g) Now take the second fraction. Set the numerator 11 of the fraction in the extreme left,
leave one column and set the denominator 12. By keeping your left hand on the 12
and right hand on the common denominator 24, ask : how many 12’s in 24? By saying
2, clear the 12 and set the 2. Now multiply 2 and 11. This value 2^ ×^ 11 = 22 should
be subtracted from the numerator already set in the abacus.
h) Check the value in the numerator. It is 15. You have to subtract 22 from this according
to your problem. This is not possible. In this case (i.e., when the numerator to be
subtracted is greater than the available numerator in the abacus), look at the common
denominator. That value should be added to the numerator before the subtraction. In
this case, you have to add 24 with 15, thus making it 39. How did you get this? This
is 2424 + 2415. Please note that there is no change in the denominator.
i) You have added 2424 = 1. This number 1 should be subtracted from the whole number
column. Now you have 2 in the whole number column.
j) After subtracting this number 1, you have 39 (24 + 15) in the numerator. Now the
value 22 of the second fraction can be subtracted from the numerator thus leaving
17 in the numerator.
k) Check the numbers now. You have 2 in the whole number column, 17 in the numerator
and 24 in denominator.
l) Your answer is^22417. Here the numerator 17 and the denominator 24 do not have a
common divisor. Hence, the fraction part cannot be simplified further.
Note :
In fraction addition, when the numerator value is greater than the denominator value,
subtract the denominator value from the numerator value. To compensate this add 1
in the whole number. In fraction subtraction, when the numerator value of the first
fraction is less than the numerator value of the second fraction, add the value of the
denominator with the numerator value of the first fraction and subtract 1 (one) from
the whole number.
12