JB/135/079/002

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To reduce a compound
fraction into a single one.

Multiply all the numerators
together for a
numerator and all the
denominators for a the
denominator.-

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, reduces
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 the 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.

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To reduce fractions into
their lowest denomination

I

f 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
remainder -

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
fraction 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.-

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3. Or 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 denomination 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 numerator into each others denominator and if the products are equal fractions are so i 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 weights &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

Identifier: | JB/135/079/002"JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering
Box	135	Main Headings
Folio number	079	Info in main headings field	vulgar fractions
Image	002	Titles
Category	private material	Number of Pages	2
Recto/Verso	recto	Page Numbering
Penner	sir samuel bentham	Watermarks	1798
Marginals		Paper Producer
Corrections		Paper Produced in Year	1798
Notes public		ID Number	46197
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