For example, try multiplying 146 x 37.
In this example, write “146” at the top of the left column, and “37” at the top of the right column.
Start by halving 146 (146 ÷ 2 = 73). Write “73” in the left column below “146. ” Next, halve 73 (73 ÷ 2 = 36 with a remainder of 1). Write “36” in the left column below “73,” ignoring the remainder. Next, halve 36 (36 ÷ 2 = 18). Write “18” in the left column below “36. ” Next, halve 18 (18 ÷ 2 = 9). Write “9” in the left column below “18. ” Next, halve 9 (9 ÷ 2 = 4 with a remainder of 1). Write “4” in the left column below “18,” ignoring the remainder. Next, halve 4 (4 ÷ 2 = 2). Write “2” in the left column below “4. ” Finally, halve 2 (2÷ 2 = 1). Write “1” in the left column below “2. ”
Each column should have 8 numbers in it. This is because it took seven steps of dividing the original number in the right column to reach 1. In the right column, start by doubling 37 (37 x 2 = 74). Write “74” in the right column below “37. ” Next, double 74 (74 x 2 = 148). Write “148” in the right column below “74. ” Next, double 148 (148 x 2 = 296). Write “296” in the right column below “148. ” Next, double 296 (296 x 2 = 592). Write “592” in the right column below “296. ” Next, double 592 (592 x 2 = 1184). Write “1184” in the right column below “592. ” Next, double 1184 (1184 x 2 = 2368). Write “2368” in the right column below “1184. ” Finally, double 2368 (2368 x 2 = 4736). Write “4736” in the right column below “2368. ”
There are 8 rows. You will strike through 5 of them. Strike through the rows beginning with 146, 36, 18, 4, and 2 in the left column, since these are even numbers. Working left to right, this means striking through the first row (146, 37), the third row (36, 148), the fourth row (18, 296), the sixth row (4, 1184), and the seventh row (2, 2368). Please note that you should strike through even numbers, even if they begin with an odd numeral. For example, you should strike through the row beginning with 146 since it is an even number, even though 146 begins with an odd numeral, 1. Likewise, you should strike though 36, since it is an even number, even though 36 begins with an odd numeral, 3. If you prefer, you can just strike through the numbers in the right side that fall into the rows that begin with an even number on the left side (as in the picture above). In this example, this means striking through the numbers on the right hand side of the first, third, fourth, sixth, and seventh rows: 37, 148, 296, 1184, and 2368.
The remaining numbers in the right column are 74, 592, 4736. Add these numbers to get the sum of 5402 (74 + 592 + 4736 = 5402). This number is the product of multiplying the original numbers in this example, 146 and 37 (146 x 37 = 5402).
Write “146,” and then “37” below it so that the numbers line up flush on the right side. Draw a line below these numbers to create a work area. You will do your calculations below this line. Multiply 7 x 6 (= 42). Write “2” down in the work area and carry the “4. ” Multiply 7 x 4 (= 28). Add the carried “4” to this sum to get a new sum, 32 (4 + 28 = 32). Write down “2” in the work area to the left of “2” you wrote down in your work area, and carry the “3. ” Multiply 7 x 1 (= 7). Add the carried “3” to this sum to get a new sum, 10 (7 + 3 = 10). Write down “10” in your work area, to the left of the “22” that is already there. You should now have the number “1022” written down in your work area. Start working on a new row in your work area, directly below “1022. ” Write “0” on the right of this new row, directly below the rightmost “2” of “1022. ” Multiply 3 x 6 (= 18). Write “8” to the left of the “0,” and carry the “1. ” Multiply 3 x 4 (= 12). Add the carried “1” to this sum to get a new sum, 13 (12 + 1 = 13). Write down “3” in your work area to the left of the “8,” and carry the “1. ” Multiply 3 x 1 (= 3). Add the carried “1” to this sum to get a new sum, 4 (3 + 1 = 4). You should now have the number “4380” written in the second row of your work area. Add the two rows in your work area (1022 + 4380). You should get the sum 5402 (1022 + 4380 = 5402). This sum, which is the same number derived by the Russian peasant method, verifies that the method produced the correct answer.
Enter 146 in the calculator by pressing the corresponding digits, 1, 4, 6. Press the multiplication (“x”) key. Enter 37 in the calculator by pressing the corresponding digits, 3, 7. Press the equals (“=”) key. The display should show “5402,” which is the same number derived by the Russian peasant method, verifying that the method produced the correct answer.
First, try checking your work again using the standard multiplication method or a calculator, just to be sure. Then, work through the problem again using the Russian peasant method. This time, double-check to make sure you are halving and doubling the numbers correctly. In addition, make sure you correctly add the numbers that remain in the right-hand column after you cross out the other numbers. Check all of your work twice to make sure that you get the correct answer.
You don’t need to know or memorize multiplication tables in order to multiply using the Russian peasant method (like you do in order to use standard long multiplication). As long as you can double and halve, you can multiply any two numbers using the Russian peasant method. You can use bits of material in order to multiply using the Russian peasant method. This can be useful when you need to multiply and you don’t have a calculator or a pencil and paper handy. For example, you could multiply the example above (146 x 37) by using lots of beans or other material. Each time you need to halve or double a number in the process, just add or take away the respective number of beans. The Russian peasant method does normally take longer than standard long multiplication, however. In addition, the Russian peasant method of multiplication can become very unwieldy if you are trying to multiply large numbers, since this will involve many multiples of 2 or numbers that are factors of numbers divisible by 2, and potentially very large ones.
