Vedic maths — mental arithmetic trainer
Practise ten mental arithmetic techniques, including methods known as Vedic maths. Each is explained using ordinary algebra. Choose a lesson, solve a problem and check the steps.
How do I use this page?
- Read a lesson and its worked example.
- Enter an answer, check it and compare the solution steps.
- Generate another exercise or take the 10-question test.
What this page does not do: predict future lottery outcomes.
Course: 10 lessons
- Multiplication by 11
- Squaring numbers ending in 5
- Products below 100
- Products above 100
- On opposite sides of 100
- Square of a sum
- Multiplication by 25
- Multiplication by 99
- Crosswise multiplication
- Division by 8
For non-terminating decimals, round to three decimal places or enter a fraction such as 1/3.
Optional local storage only. No account or server submission. Turn off to remove saved progress.
1. Multiplication by 11
Split 11 into 10 + 1. Multiply by 10 and add the original. This works even when digit sums need a carry.
Worked example
47 × 11 = 470 + 47 = 517.
Watch out
The digit-insertion shortcut needs a carry when the digit sum exceeds 9.
2. Squaring numbers ending in 5
For 10a + 5, the square is 100a(a+1) + 25. Multiply the part before 5 by its successor and append 25.
Worked example
35² = 3 × 4 × 100 + 25 = 1225.
Watch out
This form applies to integers ending in the digit 5.
3. Products below 100
Write the factors as 100−a and 100−b. Their product is 100(100−a−b) + ab. The algebra handles carries correctly.
Worked example
97 × 96 = 100 × 93 + 12 = 9312.
Watch out
Do not simply concatenate deficits: ab ≥ 100 requires carrying hundreds.
4. Products above 100
For 100+a and 100+b use 100(100+a+b) + ab. Surpluses replace the previous lesson’s deficits.
Worked example
104 × 107 = 11100 + 28 = 11128.
Watch out
With large surpluses, add numerically rather than concatenating digits.
5. On opposite sides of 100
Expand (100−a)(100+b): 10000 + 100(b−a) − ab. The last term is negative.
Worked example
98 × 103 = 10000 + 100 − 6 = 10094.
Watch out
The sign of ab matters. Write the identity before doing it mentally.
6. Square of a sum
Use (a+b)² = a² + 2ab + b². Split a number into tens and the remainder.
Worked example
23² = 400 + 120 + 9 = 529.
Watch out
Do not omit 2ab. The square of a sum is not the sum of squares.
7. Multiplication by 25
Since 25 = 100/4, multiply by 100 and divide by 4. For multiples of 4, dividing first is convenient.
Worked example
28 × 25 = 2800/4 = 700.
Watch out
Do not round intermediate division when the number is not divisible by 4.
8. Multiplication by 99
99 = 100 − 1, so n × 99 = 100n − n. This is the distributive law.
Worked example
42 × 99 = 4200 − 42 = 4158.
Watch out
Subtract the whole original number, not just its last digit.
9. Crosswise multiplication
For (10a+b)(10c+d), use 100ac + 10(ad+bc) + bd. The middle term includes both cross-products.
Worked example
23 × 14 = 200 + 110 + 12 = 322.
Watch out
Preserve place value. Multiplying units can carry into tens.
10. Division by 8
Multiplying by 0.125 is dividing by 8. Halve three times. Choose a method suited to the numbers.
Worked example
248/8: 248 → 124 → 62 → 31.
Watch out
Do not confuse 0.125 with 1.25. This trains arithmetic, not lottery prediction.
Final test: 10 questions
One new question from each lesson. No time limit. Answers and explanations appear after the test. You may stop and restart.
Further reading
Original exercises by Pewniaki. The mental-maths identities are explained algebraically; no claim of historical origin or guaranteed speed advantage is made.