136. A Hized Quantity is one having both entire and

h d

fractional parts ; as, a , or c -f



137. If the numerator of a fraction he multiplied^ or the
denominator divided, btj any quantity, the fractixm is muM-
plied by that quantity*

L Let - denote any fraction ; multiplying its numerator by
b

c, we have -— . Now, in - and -7- the unit is divided into b
b b b

equal parts, and a and a e parts, respectively, are taken. Since



FRACTIONS. 67



e times as many parts are taken in -=- as in 7, it follows that

ae. ,. a > ^

— IS c times -.
o

2. Let — denote any fraction ; dividing its denominator

by c, we have -. Now, in ;— and 7, the same number of

h c ^ b

parts is taken ; but^ since in — - the unit is divided into

h c equal parts, and in - into only h equal parts, it follows that

each part in 7 is c times as large as each part in 7-. Hence, -r
o 6 o

. .. a

18 c times z—.
oc

138. If the numerator of a fraction he divided^ or the de-
fwminatoT multiplied^ by any quantity, the fraction is divided
by that quantity,

a c
L Let — demote any fraction ; dividing its numerator by c,

we have 7. Now, in Art. 137, 1, we showed that -7- was c
„ ^g

times - . Hence, - is -7- divided by c.
