Simplification of Quotients of Fractions - Revision history

Ramamurthy: Headings modified

2023-09-01T08:54:34Z

Headings modified

← Older revision		Revision as of 14:24, 1 September 2023
Line 1:		Line 1:
	~~==Introduction==~~
	Here we will be knowing to determine the quotient when the numerator and the denominator are fractions as mentioned in Āryabhaṭīyam.		Here we will be knowing to determine the quotient when the numerator and the denominator are fractions as mentioned in Āryabhaṭīyam.

	==Verse==		==Verse==
	छेदाः परस्परहता भवन्ति गुणकारभागहाराणाम् ।		छेदाः परस्परहता भवन्ति गुणकारभागहाराणाम् ।

Ramamurthy: Category updated

2023-08-16T13:37:12Z

Category updated

← Older revision		Revision as of 19:07, 16 August 2023
Line 24:		Line 24:
	<references />		<references />
	[[Category:Mathematics in Āryabhaṭīyam]]		[[Category:Mathematics in Āryabhaṭīyam]]
			[[Category:General]]

Ramamurthy: Internal link updated.

2023-08-15T07:35:16Z

Internal link updated.

← Older revision		Revision as of 13:05, 15 August 2023
Line 20:		Line 20:
	{\frac{5}{7} \times \frac{2}{3}}=\frac{Dividend}{Divisor}=\frac{(3 \times 1)(7 \times 3)}{(4 \times 6)(5 \times 2)}= \frac{63}{240}= Quotient</math>		{\frac{5}{7} \times \frac{2}{3}}=\frac{Dividend}{Divisor}=\frac{(3 \times 1)(7 \times 3)}{(4 \times 6)(5 \times 2)}= \frac{63}{240}= Quotient</math>
	==See Also==		==See Also==
	[https://alpha.indicwiki.in/index.php?title=%E0%A4%AD%E0%A4%BF%E0%A4%A8%E0%A5%8D%E0%A4%A8%E0%A5%8B%E0%A4%82_%E0%A4%95%E0%A5%87_%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A4%AB%E0%A4%B2%E0%A5%8B%E0%A4%82_%E0%A4%95%E0%A4%BE_%E0%A4%B8%E0%A4%B0%E0%A4%B2%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3 भिन्नों के भागफलों का सरलीकरण]		[[भिन्नों के भागफलों का सरलीकरण]]
	==References==		==References==
	<references />		<references />
	[[Category:Mathematics in Āryabhaṭīyam]]		[[Category:Mathematics in Āryabhaṭīyam]]

Ramamurthy: New Page created

2023-08-15T07:26:21Z

New Page created

New page

==Introduction==
Here we will be knowing to determine the quotient when the numerator and the denominator are fractions as mentioned in Āryabhaṭīyam.
==Verse==
छेदाः परस्परहता भवन्ति गुणकारभागहाराणाम् ।
==Translation==
The numerators and denominators of the multipliers and divisors should be multiplied by one another.<ref>{{Cite book|last=Shukla|first=Kripa Shankar|title=Āryabhaṭīya of Āryabhaṭa|year=1976|location=New Delhi|pages=69-70}}</ref>

For Example:

<math>\frac{\frac{a}{b}} {\frac{c}{d}} = \frac{Dividend}{Divisor}=\frac{ad}{bc} = Quotient</math>

<math>\frac{ \frac{a}{b} \times \frac{c}{d}}
{\frac{e}{f} \times \frac{g}{h}}=\frac{Dividend}{Divisor}=\frac{(ac)(fh)}{(bd)(eg)}=Quotient</math>

If the numerator and denominator are both fractions, this verse gives the formula to simplify them. The numerator of the dividend should be multiplied by the denominator of the divisor and the denominator of the dividend should be multiplied by the numerator of the divisor.
===Example 1:===
<math>\frac{\frac{3}{4}} {\frac{5}{7}} = \frac{Dividend}{Divisor}=\frac{3\times 7}{4\times 5} = \frac{21}{20} = Quotient</math>
===Example 2:===
<math>\frac{ \frac{3}{4} \times \frac{1}{6}}
{\frac{5}{7} \times \frac{2}{3}}=\frac{Dividend}{Divisor}=\frac{(3 \times 1)(7 \times 3)}{(4 \times 6)(5 \times 2)}= \frac{63}{240}= Quotient</math>
==See Also==
[https://alpha.indicwiki.in/index.php?title=%E0%A4%AD%E0%A4%BF%E0%A4%A8%E0%A5%8D%E0%A4%A8%E0%A5%8B%E0%A4%82_%E0%A4%95%E0%A5%87_%E0%A4%AD%E0%A4%BE%E0%A4%97%E0%A4%AB%E0%A4%B2%E0%A5%8B%E0%A4%82_%E0%A4%95%E0%A4%BE_%E0%A4%B8%E0%A4%B0%E0%A4%B2%E0%A5%80%E0%A4%95%E0%A4%B0%E0%A4%A3 भिन्नों के भागफलों का सरलीकरण]
==References==
<references />
[[Category:Mathematics in Āryabhaṭīyam]]