Russian Abacus
Abacus (Russian abacus) - a simple mechanical device for performing arithmetic calculations.
Famous wooden abacus, (depicted on the left), were widely used in the USSR in the first two-thirds of the twentieth century, mainly for operations of addition and subtraction. How did the cashiers and accountants use these Russian accounts? Let's figure it out.
In the initial position in the "zeroed" abacus all the bones are aligned to the right. Each row of bones is a digit of a number, and the units are over four bones. Above units - tens, hundreds, etc., below - quarters, tenths and hundredths. With this approach, it is convenient to count money, where there are quarters in the course (for example, 25 cents). The central bones are highlighted in black (for convenience).
A set of numbers. If we want to set a number on the abacus (to perform further arithmetic with it later), we just need to move the right bones to the left. For example, to dial the number "3 251.5" we move 2 quarters (or 5 tenths), 1 unit, 5 tens, 2 hundreds and 3 thousand.
To add two numbers to the abacus, you just need to type one number with the bones, and then move each digit of the second number to the left starting from the bottom rows (namely from the bottom!). If it suddenly turns out that there are not enough bones in a row, then you need to leave as many bones in the row as there are not enough, and at the level above throw one more bones to the left.
Subtraction on abacus is made in exactly the same way as addition, from top to bottom. Only if there are not enough bones in the row, in this row you need to leave (10-x) bones, where x is the number of missing bones, and in the row above you need to remove one bone (move it to the right)
In order to multiply the number by 2 or 3, you simply add this number with yourself (multiply by 2), and repeat this procedure when multiplying by 3. Multiplication by 4 is performed as multiplication by 2, and then multiplying by 2 the result obtained . As for multiplying by 5, as you can see from this lesson, it is equivalent to dividing by 2 and then multiplying by 10. In this case, after dividing by 2, you simply transfer the digits (knuckles) to a higher level. Multiplication by large numbers is accomplished using a combination of the methods described.
The division into Russian abacus is a rather complicated procedure. To use the scores for this purpose is sometimes simply irrational. If the example is convenient, for example, you need to divide 280 by 2, then indeed, you just need to move half of the knuckles out of each row and then you will get 140. But other examples mostly require complex algorithms and a good development of attention and short-term memory.