पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

20 LOGISTICS
Ex. 18. What sum is obtained by adding together
1+½, 5+¼, and 8+⅓ ?
Ex. 19. What is the sum of
(3 + ½) + ¼ of (3 + ½) + ⅙ of {(3 + ½) + ¼ of (3 + ½)}
and ½ + ⅓ of ½ + ¼ of {½ + ⅓ of ½} ?
Rule for reducing a fraction of the bhāgāpavāha class (i.e., a
whole number minus a fraction, or a fraction minus a
fraction thereof) :
40. In the bhāgāpavāha class, the numerator of the frac-
tion should be subtracted from the whole number multiplied
by the denominator (of the fraction) ; or having multiplied
the upper denominator by the lower denominator, the upper
numerator should be multiplied by the lower denominator as
diminished by the lower numerator.¹
That is to say,
(i) a - b / c = (ac - b) / c ,
(ii) a / b - c / d of a / b (which was written in the Hindu way
a
b
as² ) = a (d - c) / bd .

• c
  d
  Ex. 20. Say the amount, when 1 - ½ , 5 - ¼ , and 8 - ⅓
  are added together.
  Ex. 21. What is obtained by adding together :
  (3 - ½) - ¼ of (3 - ½) - ⅙ {(3 - ½) - ¼ of (3 - ½)}
  and ½ - ⅓ of ½ - ¼ of (½ - ⅓ of ½) ?
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  ¹ Cf. BrSpSi, xii. 9(ii) ; GSS, iii. 126 ; MSi, xv. 11(ii)-12; GT, p. 37,
  lines 2-5 ; L (ASS), p. 32, vs. 34 ; GK, I, p. 9, vs. 27.
  ² Actually, it was writtten as
  a a
  b or b
  c+ ˙c
  d d
  the fractions being written without the separating line, and + or (˙) being
  written to denote subtraction.