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The median of rational numbers \(\frac{1}{2}, \frac{2}{3}, \frac{5}{6}, \frac{1}{4}\) and \(\frac{3}{5}\)

A) 1/2

B) 3/5

C) 2/3

D) 5/6

2 Answers

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Best answer

Correct option is (B) 3/5

LCM of 2, 3, 6, 4 and 5 = 60

\(\therefore\) \(\frac{1}{2}=\frac{1}{2}\times\frac{30}{30}=\frac{30}{60},\)

\(\frac{2}{3}=\frac{2}{3}\times\frac{20}{20}=\frac{40}{60},\)

\(\frac{5}{6}=\frac{5}{6}\times\frac{10}{10}=\frac{50}{60},\)

\(\frac{1}{4}=\frac{1}{4}\times\frac{15}{15}=\frac{15}{60}\) and

\(\frac{3}{5}=\frac{3}{5}\times\frac{12}{12}=\frac{36}{60}.\)

\(\because\) \(\frac{15}{60}<\frac{30}{60}<\frac{36}{60}<\frac{40}{60}<\frac{50}{60}\)

\(\therefore\) \(\frac{1}{4}<\frac{1}{2}<\frac{3}{5}<\frac{2}{3}<\frac56\)

\(\therefore\) Median \(=(\frac{n+1}2)^{th}\)

\(=3^{rd}\) observation in ascending order

\(=\frac{3}{5}\)

+1 vote
by (40.5k points)

Correct option is  B) 3/5

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