Reduction of Fractions to a Common Denominator - Revision history

Ramamurthy: Headings modified

2023-09-01T08:56:51Z

Headings modified

← Older revision		Revision as of 14:26, 1 September 2023
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	~~==Introduction==~~
	Here we will be knowing how to reduce fractions to a common denominator as mentioned in Āryabhaṭīyam.		Here we will be knowing how to reduce fractions to a common denominator as mentioned in Āryabhaṭīyam.

	==Verse==		==Verse==
	छेदगुणं सच्छेदं परस्परं तत् सवर्णत्वम् ।		छेदगुणं सच्छेदं परस्परं तत् सवर्णत्वम् ।

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2023-08-22T10:49:40Z

updated Redirecting link to the Hindi Page

← Older revision		Revision as of 16:19, 22 August 2023
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	Hence the sum of <math>\frac{1}{2}</math>,<math>\frac{1}{6}</math>,<math>\frac{1}{3} = 1</math>		Hence the sum of <math>\frac{1}{2}</math>,<math>\frac{1}{6}</math>,<math>\frac{1}{3} = 1</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%A4%BE_%E0%A4%B8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%B5_%E0%A4%B9%E0%A4%B0_%E0%A4%AE%E0%A5%87%E0%A4%82_%E0%A4%B2%E0%A4%98%E0%A5%81%E0%A4%95%E0%A4%B0%E0%A4%A3 भिन्नों का सार्व हर में लघुकरण]		[[भिन्नों का सार्व हर में लघुकरण]]
	==References==		==References==
	<references />		<references />
	[[Category:Mathematics in Āryabhaṭīyam]]		[[Category:Mathematics in Āryabhaṭīyam]]
	[[Category:General]]		[[Category:General]]

Ramamurthy: New Page created

2023-08-22T05:41:49Z

New Page created

New page

==Introduction==
Here we will be knowing how to reduce fractions to a common denominator as mentioned in Āryabhaṭīyam.
==Verse==
छेदगुणं सच्छेदं परस्परं तत् सवर्णत्वम् ।
==Translation==
Multiply the numerator as also the denominator of each fraction by the denominator of the other fraction; then the (given) fractions are reduced to a common denominator.<ref>{{Cite book|last=Shukla|first=Kripa Shankar|title=Āryabhaṭīya of Āryabhaṭa|year=1976|location=New Delhi|pages=70.}}</ref>

That is,

<math>\frac{a}{b}+\frac{c}{d}=\frac{a \times d}{b \times d}+\frac{c \times b}{d \times b}=\frac{a \times d}{b \times d}+\frac{c \times b}{b \times d} =\frac{ad}{bd}+\frac{cb}{bd} =\frac{ad+cb}{bd}</math>

<math>\frac{a}{b}-\frac{c}{d}=\frac{a \times d}{b \times d}-\frac{c \times b}{d \times b}=\frac{a \times d}{b \times d}-\frac{c \times b}{b \times d} =\frac{ad}{bd}-\frac{cb}{bd} =\frac{ad-cb}{bd}</math>
===Example :===
What is the sum of <math>\frac{1}{2}</math>,<math>\frac{1}{6}</math>,<math>\frac{1}{3}</math>?

Multiply the numerator and denominator of each fraction with the denominator of other fractions.

<math>\frac{1}{2}=\frac{1}{2} \times \frac{6}{6} \times \frac{3}{3}=\frac{18}{36} </math>

<math>\frac{1}{6}=\frac{1}{6} \times \frac{2}{2} \times \frac{3}{3}=\frac{6}{36} </math>

<math>\frac{1}{3}=\frac{1}{3} \times \frac{2}{2} \times \frac{6}{6}=\frac{12}{36} </math>

Now the denominators are same for the given fractions.

We have to add <math>\frac{18}{36}</math>, <math>\frac{6}{36}</math>, <math>\frac{12}{36}</math> to get the sum

<math>\frac{18}{36}+\frac{6}{36}+\frac{12}{36}=\frac{18+6+12}{36}=\frac{36}{36}=1</math>

Hence the sum of <math>\frac{1}{2}</math>,<math>\frac{1}{6}</math>,<math>\frac{1}{3} = 1</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%A4%BE_%E0%A4%B8%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%B5_%E0%A4%B9%E0%A4%B0_%E0%A4%AE%E0%A5%87%E0%A4%82_%E0%A4%B2%E0%A4%98%E0%A5%81%E0%A4%95%E0%A4%B0%E0%A4%A3 भिन्नों का सार्व हर में लघुकरण]
==References==
<references />
[[Category:Mathematics in Āryabhaṭīyam]]
[[Category:General]]