Russian peasant multiplication

The Russian peasant multiplication, also called the Russian peasant algorithm, uses a halving and doubling method to multiply whole numbers. I will illustrate the method with some good examples that you should study carefully.

Russian peasant multiplication

Did you understand the example shown in the figure above? If not, do not worry at all. Just keep reading this lesson and you will realize that it is easy and straightforward.

A few important things to keep in mind when using the Russian peasant multiplication to do multiplication

  • The first row always has the multiplication problem that you are doing.
  • When halving, disregard any remainder. Just put the quotient in the halving column. For example, suppose 15 is already in your halving column. 15 ÷ 2 = 2 × 7 + 1. Put 7 in the halving column beneath 15.
  • When a number in the halving column is 1, cross out all rows that have an even number in the halving column.
  • The halving column may not have any even numbers even if it has a 1 in it.
  • The answer is found by adding the remaining numbers in the doubling column.

Keeping this guideline in mind, you could also do the multiplication of 15 times 10 by putting 10 in the halving column and 15 in the doubling column. The answer is still the same as shown below. Notice also how we crossed out all rows that have an even number in the halving column. We did this because as already stated, there is a 1 in the halving column.

Russian peasant multiplication

More examples showing how to multiply using the Russian peasant multiplication.


Example # 1: 11 × 12


Halving                              Doubling

   11                    ×                  12

   5                      ×                  24

   2                      ×                  48

   1                      ×                  96

Using the Russian peasant multiplication, the sum is 12 + 24 + 96 = 132


Example # 2: 37 × 42


Halving                              Doubling

   37                    ×                  42

   18                    ×                  84

   9                      ×                168

   4                      ×                336

   2                      ×                672

   1                      ×              1344

Using the Russian peasant multiplication, the sum is 42 + 168 + 1344 = 1554


Example # 3: 20 × 20


Halving                              Doubling

   20                    ×                  20

   10                    ×                  40

   5                      ×                  80

   2                      ×                160

   1                      ×                320

Using the Russian peasant multiplication, the sum is 80 + 320 = 400.

Your turn! Try the following few multiplications using the Russian peasant multiplication.

16 × 15

100 × 6

24 × 24

100 × 1

100 × 100

100 × 6

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