What percent is the least rational number of the greatest rational num

1.	What percent is the least rational number of the greatest rational number, if \(\frac{1}{2}\), \(\frac{2}{5}\), \(\frac{1}{3}\) and \(\frac{5}{9}\) are arranged in ascending order ?
Answer» Since LCM of 2, 5, 3, 9 = 270,\(\frac{1}{2}=\frac{135}{270}\), \(\frac{2}{5}=\frac{108}{270}\),\(\frac{1}{3}=\frac{90}{270}\),\(\frac{5}{9}=\frac{150}{270}\) \(\therefore\) Arranged in ascending order the numbers are \(\frac{90}{270}\),\(\frac{108}{270}\),\(\frac{135}{270}\),\(\frac{150}{270}\),i.e.,\(\frac{1}{2}\),\(\frac{2}{5}\),\(\frac{1}{2}\) and \(\frac{5}{9}\). \(\therefore\) Required percent =(\(\frac{1}{3}\)÷ \(\frac{5}{9}\)) x 100% = \((\frac{1}{3}\times \frac{9}{5}\times100)\)% = 60%

What percent is the least rational number of the greatest rational number, if \(\frac{1}{2}\), \(\frac{2}{5}\), \(\frac{1}{3}\) and \(\frac{5}{9}\) are arranged in ascending order ?

Answer»

Since LCM of 2, 5, 3, 9 = 270,\(\frac{1}{2}=\frac{135}{270}\), \(\frac{2}{5}=\frac{108}{270}\),\(\frac{1}{3}=\frac{90}{270}\),\(\frac{5}{9}=\frac{150}{270}\)

\(\therefore\) Arranged in ascending order the numbers are \(\frac{90}{270}\),\(\frac{108}{270}\),\(\frac{135}{270}\),\(\frac{150}{270}\),i.e.,\(\frac{1}{2}\),\(\frac{2}{5}\),\(\frac{1}{2}\) and \(\frac{5}{9}\).

\(\therefore\) Required percent =(\(\frac{1}{3}\)÷ \(\frac{5}{9}\)) x 100% = \((\frac{1}{3}\times \frac{9}{5}\times100)\)% = 60%

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