Moonlight of Mathematics, Part 1 (1936) - Page 18

1	1
4	7
1	1	Result of reduction original: "Savarnitaṃ jātam"	2	5
3	4		5	24
1	1
5	6

2	6
3	5
1	1	Result of reduction	3	2
2	6		10	9
2	7
4	9
1	1
4	9

And so it is done everywhere.

Thus ends the Six Classes of Fraction Reduction.

original: "Savarnajātiṣaṭkam." These six classes are the foundational ways fractions were categorized in Indian mathematics to prepare them for addition and subtraction.

Now, the rule for the Addition and Subtraction of Simple Fractions.

original: "Bhinnasaṅkalitavyavakalita." Bhinna means broken or fractional; saṅkalita is addition, and vyavakalita is subtraction.

The addition or subtraction of numerators

of fractions with common denominators is performed as before.

This "Rule" (Sūtra) instructs the student that once fractions have a common denominator, they can be treated like whole numbers.

Example.

Friend, if you have the skill, quickly sum together
the parts represented by the lunar days, the limbs,
the directions, and the Rāmas, and tell me the total.
Then, tell me what remains if you subtract that sum
from a whole unit—if you do not find the labor of
fractions too wearisome! ॥ 9 ॥
The poet uses bhūta-saṃkhyā, a system where words represent numbers: "Lunar days" (tithi) = 15; "Limbs" (aṅga) = 6; "Directions" (dik) = 10; "Rāmas" (rāma) = 3. The fractions are 1/15, 1/6, 1/10, and 1/3.

Statement	1 ,	1 ,	1 ,	1	Result of addition	2	Subtracting these from a unit original: "Rūpāt"
	15	6	10	3		3

Result of subtraction	1
	3

Thus ends the addition and subtraction of simple fractions.