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Vulgar Fractions.

To reduce a compound
fraction into a single one.

Multiply all the numerators
together for a
numerator and all the
denominators for a the

If a numerator of one
term is a compound fraction to
be equal to a denominator
in another term
reject both and divide
those numerators and
denominators which are
divisible by each other or
by the same number,
which quotients multiplied
into the remaining numerators
& denominators, reduce
the compound fraction to a
single one in its lowest terms.

To reduce mixed numbers
and integers into improper
fractions. I shall divide
this case into three parts—

1. If the integer have no an
assigned denominator,—

Multiply the integer
by the assigned denominator.
the product is the numerator
to the assigned denominator.—

2. If the integer has no
assigned denominator,—

An unit subscribed must
be the denominator.—

3. If the integer have a
fraction annexed,

Multiply the integer by
the denominator, and to
the product add the numerator;
the sum is the
numerator to the denominator
of the annexed fraction.

To reduce an improper
fraction into its equivalent
whole or mixed number,

Divide the numerator
by the denominator, the
quotient gives the integer &
under the remainder subscribe
the denominator.

---page break---

To reduce fractions into
their lowest denomination.

If the numerator and denominator
are even numbers
take half the one and half
the other; and when either
of them is an odd number
divide them by any
number that will divide
both numerator and
denominator without any

Or by finding the greatest
common measure by
the following rule,—

Divide the greater number
by the lesser and that divisor
by the remainder &
so on continually till there
be no remainder left. This
will be the last divisor be the
greatest common measure
and if it be 1 then are
they prime numbers & are
already in their lowest
terms; but if otherwise
divide the numbers by the
last divisor and their quotients
will be their least
terms required.—

To alter or change different
fractions into one denomination
retaining the same value.

1. Multiply all the denominators
into each other
for a new and common
denominator, and each
numerator into all the
denominators but its own
for a new numerator.

2. When there are only
two fractions to be reduced
if one of the denominators
is a multiple of the other
divide; and by the quote
multiply the numerator
and denominator of that
fraction which hath the
least denominator and
the fraction thus found
will be equivalent to the
given ones.—

---page break---

3. Or if both the denominators
have a common
multiple divide each of
the denominators thereby
and multiply the contrary
numerators & denominators
by each contrary quotient.

To reduce a fraction to
an equivalent one of any
other assigned denominator
viz to find a numerator
which with the assigned
denominator will make a
fraction equivalent to the
proposed one when possible.

Multiply the assigned
denominator by the numerator
of the proposed fraction
and divide the product by
the denominator: the quote
(if there be no remainder) is
the numerator sought.—

To find whether one
fraction be greater or less in
value than another.

Multiply the numerators
into each others denominator
and if the products are equal
the fractions are so; otherwise
the numberator of the greatest
fraction multiplied by
the denominator of the other
will be the greatest product.

To reduce coins weights
measures &c. into fractions.

Reduce the coin weight
&c. into the lowest name
mentioned for a numerator
and put the number of those
parts contained in an unit
of the integer to which the
proposed fraction is to be
reduced for the denominator
then reduce the fraction into
its lowest terms.—

To reduce a fraction of
an unit of a higher denomination
to an equivalent
fraction of an unit of a
lower species of the same
kind with the higher.

---page break---

Multiply the numerator
of the given fraction by the
number of units in the
next inferior species that
make an unit of the denomination
of your fraction
and that product multiply
by the number of units in
the next inferior denomination
that 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—

To reduce a fraction of
an unit of a lower denomination
to an equivalent fraction
in the denomination of an

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 then
go on till you come to the
highest species required
and the last product is
a denominator to the
numerator of the fraction

To find the value of a
fraction in Coin Weight
Measure Time &c.—

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 fraction, &
divide the product by the
denominator the quotient
is so many integers of</p>

Identifier: | JB/135/079/002
"JB/" can not be assigned to a declared number type with value 135.


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vulgar fractions





private material

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sir samuel bentham




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