Hacker News Reader

I found myself thinking about multiplication tables in the shower today. I think you can get away with knowing the tables for 2, 3, and 7 really well. The rest is just tricks:

4: 2x twice

5: add a zero and divide by 2

6: a 3x followed by a 2x

8: 2x three times

9: 3x twice

Beyond that, it’s repetition of those tricks, plus the distributive property of multiplication over addition.

View on HN

Also (x+1)(x-1) = xx -1 helps if you know the squares 1x3 = 2x2-1, 2x4 = 3x3-1, 3x5 = 4x4-1, 4x6 = 5x5-1, 5x7 = 6x6-1, 6x8 = 7x7-1, 7x9 = 8x8-1, ...

Nice, though I still prefer the trick for 9 that I was taught:

9: 10x, then subtract once.

Another: for X from 1 to 10, the digits of 9x will add to 9, and the leading digit will be x-1. You can do this visually by putting up all your fingers and putting down the Xth one - this splits your fingers into two groups, the first is the tens place digit while the second is the ones place digit.

They keep adding to nine. 137×9 = 1233 . 34457×9=310113. When it breaks down: 99x9=891 sums to 18, sums to 9.

99 on its own is also an example where it breaks down, which is why I stopped at 10, but yes all multiples of 9 in base 10 have digits summing to a multiple of 9.

Reply on news.ycombinator.com