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Collectanea for Posology
157
make an unit of
the last denomination,
and thus
proceed till you
come to the lowest
you design; then
make the last product
a numerator
to the denominator
of the fraction
given.
Case 10
To reduce a fraction
of an unit of a lower
denomination
to an equivalent
fraction in the
denomination of
an higher:
Rule.
Multiply the denominator
by
the number of units
in the given fraction
that is equal
to an unit of the
next superior denomination,
and
the product by such
a number of units
of its denomination,
as is equal to an
unit of the next
above it; and thus
go on till you come
to the highest species
required, and
the last product is
a denominator to
the numerator of
the fraction given.
Case 11.
To find the value
of a fraction in
coin, weight, measure,
time, &c
Rule.
Multiply the numerator
of the given fraction by
the number of units
of the next
inferior species that
makes one of the
denomination of
your
your fraction, and
divide the product
by the denominator;
the quotient is so
many integers of
that lower species;
and if there is a
remainder, proceed
as before, still reducing
and dividing,
till you come to the
lowest species; and
the several quotients
with the remainder
(if any, which is always
the numerator
of a fraction of
the lowest species)
are the answer.
If the fraction to
be valued be an improper
one, divide
the numerator by
the denominator,
and the quotient is
an integer of the
same species with
the fraction; then
reduce the remainder
as before.
If the fraction to be
valued be an improper
one, divide the
numerator by the denominator,
and the
quotient is an integer
of the same species
with the fraction:
then reduce the remainder
as before.
Addition of Fractions.
In order to prepare
fractions for addition
or subtraction, all
compound fractions
must be reduced to
single ones; and if
they are of different
denominations they
must be brought into
the same denomination,
and reduced
so as all the fractions
shall have one common
denominator.
Rule.
Add together all the
numerators, for a
new numerator: under
which subscribe the
common denominator.
Subtraction of
Fractions.
The fractions being
prepared, as before
directed in addition,
then,
Rule.
Subtract one numerator
from the other,
and their difference
will be a new numerator,
under which
subscribe the common
denominator.
Multiplication of
Fractions.
To prepare fractions
for either multiplication
or division, reduce
compound fractions
to single ones:
bring mixed numbers
into improper
fractions, and express
whole numbers fractionwise;
also reduce
fractions into their
lowest terms. Then,
Rule.
Multiply the numerators
into one another
for a new numerator,
and the
denominators one
into another for
a new denominator
Hence it may be
observed, that if the
multiplier be a proper
fraction, the
product will always
be less than the multiplicand.
Division of Fractions.
The fractions being
prepared as directed
for multiplication; division
may be thus
performed.
Rule.
Multiply the number
of the dividend into
the denominator
of the dividing fraction
for a numerator,
and the other
numerator and denominator
together
for a new denominator
2 If the divisor and
dividend have both
the same denominator,
the quotient may
be found by dividing
one numerator by another.
2. If the divisor and
dividend have each
the same numerator;
divide one of the denominators
by the
other, which will give
the quotient required.
3. If the numerator
and denominator of
the dividend can be
divided without a remainder,
by the numerator
& denominator
of the divisor,
their quotients will
answer the question.
4. If a number can
be found that will
divide both the numerators,
or both the
denominators (viz:
those of the divisor &
dividend) without a
remainder; use those
quotients instead of the
given numerators &
denominators, which
will give the result
in its lowest terms.
Identifier:  JB/135/089/001 "JB/" can not be assigned to a declared number type with value 135.



135 
posology 

089 
collectanea for posology 

001 
decimal fractions / addition of fractions / subtraction of fractions / multiplication of fractions / division of fractions 

collectanea 
3 

recto 
f154 / / f157 

in two pieces (both stamped) 
46207 
