Vedic mathematics is a system of mathematics that originated in ancient India. It is based on a set of 16 sutras (aphorisms) and 13 sub-sutras, which provide various techniques and shortcuts for performing mathematical calculations. Here are a few Vedic math tricks for fast calculation:

1. Vertically and Crosswise (Nikhilam Method):

   – To multiply two numbers close to a base, subtract the difference from the base and multiply the result by the base.

   – Example: To multiply 98 and 97, take 100 as the base. Subtract the difference (2) from the base: 100 – 2 = 98. Multiply the result by the base: 98 * 100 = 9,800. Add the square of the difference (2^2 = 4): 9,800 + 4 = 9,804 (the product of 98 and 97).

2. All from 9 and the Last from 10:

   – To find the complement of a number with respect to 9 or 10, subtract each digit from 9 (for complements to 9) or subtract each digit from 10 (for complements to 10).

   – Example: To find the complement of 72 with respect to 9, subtract each digit from 9: 9 – 7 = 2, 9 – 2 = 7. The complement of 72 with respect to 9 is 27.

3. Proportionately:

   – If two numbers have a common ratio with a third number, their product is equal to the product of the first number and the ratio, divided by the ratio of the second number.

   – Example: If 3:4 = 5: x, then 3 * x = 4 * 5.

4. Digital Roots:

   – The digital root of a number is the single-digit result obtained by repeatedly adding the digits together until a single digit is left.

   – Example: The digital root of 345 is calculated as 3 + 4 + 5 = 12, 1 + 2 = 3. Therefore, the digital root of 345 is 3.

5. Base Method for Multiplication:

   – Multiply using a base close to the numbers being multiplied and adjust the result accordingly.

   – Example: To multiply 98 and 43 using a base of 100, calculate (100 – 98) * (100 – 43) = 2 * 57 = 114. Adjust the result by subtracting the difference from the numbers being multiplied: 98 – 2 = 96 and 43 – 57 = -14. The final result is 96 and -14 combined, which gives 96 – 14 = 82.

These are just a few examples of Vedic math tricks. Vedic mathematics offers a wide range of techniques for various mathematical operations. By practicing and applying these methods, you can improve your calculation speed and mental math abilities.