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11
CHAPTER III-FRACTIONS.
than one for their numerators, when the sum (of those fractions) has either one or (any number) other than one for its numerator:
87. (Either) numerator mulitiplied by a chosen (number), then combined with the other numerator, thon divided by the numerator of the (given) sum (of the intended fractions) so as to leave no remainder, and then divided by the (above) chosen number and mulitiplied by the denominator of the (above) sum (of the intended fractions), gives rise to a (required) denominator. The donominator of the other (fraction), however, is this (denominator) multiplied by the (above) ohosen (quantity).
Examples in illustration thereof.
88. Say what the denominators are of two (intended fractional) quantities which have 1 for each of their numerators, when the sum (of those fractional quantities) is either or; us also of two (other fractional quantities) which have 7 and 9 (rospectively) for (their) numerators.
The second rule (is as follows):--
29. The numerator (of one of the intended fractions) as mplied by the denominator of the sum (of the intended fractions), when combined with the other numerator and then divided by the numerator of the sum (of the intended fractions), gives rise to the denominator of one (of the fractions). This (denominator), when multiplied by the denominator of the sum (of the intended fractions), becomes the denominator of the other (fraction).
87. Algebraically, if is the sum of two intended fractions with a and b
59
as their numerators, then the fractions are
も
up+b ท
and
a
ap+b n
m
is any number so chosen that ap + b in divisible by m. it will be found, is
118
89. This rule is only a particular case of the rule given in stanza No. 87, as the denominator of the sum of the intended fractions in itself substituted in this rule for the quantity to be chosen in the previous rule.
x-xp
1
where p
m P
The sum of these fractions,
