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

16 LOGISTICS
Rule for the multiplication of fractions :
33(i) The product (of the given fractions) is obtained on
dividing the product of the numerators by the product of the
denominators.¹
Ex. 10. 2 plus ½ is multiplied by 1 plus ½, and 60 plus ⅓
is multiplied by ⁵⁄₂ : what are the products, say separately.
Rule for the division of fractions :
33(ii). Having interchanged the denominator and the
numerator of the divisor, apply the previous rule (i.e., the
rule for multiplication).
Ex. 11. 6 plus ¼ is divided by 2+½, and 60 plus ¼ is
divided by 3+⅓ : say the quotients separately.
Rule for squaring a fraction :
34(i). The square of the numerator divided by the
square of the denominator is the square of the fraction.³
Ex. 12. Say, friend, if you know, the square of 2 plus ½,
of 15 plus ¼, of ½, and of ⅓.
Rule for finding the square root of a fraction :
34(ii). The square root of the numerator divided by
the square root of the denominator, gives the square root
(of the fraction).⁴
Rule for cubing a fraction :
35(i). The cube of the numerator divided by the cube
of the denominator gives the cube (of the fraction).⁵
¹ Cf. BrSpSi, xii. 3(ii) ; GSS, iii. 2; MSi, xv. 15(i) ; GT, p. 19,
line 26 ; SiŚe, xiii. 9(i) ; L (ASS), p. 36, vs. 39 ; GK, I, p. 12, lines 2-3.
² Cf BrSpSi, xii. 4 ; GSS, iii. 8(i) ; MSi, xv. 15(ii) ; GT, p. 21,
line 3-6 ; SiŚe, xiii. 10 ; L (ASS), p. 37, vs. 41 ; GK, I, p. 12, lines 11-12.
³ Cf. BrSpSi, xii. 5(i) ; GSS, iii. 13 ; MSi, xv. 16(i) ; GT p. 22,
line 24; SiŚe, xiii. 9(ii); L (ASS), p. 38, lines 2-3; GK, I, p. 12, lines 17-18.
⁴ Cf. BrSpSi, xii. 5(ii) ; GSS, iii. 13 ; MSi, xv 16(ii) ; GT, p. 23,
line 25 ; L (ASS), p. 38, lines 2-3 ; GK, I p. 12, lines 17-18.
⁵ Cf. GSS, iii. 13 ; MSi, xv. 17(i) ; GT, p. 25, line 13 ; L (ASS), I,
p. 38, lines 2-3 ; GK, I, p. 12, lines 17-18.