View source for Simplification of Quotients of Fractions

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==
[[भिन्नों के भागफलों का सरलीकरण]]
==References==
<references />
[[Category:Mathematics in Āryabhaṭīyam]]
[[Category:General]]