> But you can break this into a different problem knowing that 2^3 = 8, and doing 7*2*2*2.
Doing that multiplication all the way through is super slow. When they said "can't" they meant in an effective sense, since they did mention repeated addition as an option. And that's not an effective way to get there.
> There are other ways of seeing the multiplication table as well. For example 9 times something can be thought of as 9*x = 10*x-x.
Yes, you can do that one. But that's just about the only fast trick there is.
> Yes, you can do that one. But that's just about the only fast trick there is.
I dunno about that. For division, anyway, there's a bunch of fast tricks that give you a decent approximation (i.e. decent precision, maybe to the nearest integer)
Someone recently was surprised that I worked out the VAT (Value Added Tax, 15%) on a very large number in a few seconds. It's because its 10% of the number plus `(10% of the number)/2`.
It's easy to get 10% of any number. It's easy to halve any number. It's a fast trick because there's two easy operations.
There's a bunch of similar "tricks": 1%, 10%, 25% and 50% are fast to calculate in your head (at most 2 easy operations, like `(half of half of N)`). Then you either add or subtract N. Or you multiply N by 2.
At most three easy operations gives you 1%, 2%, 4%, 5%, 10%, 11%, 12%, 14%, 15%, 20%, 21%, 24%, etc
To someone who doesn't know how you are getting the answer it might seem like you are a human calculator because you get so many of those quickly, and they don't see the ones you don't do in 3 easy operations (say, 13%, which is 10% + 1% + (1% * 2)).
IOW, it looks like a very impressive trick, but it isn't.
Doing that multiplication all the way through is super slow. When they said "can't" they meant in an effective sense, since they did mention repeated addition as an option. And that's not an effective way to get there.
> There are other ways of seeing the multiplication table as well. For example 9 times something can be thought of as 9*x = 10*x-x.
Yes, you can do that one. But that's just about the only fast trick there is.