Speed tricks

Fifteen ways to do a sum in your head in a line or two. Each one is built on a sutra from Bharati Krishna Tirtha's 1965 book Vedic Mathematics, and each page has a calculator that works the steps on the numbers you type.

• Square numbers ending in 5Any number that ends in 5: 35², 85², 115².
• Multiply numbers near 10, 100 or 1000Both numbers are close to the same power of ten: 97 × 94, 103 × 108, 996 × 989.
• Multiply any two numbers in one lineAny multiplication. Fastest for 2-digit and 3-digit numbers.
• Subtract from 100, 1000, 10000Subtracting from a power of ten, like 1000 − 387 or 10000 − 2456 (change at the store).
• Multiply by 9, 99 or 999Multiplying by a string of nines that has at least as many digits as the other number: 42 × 99, 357 × 999.
• Same start, last digits add to 10Both numbers start the same and their last digits add to 10: 43 × 47, 62 × 68, 104 × 106.
• Square numbers near a baseSquaring numbers near 10, 100 or 1000: 97², 104², 1012².
• Multiply by 11Any number times 11.
• Divide by 9 with running sumsDividing any number by 9.
• Check answers with digit sumsChecking any multiplication (or addition) answer in seconds.
• Multiply by 5, 25, 50 and 125Multiplying by 5, 25, 50 or 125.
• Multiply with a working base like 50Both numbers sit near 20, 30, 40, 50 ... like 46 × 43 or 52 × 48.
• Square any two-digit numberSquaring any two-digit number, like 47² or 83².
• Square roots by lookingSquare roots of perfect squares up to 9801.
• Cube roots in two secondsCube roots of perfect cubes up to 970299 (roots up to 99).

Practice them with lessons, Katas and daily rounds in the game. The sutras are not found in the Vedas: each one is ordinary algebra you can check, and the 29 sutras page explains every one.