Vedic mathematics, mental math shortcuts, speed calculation, algebra tricks, and everyday estimation methods to solve problems faster.
A Vedic sutra for multiplying numbers close to a base (10, 100, 1000, etc.). Works by finding how far each number is from the base.
A general Vedic multiplication method that works for any two numbers. Uses vertical and crosswise multiplication patterns.
Quick method to square any number near 50 using the identity (50±d)² = 2500 ± 100d + d².
Instantly square any number ending in 5. Multiply the tens digit by (tens digit + 1), then append 25.
Transform numbers with large digits (6-9) into "vinculum" form using complements from 10, making calculations easier.
Instantly multiply any two-digit number by 11 by splitting and adding the digits.
x% of y = y% of x. When one direction is hard, flip it! This works because (x/100)×y = (y/100)×x.
Multiply by 10 and divide by 2 (or vice versa) for instant results.
Subtract each digit from 9 except the last, which you subtract from 10. Works for any power of 10.
Quickly check if a number is divisible by 2 through 12 without dividing.
Use the identity (a+b)(a-b) + b² = a² to square numbers quickly by going to the nearest easy number.
Memorize common fraction-to-decimal conversions for instant calculation.
Split large multiplications into simpler parts using the distributive property.
A quick way to verify multiplication and addition results by checking digit sums modulo 9.
Multiplying any number by a string of nines is instant: subtract 1 from the number for the left part, then take the complement for the right part.
When numbers are near a convenient working base that is a multiple of a power of 10, use a proportional base to simplify the multiplication.
The Dwandwa (duplex) method squares any number by summing duplex values digit by digit — a general Vedic squaring technique.
Multiply by 10 and subtract the original number — much faster than multiplying by 9 directly.
Since 25 = 100 ÷ 4, multiply by 100 and divide by 4 for instant results.
Multiply by 10, then add half of that — because 15 = 10 + 5 and 5 is half of 10.
When one factor is even, halve it and double the other to reach an easier multiplication.
Add the big place values first (left to right) instead of the traditional right-to-left carrying — easier to hold in your head.
For numbers a little above 100, use the surplus from 100 to multiply almost instantly.
Any percentage can be built from 10%, 5%, and 1% — quick to find and easy to combine.
Use (a+1)² = a² + 2a + 1. Square the round number below, add twice it, add 1.
Multiplying by 4 is doubling twice; by 8 is doubling three times. No memorised tables needed.
Gauss's formula: the sum of the first n whole numbers is n(n+1)/2 — no adding required.
The sum of the first n odd numbers is always a perfect square, exactly n².
a² − b² = (a + b)(a − b). Turns a subtraction of squares into an easy product.
Multiply two binomials by combining First, Outer, Inner, Last terms.
Two numbers equally spaced around a middle value m multiply to m² − d², using the difference of squares.
Find 10% first, then build 15% or 20% from it in your head.
Estimate how many years it takes an investment to double: divide 72 by the annual interest rate.
A fast approximation: to go C→F, double and add 30. For exact values use ×9/5 + 32.
Multiply miles by 1.6 for km, or divide km by 1.6 for miles. Consecutive Fibonacci numbers are handy approximations.
To find the better deal, divide price by quantity to get the price per unit and compare.
Bracket the number between two perfect squares, then refine with a quick average step.
Round the total up to a friendly number, divide by the number of people, then adjust down slightly.