# Multiplication Algorithm

Although I do NOT have a Curta, I have figured out an accurate version for multiplication that is a modification of addition. This process will take a long time for numbers that involve many digits, but it is easy.

2. Set larger multiplicand (or number in laymans terms) on the side of the drum using the set counters

3. Rotate crank the same number of turns as the smaller number, as indicated in the WHITE turns field

4. The final value is expressed in the BLACK answer field

For example, we have a problem that states 90X10, we set the number 90 on the side and rotate the crank ten times. The final answer should be 900.

I have found another multipication algorithm at www.vcalc.net. it is explained here (credits go to the aforementioned website).

13.6 x 1.15 = ?

2. Setting register: with knobs 1 to 3 set '136". For marking the decimal point use one of the white mobile decimal markers (see picture "view of the CURTA"). Place one of the decimal markers at the base of the machine between the setting columns 1 and 2 and read 13.6.

3. Handle: 5 plus turns

4. Carriage: position 2

5. Handle: 1 plus turn

6. Carriage: position 3

7. Handle: 1 plus turn

8. White dial: set a decimal marker between the second and the third dial slot and read 1.15.

Decimal rule for multiplications:

The number of decimal places in the black dial is equal to the sum of the decimal places in the setting dial and the white dial.

In this example we have 1 decimal place in the setting dial and 2 in the white dial. Therefore in the black dial we have 1 + 2 = 3 decimal places. Set a decimal marker between slots 3 and 4 in the black dial.

Answer: Black dial: 15.640 Check: Setting dial: 13.6, White dial: 1.15

Short-cut multiplication:

457 x 89 = ?

2. Setting register: with knobs 1 to 3 set 457". Normally we would now make 9 turns of the handle with the carriage in position 1 and 8 turns with the carriage in position 2, that is all together 17 turns of the handle. The same calculation can be done, however, with only 3 turns of the handle. 89 = (100 - 11) or ( -11 + 100). We therefore calculate 457 x ( -1 - 10 + 100).

3. Handle: 1 minus turn (with handle in upper position): = -1

4. Carriage: position 2

5. Handle: 1 minus turn: = -10

6. Carriage: position 3

7. Handle: 1 plus turn (with handle down in its normal position): = +100

Answer: Black dial: 40673 Check: White dial: 89, Setting dial: 457

This short-cut method is recommended whenever the numbers to be developed for the multiplier are 6, 7, 8, or 9. It will save considerable time and effort.

Serial multiplication (A*B*C*D...)

**********

Serial multiplication without clearing (method 1):

5*7*12*36

First, enter 5 in SR, and crank 7 times to get 35 in RR

Now enter 12 in SR. Since we want to get 35 *twelve* times, and we already have 35 *one* time in the RR, we need (12-1) *more* 35s. So decrease 12 by one in the SR to 11.

Now so you don't forget how many times to turn, move the registers so the leftmost digit of current result (35) lines up with rightmost digit of SR (11). See a 3, crank three times. Move one to the right, see a 5, crank 5 times. Now you have 420.

Enter (36-1)=35 in SR. Line up the 5 with the 4 in 420. Crank 4 times, twice in the next position, 0 times in the last position. Now you have 15120.

**********

Serial multiplication without clearing (method 2):

5*7*12*36

First, enter 5 in SR, and crank 7 times to get 35 in RR

Now enter 11.9 in SR. Since we want to get 35 *twelve* times, and we already have 35 *one* time in the RR, we'll move the decimal one to the left. Now we have 35 *0.1* times, and we need (12-0.1) *more* 35s. So decrease 12.0 by 0.1 in the SR to 11.9.

Now so you don't forget how many times to turn, move the registers so the leftmost digit of current result (35) lines up with rightmost digit of SR (11.9). See a 3, crank three times, UNTIL THE DIGIT GOES TO ZERO. Move one to the right, see a 5, crank 5 times, UNTIL THE DIGIT GOES TO ZERO. Now you have 420. Sending the digit to zero is the advantage of this method over method 1, you don't have to remember how many times to crank. However, you do use up more decimal places.

Enter (36-0.1)=35.9 in SR. Line up the 9 with the 4 in 420.0. Crank 4 times (UNTIL ZERO), twice in the next position, 0 times in the 3rd position. Now you have 15120.00.