Multiplication and Division
These pages discuss the rules for simple multiplication and multiplication Case II.
There is no scratch work provided for this problem. The two options are that they did their scratch work on a separate document, or they performed the arithmetic mentally. It does not say in the text, but I wonder if they defined simple multiplication as multiplying by a number less than or equal to twelve or some other number. The process for this problem seems to be 2 x 4 = 8, which gives us the ones digit. To get the tens digit they performed (2 x 1) + (1 x 4) = 6. This method is continued for the rest of the calculation. For this type of problem they did not multiply 2 x 4684114 = 9368228 then multiply 10 x 4684114 = 46841140. Finally, adding the two products 9368228 + 46841140 = 56209368.
Multiplication Case II
Now we will look at multiplication Case II. This case of multiplication is the same as our standard form. The only difference is that they do not place zeros where values do not apply.
Multiplication Case II Rule: “The multiplier being placed under the multiplion units under units tens under tens multiply by each significant multiplier separately placing the first figure in each product exactly under its multiplier then add the several products together in the sum under as they stand and their sum will be the total product”
Multiplication Case III and Case IV
These pages contain the procedures for multiplication Case III and Case IV.
Multiplication Case III
Multiplication Case III deals with numbers that contain zeros at the right hand of either or both numbers.
We see that the numbers are lined up using the first digit of each number that does not contain a zero. So the problem now becomes 318 x 36 while the zeros are just carried down.
For the case when both numbers contain trailing zeros they are lined up as depicted in this image.
Multiplication Case IV
Multiplication Case IV Rule: “When the multiplier is a composite number that is when it is produced by multiplying any two numbers in the table together exactly first by one of those figures and that product by the other and the last product will be the total required”
The examples found for Case IV do not seem to follow the rule. By the definition of the rule I would think that 615243 x 144 = 88594992 becomes (615243 x 12) x 12 = 88594992.
Multiplication Case V and Division of Whole Numbers
Multiplication Case V
Multiplication Case V deals with applications and multiplication. These problems are multiplying a price and a quantity to find the total price.
Next we see division of whole numbers.
Division of Whole Numbers
The format for these problems is a little different from our standard form. The difference is that the quotient is placed to the right of the dividend.
Additional Method of Division
Contractions in division is another method. This method of division is comparable to the Case IV of multiplication.
Here we have 178464 16. This is being simplified as (178464 4) 4.
The end of the ciphering book contains more practical examples. There are also tables for clothe measure, dry measure, wine measure, long measure, and solid measure.