Vedic maths › Multiplying by 11
Multiplying by 11
Multiplying by 11 is one of the best-known shortcuts in Vedic maths classes, though Tirthaji’s book has no section on it. It is vertically and crosswise with 11, where every crosswise sum is just two neighbouring digits added together.
The method
- The last digit of the number is the last digit of the answer.
- Moving left, add each digit to its neighbour on the right.
- The first digit of the number starts the answer.
- A sum of 10 or more keeps its last digit and carries 1 to the left.
Worked examples
253 × 11
- The last digit stays.3
- Add each digit to its neighbour on the right, moving left.5 + 3 = 8, 2 + 5 = 7
- The first digit stays.2
- Put them side by side.2 | 7 | 8 | 3
253 × 11 = 2783
78 × 11
- The last digit stays.8
- Add each digit to its neighbour on the right, moving left.7 + 8 = 15
- The first digit stays.7
- Put them side by side.7 | 15 | 8
- Carry from the right, keeping one digit in each part.8; 15: keep 5, carry 1; 7 + 1 = 8 → 858
78 × 11 = 858
4729 × 11
- The last digit stays.9
- Add each digit to its neighbour on the right, moving left.2 + 9 = 11, 7 + 2 = 9, 4 + 7 = 11
- The first digit stays.4
- Put them side by side.4 | 11 | 9 | 11 | 9
- Carry from the right, keeping one digit in each part.9; 11: keep 1, carry 1; 9 + 1 = 10: keep 0, carry 1; 11 + 1 = 12: keep 2, carry 1; 4 + 1 = 5 → 52019
4729 × 11 = 52019
Why it works
Times 11 is times 10 plus times 1: 253 × 11 = 2530 + 253. Write the two numbers one above the other, and each place of the answer adds a digit to its neighbour.
Watch out
- Carry from the right: in 78 × 11 the middle sum is 15, so keep 5 and carry 1 to the 7: 858.
- For 111, 1111 and so on the same idea adds three or four neighbours at a time, and the carries pile up faster.
Try these
Work each one out, then tap it to see the answer.
36 × 11
3 | 9 | 6 → 396
52 × 11
5 | 7 | 2 → 572
87 × 11
8 | 15 | 7 → 957
341 × 11
3 | 7 | 5 | 1 → 3751
695 × 11
6 | 15 | 14 | 5 → 7645
Practise it in the game: Speed Tricks, 2.2 ×11. Free, with no sign-up.
Source: Vedic maths courses teach this shortcut; Tirthaji’s book only has multiplying by 11 among its vertically and crosswise examples, and the same rule is in the Trachtenberg system. The explanation, examples and questions here are our own.
More Vedic maths
- Squares ending in 5: 75²: 7 × 8 = 56, then 25: 5625.
- All from 9, the last from 10: 1000 − 357: 9 − 3, 9 − 5, 10 − 7: 643.
- Multiplying near 100: 97 × 96: 97 − 4 = 93, 3 × 4 = 12: 9312.
- Squaring near 100: 96²: 96 − 4 = 92, 4² = 16: 9216.
- Vertically and crosswise: 23 × 41: 2 × 4 | 2 × 1 + 3 × 4 | 3 × 1: 943.
- Multiplying by 9, 99, 999: 437 × 999: 436, then 999 − 436 = 563: 436563.
- Last digits adding to 10: 63 × 67: 6 × 7 = 42, 3 × 7 = 21: 4221.
- Checking with digit sums: 437 × 26 = 11362? 5 × 8 → 4, and 11362 → 4: it passes.
- Dividing by 9: 2312 ÷ 9: 2, 2 + 3, 5 + 1: 256, remainder 6 + 2 = 8.
- Squaring with the duplex: 43²: 4² | 2 × 4 × 3 | 3² = 16 | 24 | 9: 1849.
Where Vedic maths comes from, all 16 sutras, and our sources: Vedic maths, explained.