One of historically retained and fancy methods of multiplication often called the Russian peasant algorithm. You don’t need multiplication facts to use the Russian peasant algorithm; you only need to double numbers, cut them in half, and add them up. Here are the rules:
Russian Peasant Multiplication is actually a way of simultaneously converting a number to binary and multiplying it by another number. To make it simple we take easy example: 10 x 6.
10 = 1010 in binary (reading the remainders upwards). This means that
10 = 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0 = 2^3 + 2^1 = 8 + 2
| Divide by 2 | Remainder | Power of 2 | Double | Sum |
|---|---|---|---|---|
| 5 | 0 | 1 | 6 | 0 |
| 2 | 1 | 2 | 12 | 12 |
| 1 | 0 | 4 | 24 | 0 |
| 0 | 1 | 8 | 48 | 48 |
This also corresponds to how binary numbers are multiplied, because all we do is multiply 6 by either a one or a zero in each place (which is really just selecting whether to include it in the sum), and shift it one place to the left each time (which is really a doubling):
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