Rapid Math

Multiplication

To calculate $5 \times n$, it is often faster and safer to take half of $n$ and then multiply by 10 and then divide by 2. For instance, $5 \times 92 = 10 \times 46 = 460$.
To calculate $k \times n$ where $k$ is a multiple of 2, it is often faster and safer to multiple successively by 2.

It is useful to simply memorize as many squares as you can.
If you know most of your squares but forget one, you can reconstruct it from the previous one: $(n+1)^2 = n^2 + n + (n + 1)$. For example, $13^2 = 12^2 + 12 + 13 = 169$. This is an algebraic identity, but you can also visualize the identity by imagining a square with side $n$ and then expanding each side by 1: the expansion will add a rectangle of $1 \times n$ to the top and another to the side, plus a $1 \times 1$ square in the new upper right corner.
If you need to figure out the product of two numbers that are two apart, just subtract 1 from the square of the number between them: $(n-1)(n+1) = n^2 -1$. For example, $13 \times 15 = 14^2 -1 = 196- 1 = 195$.
Similarly, $(n-2)(n+2) = n^2 – 4$. To generalize, $n – k)(n + k) = n^2 – k^2$. If you would like, for two numbers you can find $n$ by averaging them and $k$ by taking half their difference, but at some point this will probably becomes less efficient for you than long multiplication.