Division by a Fractional Expression
In this section numbers are divided by groups of fractions
Example:
Problem 32: A quantity, it's 1/3, and it's 1/4, added together, become 2. What is the quantity?
Multiply 1 1/3 1/4 so as to get 2.
1 becomes 1 1/3 1/4
\2/3 becomes 1 1/18
\1/3 becomes 1/2 1/36
\1/6 becomes 1/4 1/72
\1/12 becomes 1/8 1/144Take 12 times 12.
1 becomes 12
2 becomes 24
\4 becomes 48
\8 becomes 96
Total: 144We will apply our fractions to 144. For the given expression we have
\1 becomes 144
\1/3 becomes 48
\1/4 becomes 36
Total: 228The products above, taken as parts of 144, are equal to
228, 152, 76, 38, 19
The sum of the numbers here that correspond to the multipliers checked is equal to 285 and requires 3 more to make up 288, or 2 times 144. As 1 1/3 1/4 times 144 is 228 we shall have as a continuation of our first multiplication,
\1/228 becomes 1/144 or 1 as part of 144
\1/114 becomes 1/72 or 2 as a part of 144Adding together all the multipliers checked in this multiplication, we have 1 1/6 1/12 1/114 1/228 as the required quantity.