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CHAPTER III--FRACTIONS.

rules, when the sum (of all the intended fractions) is one; and also (the rule) for getting at (the value of) the part that is left out:--

95. The denominators derived in accordance with (any) chosen rule, when (severally) multiplied by the denominators derived in accordance with another rule, become the (required) denominators. The sum (of all the fractions), diminished by the sum of the specified part (thereof), gives the measure of the optionally left-out part.

Examples in illustration hereof.

96. The number of fractions (obtained) by rule No. 77 is 13, and 4 (is obtained) by rule No. 78. When the sum (of the fractions arrived at with the help of these rules) is 1, how many are the (component) fractions ?

97. The number of fractions (obtained) by rule No. 78 is 7, and 3 (is obtained) by rule No. 77. When the sum (of the fractions arrived at) with the help of these (rules) is 1, how many are the (component) fractions?

98. Certain fractions are given with 1 for each of their numerators, and 2, 6, 12 and 29 for their respective denominators. The (fifth fractional) quantity is here left out. The sum of all (these five) being 1, what is that {fractional) quantity (which is leftout)?

Here end Simple Fractions,


Compound and Complex Fractions.

The rule for (simplifying) compound and complex fractions:--

99. In (simplifying) compound fractions, the multiplication of the numerators (among themselves) as well as of the denominators (among themselves) shall be (tho operation). In the operation (of simplification) relating to complex fractions, the denominator of (the fraction forming) the denominator (becomes) the multiplier of the number forming the numerator (of the given fraction).


98. The complex fraction pro dealt with is of the sort which has an integer for the numerator and a fraction for the denominator