# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२०५

एतत् पृष्ठम् परिष्कृतम् अस्ति
9
CHAPTER II -- ARITHMETICAL OPERATIONS

CHAPTER II.

ARITHMETICAL OPERATIONS

The First Subject of Treatment.

Hereafter We shall expound the first subject of treatment, which is named Parikarman.

Multiplication.

The rule of work in relation to the operation of multiplication, which is the first (among the parikarman operations), is as follows:--

1. After placing (the multiplicand and the multiplier one below the other) in the manner of the hinges of a door, the multiplicand should be multiplied by the multiplier, in accordance with (either of) the two methods of normal (or) reverse working, by adopting the process of (i) dividing the multiplicand and multiplying the multiplier by a factor of the multiplicand, (ii) of dividing the multiplier and multiplying the multiplicand

1. Symbolically expressed, this rule works out thus :-- In multiplying ab by cd, the product is (i) ${\displaystyle {\tfrac {ab}{a}}\times (a\times cd);}$ or (ii) ${\displaystyle (ab\times c)\times {\tfrac {cd}{c}}}$; or (iii) ${\displaystyle ab\times cd}$. Obviously the object of the first two devices here is to facilitate working through the choice of suitable factors.

The anulōma or normal method of working is the one that is generally followed. The vilōma or the reverse method of working is as follows:--

To multiply 1998 by 27 :
1998
27
 2 x 1 == 2 x 9 == 2 x 9 == 2 x 8 == 7 x 1 == 7 x 9 == 7 x 9 == 7 x 8 ==
5 3 9 4 6 2 1 8 1 8 1 6 7 6 3 6 3 5 6