Check answers with digit sums

From the sutra Guṇita Samuccayaḥ, The product of the sums is the sum of the product, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sutra

Try it with your numbers

First number Second number

Show stepsNew numbers

When to use it

Checking any multiplication (or addition) answer in seconds.

The idea

Add the digits of each number until one digit is left (9 counts as 0). The digit sums must multiply to the digit sum of the answer.

Worked example: 23 × 14 = 322

1. 5 × 5Digit sum of 23 is 5 and of 14 is 5 (casting out nines).
2. 75 × 5 = 25, which reduces to 7.
3. 7 = 7 ✓Digit sum of 322 is 7. They match, so the product passes the check.

Practice this trick

All 15 speed tricks, each with its calculator. The speed tricks use sutras from Bharati Krishna Tirtha's 1965 book Vedic Mathematics; the lessons, problems and pictures here are our own.