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50
GANITARĀRASANGRAHA.
(number) which is immediately) next to it in value) and then halved.
The rule for arriving at the required) denominatorg (in the case of certain intended fractions), when their numerators are (each) one or other than one, and when tlfe (fraction coustituting their) sum has one for its numerator :
78. When the sum of certain intended fractions) bas one for its numerator, thon (their required denominators are arrived at by taking) the denominator of the sum to be that of the first (quantity), and (by taking, this denominator) combinod with its own (related) numerator to be (the denominator) of the next (quantity) and so on, and then by multiplying (further each such denominator in order) by that which is immediately) next to it, the last (denominator) heing (however multiplied) by its own (related) numerator.
Examples in illustration thereof. 79. The sums of certain intended fractions) having for their numerators 7, 9. 3 and 13 (respectively) are (firstly) 1, (secondly)
aud (thirdly) . Say what the denominators of those fractional quantities) are.
The rule for arriving at the denominators (of certain iutendod fractions) having one for their numerators, when the gum (of those fractions) has one or any quantity) other than one for its numerator: -
78. Algebraically, if the sum is -, and a, b, c, nld are the given numeratore, the fractions bummed up aro an below:
-Hin + a) * (* + a) (n + a + b)
(+ a + b) (x + a + 0 + c)"
d (
+ a + b + c)
a(n + a + b) + b (+ ) ( + a + b)
c + " + a + b (n + a + (n + a + b + c)
*
N * + a)(
+ b + #
+ a + b
1
+ a + 6
