Division Algorithm

Division:

42 / 7 = ?

(Dividend) / (Divisor) = (Quotient)

The divisor 7 is set in the setting register and plus turns of the handle are made until the

dividend 42 is built up in the black dial. The white dial registers each turn made. It indicates

how often the divisor is contained in the dividend and thus shows the quotient.

1. Machine ready! (reversing lever in upper position!).

2. Setting register: with knob 1 set "7" (Divisor).

3. Handle: while watching the black dial make plus turns until the dividend 42 appears in the black dial. (If by doing a turn too many you overstep the required dividend, the black dial showing e. g. 49, you will have to make each time a minus turn immediately.)

As soon as the number 42 (dividend) appears in the black dial you can read off the quotient 6 in the white dial.

Answer: White dial: 6 (quotient) Check: Black dial: 42 (dividend), Setting dial: 7 (divisor)

For divisions giving quotients with several digits, before operating you place the carriage into one of its higher positions, corresponding to the number of digits expected for the quotient. If, for instance, you start operating with the carriage in position 3 you will obtain a quotient of 3 digits. However, to avoid unnecessary thinking, the general rule to follow is to start every division with the carriage in its highest position (pos. 6 for CURTA I and pos. 8 for CURTA II). As soon as the required degree of accuracy (number of digits) for the quotient has been attained or when the division finishes you break off the calculation as the following example will show.

Remark: When the divisor is a large number it may not always be possible to start operating in the highest position of the carriage and one of the next lower positions will have to be chosen so that all the digits of the divisor are transferred into the left-hand part of the black dial with the first plus turn of the handle.

1728 / 12 = ? 1. Machine ready!

2. Setting register: with knobs 1 and 2 set 12".

3. Carriage: place in its highest position (pos. 6 CURTA I, pos. 8 CURTA II).

4. Handle: plus turns until the dividend 1728 is attained or overstepped in the black dial.

When the dividend has several digits as in this case, it is sufficient to start with that the first 2 or 3 highest digits of the dividend are reached in the black dial. After 2 plus turns the black dial shows 24...0. The first 2 digits (17...) of the dividend have been overstepped. One minus turn (the black dial now shows 12...0).

5. Carriage: place in the next lower position (pos. 5 CURTA I; pos. 7 CURTA II).

6. Handle: after 5 plus turns the first three highest digits of the dividend (172...) have been overstepped, the black dial showing 180...0. 1 minus turn. (The black dial now shows 168...0.)

7. Carriage: place in the next lower position (pos. 4 CURTA I; pos. 6 CURTA II).

8. Handle: after 4 plus turns the dividend 1728 has been reached in the black dial and the calculation can be broken off.

9. Black dial: set a decimal marker after the last whole number of the dividend, that is immediately behind the "8 . In the setting dial we have the whole number 12; there is no need to set a decimal marker.

Decimal rule for divisions: the decimals in the black dial (dividend) minus the decimals in the setting dial (divisor) give the number of decimals in the white dial (quotient).

In this case with CURTA I we find 3 - 0 = 3 decimal places and with CURTA II 5 - 0 = 5 decimal places in the white dial.

10. White dial: set a decimal marker immediately behind the last 4 of 144, leaving 3 zeros for CURTA I and 5 zeros for CURTA II after the decimal point. The quotient in the white dial is 144.0...

Answer: White dial: 144.0... (quotient) Check: Black dial: 1728 (dividend), Setting dial: 12 (divisor)

17.29 / 1.2 = ?

For divisions that do not finish it is sufficient to attempt building up in the black dial a number that comes as near as possible to the given dividend. To start with the decimals of the dividend and the divisor are not taken into consideration.

1. Machine ready!

2. The instructions of the previous example (1728 / 12) are to be followed exactly up to and including fig 7. Then continue as follows:

3. Handle: after 5 plus turns, the black dial showing 1740, the dividend has been over-stepped. 1 minus turn.

4. Carriage: place into next lower position.

5. Handle: after 1 plus turn, the black dial showing 17292, the dividend has been overstepped again. 1 minus turn.

6. Carriage: place into next lower position.

Handle: after 9 plus turns, the black dial showing 172908, the dividend has been overstepped. 1 minus turn.

7. Carriage: place into next lower position.

Handle: after 4 plus turns, the black dial showing 1729008, the dividend has been overstepped. 1 minus turn.

With CURTA model I the 6 digits of the white dial have now been developed and the calculation is finished.

With CURTA model II another 2 digits can be developed in the white dial for the quotient, since the carriage can be moved to 2 further positions (pos. 2 and 1).

8. Carriage: place into next lower position.

Handle: 4 plus turns, 1 minus turn.

9. Carriage: place into next lower position.

Handle: 4 plus turns, 1 minus turn.

The 8 digits of the white dial are now developed and the calculation is finished.

10. Markers: Set the decimal markers: in the setting dial between columns 2 and 1 (1.2), and in the black dial immediately after the last whole number of the dividend, that is behind the "7" (17.289...). Applying the decimal rule we find for the white dial of CURTA I 5 - 1 = 4 decimal places, and for that of CURTA II 7 - 1 = 6 decimal places.

Answer: White dial: 14.4083[33] (quotient) Check: Black dial: 17.2899..6 (dividend), Setting dial: 1.2 (divisor)

Remainder: When closing the division the remainder can always be determined as the difference between the given dividend and the number in the black dial. Here the remainder would be for CURTA model I: 17.29 - 17.28996 = remainder 0.00004;

for CURTA model II: 17.29 - 17.2899996 = remainder 0.0000004.

(Remark: If, for instance, only 3 digits of the quotient bad been asked for you could have broken off the calculation when 17.28 was reached in the black dial. The corresponding quotient would have been 14.4 and the remainder 0.01.)

In cases where the remainder is irrelevant it is advisable to work out the last digit of the quotient to the highest possible accuracy by leaving in the black dial the number giving the nearest approximation to the required dividend. Those who are already familiar with calculating machines can equally well divide by the subtractive method for which they will have to set the reversing lever (fig 8 front page) into its lower position. The decimal rule remains unaltered. Division by the subtractive method is however advisable only in cases where the dividend is already in the left-hand side of the black dial as a result of some previous operation (f. ex. an addition or multiplication, see CURTA Computing Ex. p. 7).