Most multiplications you meet in daily life have a shape you can take advantage of: one number is 11, or 5, or a string of 9s, or both numbers are close to 100. Vedic Maths has a shortcut for each of these shapes, and once you can spot them, many multiplications take a few seconds in your head. This guide covers six of the most useful, explains when each one works and why, and ends with a practice set.
For a method that works on any two numbers, see our guide to Urdhva Tiryagbhyam, the general Vedic multiplication method. The tricks below are the fast special cases.
To multiply a two-digit number by 11, write its first digit, then the sum of its two digits, then its last digit.
If the middle sum is 10 or more, carry the 1 into the first digit. For 78 × 11, the middle is 7 + 8 = 15, so write 5 and carry 1 onto the 7. The answer is 858.
Longer numbers work the same way: keep the end digits and add each neighbouring pair in between. For 324 × 11, write 3, then 3 + 2 = 5, then 2 + 4 = 6, then 4. The answer is 3,564.
Why it works: 11 is 10 + 1, so multiplying by 11 adds the number to itself shifted one place left. The neighbouring sums are where the two copies overlap. For 111, three copies overlap, so add three digits at a time: 35 × 111 is 3, then 3 + 5, then 3 + 5, then 5, which gives 3,885.
Multiply the digits in front of the 5 by one more than themselves, then write 25 after the result. For 25 × 25, that is 2 × 3 = 6, so the answer is 625. For 65 × 65, it is 6 × 7 = 42, so the answer is 4,225. Our guide to Vedic Maths square tricks covers this method and two other ways to square.
This is the Ekadhikena Purvena sutra, "by one more than the one before", in a more general form. It works when two numbers have the same front digits and their last digits add up to 10.
For 33 × 37, the last digits 3 and 7 add up to 10. The left part is 3 × 4 = 12 and the right part is 3 × 7 = 21. Side by side, the answer is 1,221.
For 24 × 26, the unit digits add to 10. So the left part is 2 × 3 = 6 and the right part is 4 × 6 = 24, which gives 624.
For 21 × 29, the right part is 1 × 9 = 9, written as 09, so the answer is 609. Bigger front parts work too: for 163 × 167, the left part is 16 × 17 = 272 and the right part is 3 × 7 = 21, so the answer is 27,221.
Both conditions matter. For 34 × 46, the last digits add up to 10 but the front digits differ, so the trick doesn't apply. The real answer is 1,564.
The sutra Ekanyunena Purvena, "by one less than the one before", handles a multiplier made only of 9s, as long as the other number has the same number of digits.
For 44 × 99, the left part is 44 − 1 = 43, and the right part is 99 − 43 = 56. The answer is 4,356. You can confirm it another way: 44 × 100 is 4,400, and 4,400 − 44 = 4,356.
For 64 × 99, the left part is 63 and the right part is 99 − 63 = 36, so the answer is 6,336. With three 9s, for 567 × 999, the left part is 566 and the right part is 999 − 566 = 433, so the answer is 566,433.
If the other number has fewer digits, pad it with zeros in front. For 7 × 99, treat 7 as 07: the left part is 06 and the right part is 99 − 6 = 93, so the answer is 693.
Since 5 is half of 10, multiplying by 5 is the same as halving and then multiplying by 10. For 68 × 5, half of 68 is 34, so the answer is 340. For an odd number, the half ends in .5, and multiplying by 10 just removes the point: half of 55 is 27.5, so 55 × 5 is 275.
The same idea works for 25, which is a quarter of 100, and 50, which is half of 100. For 48 × 25, a quarter of 48 is 12, so the answer is 1,200. For 86 × 50, half of 86 is 43, so the answer is 4,300. For more on this idea, see the doubling and halving trick.
When both numbers are just below 100, find how far each is from 100.
For 97 × 96, the differences are 3 and 4. The left part is 97 − 4 = 93 and the right part is 3 × 4 = 12, so the answer is 9,312. Above 100, add instead: for 103 × 108, the left part is 103 + 8 = 111 and the right part is 3 × 8 = 24, so the answer is 11,124. This is the Nikhilam method, and our Nikhilam sutra guide covers numbers on either side of the base, and other bases.
| If you see | Use |
|---|---|
| A number times 11 | Trick 1 |
| A number ending in 5, squared | Trick 2 |
| Same front digits, last digits adding to 10 | Trick 3 |
| A multiplier of 9s | Trick 4 |
| A multiplier of 5, 25 or 50 | Trick 5 |
| Both numbers close to 100 | Trick 6 |
To check any answer, compare digital roots. For 44 × 99, the roots are 8 and 9, which multiply to 72, so 9, and 4,356 also reduces to 9. Our guide to digital roots explains how.
Answers: (1) 517: the middle is 11, so carry the 1. (2) 1,353. (3) 3,016: 5 × 6 is 30 and 2 × 8 is 16. (4) 5,625. (5) 3,762: the left part is 37 and the right part is 62. (6) 430. (7) 1,600: a quarter of 64 is 16. (8) 9,212: the differences are 2 and 6, 98 − 6 = 92, and 2 × 6 = 12.
Use these tricks against real questions in the multiplication game, or practise one at a time in practice mode. For more Vedic methods, see Vedic Maths multiplication tricks, or browse all our Vedic Maths guides.
Multiplying by 11. It needs only one addition, works for any two-digit number, and gives you a quick win to build on before the tricks with more conditions.
The right part is the 9s minus the left part, so the two need to line up. If the other number is shorter, pad it with zeros in front so it has as many digits as there are 9s.
No. Every trick still uses small multiplication facts, like 3 × 4 or 2 × 6, so knowing the tables makes each one faster. The tricks save the work of long multiplication, not the facts behind it.