Vedic Maths Tricks, Practised Online.

Multiply the leading part by the next number, then append 25.

Cross-subtract the deficits for the left part, and multiply the deficits for the right part.

Cross-add the surpluses for the left part, and multiply the surpluses for the right part.

Multiply vertically at the ends and crosswise in the middle, carrying as you go.

Keep the outer digits and place the sum of each neighbouring pair between them, carrying where needed.

The left part is the number minus 1; the right part is its complement to 10, 100 or 1000.

× 5 = halve, then × 10 · × 25 = × 100, then ÷ 4 · × 50 = × 100, then ÷ 2.

Multiply the tens digit by the next number, then write the product of the units as two digits.

Multiply the tens digits, add the units digit, then write the units squared as two digits.

Halve one factor and double the other until one becomes easy.

Add the deviation to 25 for the left part; square the deviation for the right part.

Apply the deviation a second time for the left part, and square it for the right part.

Build the answer from duplexes: a single digit’s duplex is its square, and a pair’s duplex is twice their product.

Left: number + twice the deviation · Middle: 3 × deviation² · Right: deviation³ (borrow if negative).

a² − b² = (a + b)(a − b).

For divisors just below a base, bring the digits down and add the complement repeatedly.

For divisors just above a base, use the negative complement and add down.

Flag all but the first digit of the divisor, divide by the first digit, and subtract the cross products.

÷ 5 = × 2, then ÷ 10 · ÷ 25 = × 4, then ÷ 100 · ÷ 125 = × 8, then ÷ 1000.

Subtract every digit from 9 and the last digit from 10.

Add the highest place values first and adjust as you go.

Write digits 6 to 9 as bar digits (−4 to −1) and carry 1 to the next place, which shortens long additions.

Round to the nearest ten or hundred, then take back the difference.

Cross-multiply for the numerator, and multiply the denominators for the denominator.

Group the digits in threes. The last digit of the root comes from the last digit of the cube, and the first digit comes from the left group.

Pair the digits from the right. The last digit of the square tells you the last digit of the root, and the leftmost pair gives the first digit.

Iterative duplex subtraction gives roots of non-perfect squares to any precision.

Reduce every number to its digit sum and check that the same operation still holds.

Test divisibility by 7, 13, 19, 29 and more: multiply the last digit by the multiplier (5 for 7, 4 for 13, 2 for 19, 3 for 29), add it to the rest, and repeat.

For 1/19 use multiplier 2 and build the 18-digit cycle from right to left.

x% of y equals y% of x. Pick whichever is easier.