the prefent cafe, I have nothing to do but 
to add the two numerators together for a 
new numerator, and fubfcribe the common 
denominator: the fraction will then ftand 
thus ^> that is, four fourths, equal to one 
whole: four fourths of a hundred make a 
hundred. 
But fuppofe the fractions were -J. and f-, 
I cannot add them together until I have 
brought them to the fame denomination: 
that is, until their denominators are alike; 
eighths and fourths cannot be accumulated 
in one homogeneous fum. I confider that 
in multiplying feparately any two figures 
by any one other figure, I neither increafe 
nor diminish their relative value; for, if I 
double, that is, if I multiply by 2, the two 
figures which I will fuppofe to fignify the 
half of a (hilling, viz. |, the i becomes a 2 
and the 2 a 4, thus . Now one half of a 
fhilling is fix pence, and two fourths are twice 
three pence: hence, I firft quadruple, that 
is, multiply the two figures of the fecond frac- 
tion by 4, the denominator of the firft, and the 
product is 44- . I then multiply both the 
figures of the firft fraction by 8, the denomi- 
nator of the fecond, and find the product -A- 
Thus I have brought them to one denomi- 
nation ; 
