c) Now clear the number set in the first abacus. You are ready for your second
fraction. Convert^12 1311 into improper fraction according to the procedures
mentioned above. You will get the improper fraction as^16713.d) Now you have to set this value in the second abacus. The numerator and the
denominator of the first fraction are already set in that abacus. Where do you
set the values of the second fraction? The numerator of the second fraction
should be placed to the right side of the numerator of the first fraction by
leaving two columns in between. In this case, you have to set your 167 from
the fifth column in the left side of the abacus. The denominator of the first
fraction should be set in the sixth and fifth columns from right leaving two
columns in between the denominators.
e) Now clear the numbers of the first abacus. In the second abacus you have 62
and 167 in the numerator side and 12 and 13 in the denominator side.
f) Now a new idea “CANCELLATION” is introduced. The numerators and denominators
can be made smaller by a common divisor, if possible so that the calculations
would be easier. For clarity, the calculations can be done in the first abacus
which is free now. Consider, number 62 – the numerator and 12 – the denominator.
2 is a common divisor. Both 62 and 12 can be divided by 2 thus making them 31
and 6 respectively. Now you have 31 and 167 in the numerator side and 13 and
6 in the denominator side.
g) CANCELLATION SHOULD BE DONE ONLY BETWEEN THE NUMERATOR AND
DENOMINATOR. ON ANY ACCOUNT, CANCELLATION SHOULD NOT BE MADE BETWEEN
THE NUMERATOR AND NUMERATOR OR DENOMINATOR AND DENOMINATOR.
h) Now, take 31 and 167. Treat this as 31×167. Now, this is in the form of your
usual multiplication. Using your first abacus, solve the problem. The answer is
5177.
i) Clear the numerator side of the second abacus. Set the number 5177 in the
extreme left.