The Russian Peasant Multiplication method is an ancient technique for multiplying two numbers using a process of halving one number and doubling the other, discarding rows where the halved number is even, and summing the remaining doubled numbers.
Here's a step-by-step breakdown with an example (24 x 16 from the provided video):
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Set up two columns: Write the two numbers you want to multiply at the top of two columns. In our example, these are 24 and 16.
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Halve and Double:
- In the left column, repeatedly halve the number, discarding any remainders (integer division). Continue until you reach 1.
- In the right column, repeatedly double the corresponding number.
This looks like:
Halve (Discard Remainder) Double 24 16 12 32 6 64 3 128 1 256 -
Discard Even Rows: Go through the left column and cross out any rows where the number in the left column is even.
This leaves us with:
Halve (Discard Remainder) Double 241612326643 128 1 256 -
Sum the Remaining Doubles: Add up the numbers that were not crossed out in the right column.
128 + 256 = 384
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The Result: The sum is the product of the original two numbers. Therefore, 24 x 16 = 384.
Why does it work?
The method essentially decomposes one of the numbers into a sum of powers of 2. By repeatedly halving and doubling, you are identifying which powers of 2 are present in the binary representation of the halved number. The doubling process then scales the other number accordingly. By discarding the even rows, you are discarding powers of 2 that are not present. Finally, the summation recombines the scaled values to arrive at the product.
