tor of the Dividend by the Numerator of the 
Diviforyfor a new Denominator. Let us place 
thefe two fractions as in common divifion 
and try T)T(^- 
There is yet a fhorter and a plainer rale, 
viz. Reverfe one of the fractions - 3 then multiply 
the two numerators and the two denominator si 
thus 4-)l(44 
The quotient, I find, is 15 divided by 14.' 
But why this multiplication fhould be, in fact, 
divi/ion^ is by no means obvious : nor do I 
recollect any author who explains it furH- 
ciently. Firft, let us confider, thatfevenths 
cannot be divided into thirds: therefore, fup- 
pofe I had never heard of any rule for di- 
viding one fraction by another, I fhould na- 
turally begin by multiplying the numera- 
tors and denominators reciprocally, for two 
new numerators; and the denominators, for 
a common denominator: the refult of which 
operation would be 4:4-, 44. Now all the 
difficulty is vanifhed. 'Since the denomina- 
tors are the fame, they become ufelefs, and 
I can add, fubtract, multiply, or divide the 
numerators in the fame manner as if they 
were whole numbers. Now as 4:4- is equi- 
valent to the dividend, and 44 equal to the 
divifor, the quotient mull be 44 
But 
