[peterburkimsher]

When I was in primary school, I had to memorise the "times tables".

I realised that the digits of multiples of 9 that are under 100 always add up to 9. I was surprised when I discovered that other students didn't notice this.

Others tables are easy: 10x (just add a 0), 5x (half of 10), 2x, 4x, 8x (keep multiplying by 2). That only leaves 3x, 6x, 7x, and 12x to memorise.

Now I have a calculator watch, I don't need to remember the times tables. But when I was younger, it was very important to my teachers. I wish methods like this were taught instead of "just memorise it".

[dpwm]

I was actually taught this in a small village primary school as a way to remember the 9 times table up to 90. I think we were also taught how to apply it quickly: If you want n * 9, the first digit is n - 1 and the second is 9 - (n - 1).

Of course, it fails at 99. It wasn't until much later that I learnt that all multiples of 9 have the property of their digits adding up to multiples of 9 and that there exist proofs.

[superflyguy]

An easy way of lower multiples of nine is to hold your hands in front of you, and if you want to work out, say, 4 times 9 put down your forth finger and look at the number of fingers on each side of that finger...

[macintux]

Another useful trick the other direction, which I'm sure is mentioned somewhere in the article or the comments but what the heck: if the sum of the digits of a number is divisible by 3, so is the original number itself.

123: 1 + 2 + 3 = 6, 6 rem 3 == 0, so 123 is cleanly divisible by 3.

123456789: sum is 45, 4+5 is 9, 9 rem 3 == 0, so 123456789 is divisible by 3.

[Scarblac]

3 is easy, the sum of the digits is divisible by 3. So 6 is easy too, divisible by 3 and 2.