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

REDUCTION OF FRACTIONS 21
The commentator interprets ‘rûpatrayamardhonam’ as meaning
3 - ½ of 3 and not (3 - ½), so the first expression according to him is
(3 - ½ of 3) - ½ of (3 - ½ of 3) - ⅓ of [(3 - ½ of 3) - ½ of (3 - ½ of 3)].
The interpretation given by us is more natural and plausible,
especially when we see that a similar interpretation has been given to
the verse of Ex. 19, which is analogous to this one.
Rule for reducing a chain (vallî) of measures :
41. To reduce a chain (vallî), multiply the foremost
denominator and numerator by the lower denominator, and
(then) from or to the foremost numerator subtract or add
(as the case may be) the lower numerator.¹
Ex. 22. What amount is obtained by reducing
5 purâṇas , 3 paṇas , 1 kâkiṇî , - 1 varâṭaka , - ⅕ of that (i.e., of
a varâṭaka) (to purâṇas) ?
Converting each measure to the previous one, and writing them one
below the other in the Hindu way, we have
5
1
3
16
1
4
1+
20
1+
5
where + indicates subtraction.
Now applying the rule to the uppermost two fractions of this chain,
we get
83
16
1
4
1+
20
1+
5
¹ Cf. MSi, xv. 18 ; GT, p. 39, lines 7-10.