Multiplication
and Division

These
pages discuss the rules for simple multiplication and multiplication Case II.

Simple
Multiplication

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: ÒThe 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 productÓ

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: ÒWhen 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 requiredÓ

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.