Example

Tell me, what would be the result when two hundred and seventy-five original: "pañca-mahīdhara-nayana," literally: five (5), mountains (7), and eyes (2), read from right to left as 275 is multiplied by eighteen original: "dhṛti," a poetic word for the number 18? Calculate this using the method of splitting the digits, splitting the place values, and by the method of common factors Apavartana: the process of simplifying numbers by a common divisor or factoring. ॥ 2 ॥

Statement: Multiplicand Guṇya: the number to be multiplied is 275. Multiplier Guṇaka is 18. The product is 4950.

Now, by splitting the multiplier into parts of 7 and 11: when the multiplicand is multiplied by these two, the results are 1925 and 3025. Adding these together in their respective positions, the sum is the same: 4950.

By splitting the multiplier by place value into 10 represented here by the digit 1 in the tens place and 8: when the multiplicand is multiplied by these, the results are 2750 and 2200. Adding these together, the sum is the same: 4950.

Alternatively, the multiplier 18 is divided by 3, giving 6. When the multiplicand is multiplied by these two factors (3 and 6) sequentially, the result is the same: 4950.

In this process, there is no difference between the multiplicand and the multiplier. If the multiplicand is treated as the multiplier, and the multiplier as the multiplicand, the result remains the same. Just as five multiplied by three is fifteen, so too is three multiplied by five fifteen. This logic applies to all multiplication procedures.

The Rule-Verse for Division in the Āryā Meter

Example

For the purpose of dividing the previous product:
Statement: Dividend Bhājya: the number to be divided is 4950. Divisor Bhājaka is 18. After performing the division, the result is 275.

Alternatively, both the dividend and the divisor are reduced simplified by nine, resulting in 550 and 2. After performing this division, the result is 275.

• The method for "Derivation of the Divisor" will be explained later in the section on fractions.

* "Derivation of the Divisor" original: "hārotpatti" refers to the method of searching for common factors. This belongs to the eleventh category of mathematical operations called "Extraction of Fractions" Bhāgādāna: the process of simplifying or breaking down complex ratios, where the fixed digits of the multiplicand and multiplier are separated.