For, a fraction is an expression of division, the numerator answer-
ing to the dividend, and the denominator to the divisor. (Art. 66.)
Thus, the value of the fraction -=- is a.
GENERAL PRINCIPLES OP FRACTIONS.
114( ^ the numerator he muUipUed, or the denomincUor di-
vided, hy any quantity, the fraction is multiplied by the same
quantity.
For, let -J- denote any fraction ; t^en,

ab

- = a.
Now, if we multiply its numerator by any quantity 6, we have,

— = ab,

and, in like manner, if we divide its denominator by 6, we obtain
also ab. Hence, in both cases the value of the fraction has been
multiplied hy 6.
115. ^ the denominator be mvhiplied, or the numerator di-
vided, hy any quantity, the fraction is divided by the same
quantity.
Define an Entire Algebraic Quantity., A Mixed Algebraic Quantity.
The Value of a fraction. If the nnmprator be multiplied, or the denomi-
nator dividea, how is the fraction affected ' If the denominator be mul-
tiplied, or the numerator divided ?

7*



78 ELEMENTABY ALGEBRA.
For, let -V- denote any fraction ; then,

aW ,
— = ao.
b

Now, if we multiply its denominator by any quantity b, we
have,

-F = «.
and, in like manner, if we divide its numerator by i, we obtain
also a. Hence, in both cases the value of the fraction has been
divided by 6.
116« Jf the numerator and denominator he both multiplied,
or hoih divided, hy the same guantity, the value of the fraction
win not be changed.
ab , ,

For, let -T- denote any fraction ; then,

a J

- = a.
