This method involves a process of halving and doubling, which reduces one factor to powers of two and uses the distributive property of multiplication over addition to calculate a product.
Multiplication
25 37
3 296
1 592
------------------------- Therefore, 37 + 296 + 592 = 925
925 ( 25 x 37 = 925 )
Process
1. Create
column beneath each of the factor.
2. Repeatedly halve the number in the left hand column, drop any remainder, until reach to 1.
3. Repeatedly
multiply the right column by 2.
4. Erase
the rows that have any even number on the left column.
5. Add
remaining numbers in the right hand column to get the answer.
Behind the Scene
The fact
that this procedure is dependent on multiplication by two, suggests that this
is founded in binary system. Let’s see the binary representation of 25.
Power
of 2
|
24
|
23
|
22
|
21
|
20
|
Decimal
equivalent
|
16
|
8
|
(4)
|
(2)
|
1
|
Binary
representation
|
1
|
1
|
0
|
0
|
1
|
We found binary representation of 25 is 110012. Now take
another look at our multiplication.
Multiplication Binary Decimal
25 37 1 x 20 1
3 296 1 x 23 8
1 592 1 x 24 16
------------------------- -------- ----+
925 110012 25
So, we
can see that adding two additional columns clearly show the relationship
between the multiplication with the binary system. Because the binary digit
represents the remainder in division by power of "two", digit "one" corresponds to odd
numbers in the column and "zero" corresponds to even number, thus only the rows
with odd numbers will contribute to the multiplication.
Russian
peasant multiplication is actually a quick way to convert two numbers to binary
form, multiply them together, and convert back to our number system. The
connection is not surprising, because binary numbers use base two, and Russian
Peasant Multiplication depends on multiplying and dividing by two.
reminder —> remainder
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