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SECTION VIII. 
Of ’I IIL IlLDUCTION OF FRACTIONAL AND HADICAt 
. QUANTITIES. 
f r^HE Reduction of fractional and radical quantities 
g is of use in changing an expression to the most 
simple and commodious form it is capable of; and 
that, either by bringing it to its least terms, or all the 
members thereof (if it be compounded) to the same 
denomination. 
A Fraction is reduced to its least terms, by dividing 
both the Jiumerator and denominator by the greatest 
common divisor. 
Thus, by dividing by b, is reduced to ; 
And by dividing by ha, is reduced to ^ : 
Moreover, will be reduced to——, or 4d: 
5 ab I 
And l ~ aX will be reduced to 1 . 
72a \r 2 v xy ba 
Thus also, 12a< ^—by dividing every term of 
the numerator and denominator by 2a, is reduced to 
€a — b 
2 a 
And 
8a 3 .r — 12a\r 2 -f 6ax 
6a 2 x + 4 ax 2 
, by dividing every term 
by 2ax, is reduced to 
4 a* — 6ax + 3.r* 
3 a + 2x 
Lastly, 
a 3 4- 3a 2 b 4- 3ab 2 4- b 3 
, by dividing both 
a 2 4- 3ab 4* 26* 
the numerator and denominator by the compound divi- 
, 7 . , , A a* 4- 2ab 4- bb 
sor a 4- b, is reduced to i . 
a 4- 2o 
But the compound divisors whereby a Fraction cam, 
sometimes, be reduced to lower terms, are not so easily 
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