By combining the rules for multiplication and division, we can readily
evaluate expressions of the form (_a_)/(_b_) × (_c_)/(_d_) × (_e_)/(_f_)
× (_g_)/(_h_) = _x_. The simplest case, (_a_ × _c_)/(_b_) can be solved
by one setting of the slide.[3] Take as an example, (14·45 × 60)/(8·5) =
102. Setting 8·5 on C to 14·45 on D, we can, if desired, read 1·7 on D
under 1 on C, as the quotient. However, we are not concerned with this,
but require its multiplication by 60, and the slide being already set
for this operation, we at once read under 60 on C the result, 102, on D.
The figures in the answer are obvious.
When there are more factors to take into account, we place the cursor
over 102 on D, bring the next divisor on C to the cursor, move the
cursor to the next multiplier on C, bring the next divisor on C to the
cursor, and so on, until all the factors have been dealt with. Note that
only the first factor and the result are read on D; also _that the
cursor is moved for multiplying and the slide for dividing_.
_Number of Digits in Result in Combined Multiplication and
Division._—For those who use rules the author’s method of determining
the decimal point in combined multiplication and division may be used.
Each time _multiplication_ is performed with the slide projecting to the
_right_, make a − mark; each time _division_ is effected with the slide
to the right, make a | mark; _but allow the_ | _marks to cancel the_ −
_marks as far as they will_. Subtract the sum of the digits in the
denominator from the sum of digits in the numerator, and to this
difference _add_ any uncancelled memo-marks, if of | character, or
_subtract_ them if of − character.