Same start, last digits add to 10

From the sub-sutra Antyayordaśake'pi, When the last digits add to ten, in Bharati Krishna Tirtha's 1965 book Vedic Mathematics. Deep dive into the sub-sutra

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When to use it

Both numbers start the same and their last digits add to 10: 43 × 47, 62 × 68, 104 × 106.

The idea

Multiply the shared start by one more than itself. Then multiply the last digits and write that as two digits.

Worked example: 43 × 47

1. 43 × 47Shared start: 4. Last digits 3 + 7 = 10, so the trick works.
2. 20 | 4 × 5 = 20.
3. 20 | 213 × 7 = 21, written as two digits: 21.
4. 2021So 43 × 47 = 2021.

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.