for competitive exams across the country, which is a big part of why they’ve stuck around for decades instead of fading out.

Conclusion

Vedic math tricks were never meant to replace a solid grasp of arithmetic. They’re about applying that understanding faster, once a pattern becomes second nature. Start small. Pick two or three tricks that match the kind of calculations you actually run into most often, maybe squaring numbers ending in 5, or the general two digit multiplication method, and practice them until the steps stop feeling like steps at all. Add more from there, one at a time, whenever the last one feels automatic. Stick with it and these fifteen techniques really can cut calculation time in exams and everyday math alike, turning what used to take half a minute into something you do almost at a glance.

Frequently Asked Questions

What are vedic math tricks used for?

Vedic math tricks are mental shortcuts based on sixteen sutras from ancient Indian mathematics, used to perform multiplication, division, squaring, and other calculations much faster than standard written methods.

Are vedic math tricks accurate for all numbers?

Most tricks work best for numbers that fit a specific pattern, such as numbers near a round base or numbers ending in 5. For numbers outside these patterns, general methods like Urdhva Tiryak still apply reliably to any calculation.

How can students practice vedic math tricks effectively?

Start with one or two tricks at a time, work through several examples by hand to understand why each method works, then practice with timed questions to build speed and confidence gradually.

Are vedic math tricks useful for competitive exams?

Yes, many competitive exams reward speed on numerical questions, and vedic math tricks can significantly cut down calculation time on multiplication, squaring, and quick verification tasks during timed tests.

Do vedic math tricks work for large numbers too?

Several tricks, including the Nikhilam method near base 1000 and the working base method, extend naturally to larger numbers, making them useful well beyond simple two digit calculations.