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480. To multiply one number by another

To multiply one number by another, among the higher or the lower denominations, the simplest and least ambiguous method is to make of the multiplied number a dual or plural, qualified by the other as any ordinary noun would be; and this method is a common one in all ages of the language. For example: páñca pañcāçátas five fifties(250); náva navatáyas nine nineties (810); açītíbhis tisṛ́bhis with three eighties (240); páñca çatā́ni five hundreds; trī́ṇi sahásrāṇi three thousands;ṣaṣṭíṁ sahásrāṇi 60,000; daça ca sahasrāṇy aṣṭāu ca çatāni 10,800: and, combined with addition, trī́ṇi çatā́ni tráyastriṅçataṁ ca 333; sahasre dve pañconaṁ çatam eva ca 2095.

a. In an exceptional case or two, the ordinal form appears to take the place of the cardinal as multiplicand in a like combination: thus, ṣaṭtriṅçā́ṅç ca catúraḥ (RV.)36x4 (lit. four of the thirty-six kind); trī́ṅr ekādaçā́n (RV.) or traya ekādaçāsaḥ (ÇÇS. viii. 21. 1) 11x3.

b. By a peculiar and wholly illogical construction, such a combination as trīṇi ṣaṣṭiçatāni, which ought to signify 480 (3x100+60), is repeatedly used in the Brāhmaṇas to mean 360 (3x100+60); so also dvé catustriṅçé çaté 234 (not 268); dvāṣaṣṭāni trīṇi çatāni 362; and other like cases. And even R. hastrayaḥ çataçatārdhāḥ 350.