# Multiply into double no

When I was 8 years old. I see a little logic behind this which improves my speed in this type of questions.
For this first square the smaller no.(if you don’t Know how to get square many technics are here)
And double it.
Example - 12 * 24
12^2 * 2(it can done simply in mind)
144 * 2 = 288

Example - 48 * 96 = 2304 * 2 = 4608

Example - 57 * 114 = 3249 * 2 = 6498

I hope you understand it.If you do it with my logic you can do this very quickly.

2 Likes

A great technique!

I use it, especially when the application is obvious.
For example:

50 * 34 = 50 * 2 * 17 = 100 * 17

or

25 * 16 = 100 * 4

I would do 100 * 34 = 340 / 2 = 170, which amounts to the same thing; I just like multiples of the radix. It’s probably a bad habit to have all these factors set aside for a step or two, though.

Not exactly the same… @Kinma is taking one of the prime factors of 34 over to the left, which leaves him with 17 on the rhs and double of his original number on the lhs.

That’s a more general application of what @Rajadodve786 was doing. I his case the second number is double the first number. So if you look at the prime factors, you can take all of them to the left, which gives you the original number squared and leaves a 2 on the right hand side.

If you prefer division over multiplication, as would be the case with his second example \color{blue}48 * 96 you could also double the smaller number and then take half of the answer (i.e., removing the prime factor that you’ve added before):

\begin{array}{rr} &96 &-4 \\ &96 &-4 \\ \hline &92 &16 \end{array}

Crosswise you get 96-4=92 for the lhs and (-4)^2=16 for the rhs. Half of that is then 46\ 08.