Supersonic mental math techniques for squaring, multiplication, division, and algebra — with worked examples for every sutra.
Vedic Mathematics is a system of 16 sutras (aphorisms) reconstructed by Bharati Krishna Tirthaji from the Atharva Veda. Each sutra encodes a mental-math shortcut — a pattern that reduces arithmetic to small, memorable steps you can do in your head faster than a calculator.
Below is a jump-off point to every sutra, with meaning, use case, and a worked example. Follow any card to a full interactive lesson and practice quiz on TugMaster AI.
"By one more than the previous number."
Used for: Calculating squares of numbers ending in 5, multiplying numbers whose first digits add up to 10 and last digits are 5.
Example: 35² = 1225
"All from 9 and the last from 10."
Used for: Subtracting from powers of 10, multiplying numbers close to a base (10, 100, 1000).
Example: 1000 - 573 = 427
"Vertically and crosswise."
Used for: General multiplication of any two numbers. The most versatile Vedic multiplication method.
Example: 23 × 14 = 322
"Transpose and adjust."
Used for: Division by numbers slightly greater than powers of 10.
Example: 1234 ÷ 12 = 102 remainder 10
"When the sum is the same, that sum is zero."
Used for: Solving equations where the sum of coefficients on both sides are equal, quickly finding that the variable is zero.
Example: 3x + 7 = 7 + 3x (find x) = Identity / x = 0
"If one is in ratio, the other is zero."
Used for: Solving simultaneous equations where coefficients are in proportion. Also used for proportional reasoning.
Example: 2x + 3y = 6, 4x + 5y = 12 = y = 0, x = 3
"By addition and by subtraction."
Used for: Solving simultaneous equations by adding and subtracting them to eliminate variables.
Example: x + y = 10, x - y = 4 = x = 7, y = 3
"By the completion or non-completion."
Used for: Simplifying multiplication by completing to the nearest round number.
Example: 98 × 97 = 9506
"Differences and similarities."
Used for: Multiplying numbers equidistant from a round number using the difference of squares.
Example: 47 × 53 = 2491
"Whatever the extent of deficiency."
Used for: Squaring numbers near a base (10, 100, 1000). Lightning-fast mental squaring!
Example: 104² = 10816
"Part and whole."
Used for: Breaking complex problems into simpler parts. Especially powerful for multiplying by 11.
Example: 43 × 11 = 473
"The remainders by the last digit."
Used for: Finding remainders and divisibility checks using digit patterns.
Example: Is 372 divisible by 4? = Yes (remainder 0)
"The ultimate and twice the penultimate."
Used for: Working with telescoping fraction sums and specific algebraic series.
Example: 1/(2×3) + 1/(3×4) + 1/(4×5) = 3/10
"By one less than the previous."
Used for: Multiplying any number by 9, 99, 999, etc. Incredibly fast!
Example: 76 × 99 = 7524
"The product of the sum is equal to the sum of the products."
Used for: Multiplying two sums together by computing each sum first, then multiplying the results.
Example: (8 + 20) × (16 + 19) = 980
"The factors of the sum are equal to the sum of the factors."
Used for: Distributing a multiplier over a sum using the distributive property for faster mental calculation.
Example: 11(9 + 4) = 143