Learning the times tables is mostly memory, but memory is much easier when you can rebuild a fact you have forgotten. Vedic Maths gives you ways to work out any table fact quickly from facts you already know, especially the hard ones from 6 × 6 to 9 × 9 and the tables beyond 10. This guide shows five techniques, explains when each one helps, and suggests an order for learning the tables so that every new one builds on the last.
The aim isn't to calculate every fact forever. Working a fact out a few times, then checking it, is what makes it stick, until you just remember it.
The sutra Nikhilam Navatashcaramam Dashatah, "all from 9 and the last from 10", turns any fact with both numbers between 6 and 9 into the easy facts below 5. Find how far each number is below 10.
For 8 × 7, the differences are 2 and 3. For the tens, 8 − 3 = 5. For the ones, 2 × 3 = 6. The answer is 56.
For 9 × 7, the differences are 1 and 3, so 7 − 1 = 6 and 1 × 3 = 3, which gives 63. For 9 × 9, the differences are both 1, so 9 − 1 = 8 and 1 × 1 = 1, which gives 81.
If the product of the differences is 10 or more, carry. For 6 × 7, the differences are 4 and 3. The tens are 6 − 3 = 3 and the ones are 4 × 3 = 12, so 30 + 12 = 42.
Why it works: the same rule multiplies numbers near any base, such as 97 × 96 near 100. Our guide to the Nikhilam sutra covers it in full.
The same idea works above 10, with the differences added instead. For two numbers from 11 to 19:
For 13 × 14: 13 + 4 = 17, which gives 170, and 3 × 4 = 12, so the answer is 182.
For 16 × 18: 16 + 8 = 24, which gives 240, and 6 × 8 = 48, so the answer is 288.
For 19 × 17: 19 + 7 = 26, which gives 260, and 9 × 7 = 63, so the answer is 323.
This turns the whole 11 to 19 tables into the facts from 1 to 9 plus an addition. Check your answers against the times tables chart at first.
For the 11 and 12 times tables, or any two-digit fact, the vertically-and-crosswise method splits the multiplication into three small ones. Take 12 × 13:
Side by side, the answer is 156. If a part has two digits, carry into the part on its left. For 12 × 15, the parts are 1, then 5 + 2 = 7, then 10. Keep the 0 and carry the 1 to make 8, so the answer is 180.
Our full guide to Urdhva Tiryagbhyam extends this to bigger numbers.
Ekadhikena Purvena means "by one more than the one before". To square a number ending in 5, multiply the digits in front by one more than themselves, then write 25 on the end. For 25 × 25, 2 × 3 = 6, so the answer is 625. For 85 × 85, 8 × 9 = 72, so the answer is 7,225.
This makes the 15 and 25 times tables easier to anchor: 15 × 15 is 225, because 1 × 2 = 2. More shortcuts like this are in our Vedic Maths square tricks.
Many tables are just another table doubled:
You can also double one number and halve the other without changing the answer: 8 × 15 is the same as 4 × 30, which is 120. Our guide to the doubling and halving trick has more examples.
Each step uses facts from earlier steps, so you are always building on something you know. For a week-by-week plan, see how to learn times tables fast.
Answers: (1) 56: the differences are 3 and 2, 7 − 2 = 5 and 3 × 2 = 6. (2) 54: the differences are 4 and 1, 6 − 1 = 5 and 4 × 1 = 4. (3) 49: 7 − 3 = 4 and 3 × 3 = 9. (4) 224: 14 + 6 = 20, which gives 200, and 4 × 6 = 24. (5) 306: 18 + 7 = 25, which gives 250, and 8 × 7 = 56. (6) 180. (7) 96: 2 × 12 = 24, double to 48, double again to 96.
Once you can work a fact out, the next step is remembering it without working. Short, regular practice does that best: try the multiplication game, or pick one table at a time in practice mode. Every technique above has its own article in our Vedic Maths guides.
No, but it helps you get there. The techniques let you rebuild a fact you have forgotten, and working a fact out and checking it a few times is what helps it stick. The goal is still to recall the facts without working.
Nikhilam. It turns any fact from 6 × 6 to 9 × 9 into a subtraction and a small multiplication, so 8 × 7 becomes 8 − 3 = 5 and 2 × 3 = 6, which gives 56.
Doubling and halving suit most children who know the 2 times table. Nikhilam and the teens method suit children who are confident with facts up to 5 × 5 and with subtraction, often from about age 8 or 9.